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GCC Code Coverage Report
Directory:	.		Exec	Total	Coverage
File:	test/unit/preprocessing/pass_bv_gauss_white.cpp	Lines:	1279	1314	97.3 %
Date:	2021-08-16	Branches:	4784	11223	42.6 %

/******************************************************************************
 * Top contributors (to current version):
 *   Aina Niemetz, Mathias Preiner, Andres Noetzli
 *
 * This file is part of the cvc5 project.
 *
 * Copyright (c) 2009-2021 by the authors listed in the file AUTHORS
 * in the top-level source directory and their institutional affiliations.
 * All rights reserved.  See the file COPYING in the top-level source
 * directory for licensing information.
 * ****************************************************************************
 *
 * Unit tests for Gaussian Elimination preprocessing pass.
 */

#include <iostream>
#include <vector>

#include "context/context.h"
#include "expr/node.h"
#include "expr/node_manager.h"
#include "preprocessing/assertion_pipeline.h"
#include "preprocessing/passes/bv_gauss.h"
#include "smt/smt_engine.h"
#include "smt/smt_engine_scope.h"
#include "test_smt.h"
#include "theory/bv/theory_bv_utils.h"
#include "theory/rewriter.h"
#include "util/bitvector.h"

namespace cvc5 {

using namespace preprocessing;
using namespace preprocessing::passes;
using namespace theory;
using namespace smt;

namespace test {

class TestPPWhiteBVGauss : public TestSmt
{
 protected:
  void SetUp() override
  {
    TestSmt::SetUp();

    d_zero = bv::utils::mkZero(16);

    d_p = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkConst<BitVector>(BitVector(16, 11u)));
    d_x = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkVar("x", d_nodeManager->mkBitVectorType(16)));
    d_y = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkVar("y", d_nodeManager->mkBitVectorType(16)));
    d_z = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkVar("z", d_nodeManager->mkBitVectorType(16)));

    d_one = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkConst<BitVector>(BitVector(16, 1u)));
    d_two = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkConst<BitVector>(BitVector(16, 2u)));
    d_three = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkConst<BitVector>(BitVector(16, 3u)));
    d_four = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkConst<BitVector>(BitVector(16, 4u)));
    d_five = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkConst<BitVector>(BitVector(16, 5u)));
    d_six = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkConst<BitVector>(BitVector(16, 6u)));
    d_seven = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkConst<BitVector>(BitVector(16, 7u)));
    d_eight = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkConst<BitVector>(BitVector(16, 8u)));
    d_nine = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkConst<BitVector>(BitVector(16, 9u)));
    d_ten = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkConst<BitVector>(BitVector(16, 10u)));
    d_twelve = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkConst<BitVector>(BitVector(16, 12u)));
    d_eighteen = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkConst<BitVector>(BitVector(16, 18u)));
    d_twentyfour = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkConst<BitVector>(BitVector(16, 24u)));
    d_thirty = bv::utils::mkConcat(
        d_zero, d_nodeManager->mkConst<BitVector>(BitVector(16, 30u)));

    d_one32 = d_nodeManager->mkConst<BitVector>(BitVector(32, 1u));
    d_two32 = d_nodeManager->mkConst<BitVector>(BitVector(32, 2u));
    d_three32 = d_nodeManager->mkConst<BitVector>(BitVector(32, 3u));
    d_four32 = d_nodeManager->mkConst<BitVector>(BitVector(32, 4u));
    d_five32 = d_nodeManager->mkConst<BitVector>(BitVector(32, 5u));
    d_six32 = d_nodeManager->mkConst<BitVector>(BitVector(32, 6u));
    d_seven32 = d_nodeManager->mkConst<BitVector>(BitVector(32, 7u));
    d_eight32 = d_nodeManager->mkConst<BitVector>(BitVector(32, 8u));
    d_nine32 = d_nodeManager->mkConst<BitVector>(BitVector(32, 9u));
    d_ten32 = d_nodeManager->mkConst<BitVector>(BitVector(32, 10u));

    d_x_mul_one = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_one);
    d_x_mul_two = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_two);
    d_x_mul_four = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_four);
    d_y_mul_three = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_three);
    d_y_mul_one = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_one);
    d_y_mul_four = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_four);
    d_y_mul_five = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_five);
    d_y_mul_seven = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_seven);
    d_z_mul_one = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_one);
    d_z_mul_three = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_three);
    d_z_mul_five = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_five);
    d_z_mul_six = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_six);
    d_z_mul_twelve = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_twelve);
    d_z_mul_nine = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_nine);
  }

  void print_matrix_dbg(std::vector<Integer>& rhs,
                        std::vector<std::vector<Integer>>& lhs)
  {
    for (size_t m = 0, nrows = lhs.size(), ncols = lhs[0].size(); m < nrows;
         ++m)
    {
      for (size_t n = 0; n < ncols; ++n)
      {
        std::cout << " " << lhs[m][n];
      }
      std::cout << " " << rhs[m];
      std::cout << std::endl;
    }
  }

  void testGaussElimX(Integer prime,
                      std::vector<Integer> rhs,
                      std::vector<std::vector<Integer>> lhs,
                      BVGauss::Result expected,
                      std::vector<Integer>* rrhs = nullptr,
                      std::vector<std::vector<Integer>>* rlhs = nullptr)
  {
    size_t nrows = lhs.size();
    size_t ncols = lhs[0].size();
    BVGauss::Result ret;
    std::vector<Integer> resrhs = std::vector<Integer>(rhs);
    std::vector<std::vector<Integer>> reslhs =
        std::vector<std::vector<Integer>>(lhs);

    std::cout << "Input: " << std::endl;
    print_matrix_dbg(rhs, lhs);

    ret = BVGauss::gaussElim(prime, resrhs, reslhs);

    std::cout << "BVGauss::Result: "
              << (ret == BVGauss::Result::INVALID
                      ? "INVALID"
                      : (ret == BVGauss::Result::UNIQUE
                             ? "UNIQUE"
                             : (ret == BVGauss::Result::PARTIAL ? "PARTIAL"
                                                                : "NONE")))
              << std::endl;
    print_matrix_dbg(resrhs, reslhs);

    ASSERT_EQ(expected, ret);

    if (expected == BVGauss::Result::UNIQUE)
    {
      /* map result value to column index
       * e.g.:
       * 1 0 0 2  -> res = { 2, 0, 3}
       * 0 0 1 3 */
      std::vector<Integer> res = std::vector<Integer>(ncols, Integer(0));
      for (size_t i = 0; i < nrows; ++i)
        for (size_t j = 0; j < ncols; ++j)
        {
          if (reslhs[i][j] == 1)
            res[j] = resrhs[i];
          else
            ASSERT_EQ(reslhs[i][j], 0);
        }

      for (size_t i = 0; i < nrows; ++i)
      {
        Integer tmp = Integer(0);
        for (size_t j = 0; j < ncols; ++j)
          tmp = tmp.modAdd(lhs[i][j].modMultiply(res[j], prime), prime);
        ASSERT_EQ(tmp, rhs[i].euclidianDivideRemainder(prime));
      }
    }
    if (rrhs != nullptr && rlhs != nullptr)
    {
      for (size_t i = 0; i < nrows; ++i)
      {
        for (size_t j = 0; j < ncols; ++j)
        {
          ASSERT_EQ(reslhs[i][j], (*rlhs)[i][j]);
        }
        ASSERT_EQ(resrhs[i], (*rrhs)[i]);
      }
    }
  }

  Node d_p;
  Node d_x;
  Node d_y;
  Node d_z;
  Node d_zero;
  Node d_one;
  Node d_two;
  Node d_three;
  Node d_four;
  Node d_five;
  Node d_six;
  Node d_seven;
  Node d_eight;
  Node d_nine;
  Node d_ten;
  Node d_twelve;
  Node d_eighteen;
  Node d_twentyfour;
  Node d_thirty;
  Node d_one32;
  Node d_two32;
  Node d_three32;
  Node d_four32;
  Node d_five32;
  Node d_six32;
  Node d_seven32;
  Node d_eight32;
  Node d_nine32;
  Node d_ten32;
  Node d_x_mul_one;
  Node d_x_mul_two;
  Node d_x_mul_four;
  Node d_y_mul_one;
  Node d_y_mul_three;
  Node d_y_mul_four;
  Node d_y_mul_five;
  Node d_y_mul_seven;
  Node d_z_mul_one;
  Node d_z_mul_three;
  Node d_z_mul_five;
  Node d_z_mul_twelve;
  Node d_z_mul_six;
  Node d_z_mul_nine;
};

TEST_F(TestPPWhiteBVGauss, elim_mod)
{
  std::vector<Integer> rhs;
  std::vector<std::vector<Integer>> lhs;

  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 }
   *  --^--   ^
   *  1 1 1   5
   *  2 3 5   8
   *  4 0 5   2
   * ------------------------------------------------------------------- */
  rhs = {Integer(5), Integer(8), Integer(2)};
  lhs = {{Integer(1), Integer(1), Integer(1)},
         {Integer(2), Integer(3), Integer(5)},
         {Integer(4), Integer(0), Integer(5)}};
  std::cout << "matrix 0, modulo 0" << std::endl;  // throws
  ASSERT_DEATH(BVGauss::gaussElim(Integer(0), rhs, lhs), "prime > 0");
  std::cout << "matrix 0, modulo 1" << std::endl;
  testGaussElimX(Integer(1), rhs, lhs, BVGauss::Result::UNIQUE);
  std::cout << "matrix 0, modulo 2" << std::endl;
  testGaussElimX(Integer(2), rhs, lhs, BVGauss::Result::UNIQUE);
  std::cout << "matrix 0, modulo 3" << std::endl;
  testGaussElimX(Integer(3), rhs, lhs, BVGauss::Result::UNIQUE);
  std::cout << "matrix 0, modulo 4" << std::endl;  // no inverse
  testGaussElimX(Integer(4), rhs, lhs, BVGauss::Result::INVALID);
  std::cout << "matrix 0, modulo 5" << std::endl;
  testGaussElimX(Integer(5), rhs, lhs, BVGauss::Result::UNIQUE);
  std::cout << "matrix 0, modulo 6" << std::endl;  // no inverse
  testGaussElimX(Integer(6), rhs, lhs, BVGauss::Result::INVALID);
  std::cout << "matrix 0, modulo 7" << std::endl;
  testGaussElimX(Integer(7), rhs, lhs, BVGauss::Result::UNIQUE);
  std::cout << "matrix 0, modulo 8" << std::endl;  // no inverse
  testGaussElimX(Integer(8), rhs, lhs, BVGauss::Result::INVALID);
  std::cout << "matrix 0, modulo 9" << std::endl;
  testGaussElimX(Integer(9), rhs, lhs, BVGauss::Result::UNIQUE);
  std::cout << "matrix 0, modulo 10" << std::endl;  // no inverse
  testGaussElimX(Integer(10), rhs, lhs, BVGauss::Result::INVALID);
  std::cout << "matrix 0, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);
}

TEST_F(TestPPWhiteBVGauss, elim_unique_done)
{
  std::vector<Integer> rhs;
  std::vector<std::vector<Integer>> lhs;

  /* -------------------------------------------------------------------
   *   lhs     rhs        lhs    rhs  modulo 17
   *  --^---    ^        --^--    ^
   *  1 0 0    4   -->   1 0 0    4
   *  0 1 0   15         0 1 0   15
   *  0 0 1    3         0 0 1    3
   * ------------------------------------------------------------------- */
  rhs = {Integer(4), Integer(15), Integer(3)};
  lhs = {{Integer(1), Integer(0), Integer(0)},
         {Integer(0), Integer(1), Integer(0)},
         {Integer(0), Integer(0), Integer(1)}};
  std::cout << "matrix 1, modulo 17" << std::endl;
  testGaussElimX(Integer(17), rhs, lhs, BVGauss::Result::UNIQUE);
}

TEST_F(TestPPWhiteBVGauss, elim_unique)
{
  std::vector<Integer> rhs;
  std::vector<std::vector<Integer>> lhs;

  /* -------------------------------------------------------------------
   *   lhs     rhs  modulo { 11,17,59 }
   *  --^---    ^
   *  2 4  6   18
   *  4 5  6   24
   *  3 1 -2    4
   * ------------------------------------------------------------------- */
  rhs = {Integer(18), Integer(24), Integer(4)};
  lhs = {{Integer(2), Integer(4), Integer(6)},
         {Integer(4), Integer(5), Integer(6)},
         {Integer(3), Integer(1), Integer(-2)}};
  std::cout << "matrix 2, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);
  std::cout << "matrix 2, modulo 17" << std::endl;
  testGaussElimX(Integer(17), rhs, lhs, BVGauss::Result::UNIQUE);
  std::cout << "matrix 2, modulo 59" << std::endl;
  testGaussElimX(Integer(59), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *      lhs       rhs         lhs     rhs   modulo 11
   *  -----^-----    ^        ---^---    ^
   *  1  1  2   0    1   -->  1 0 0 0    1
   *  2 -1  0   1   -2        0 1 0 0    2
   *  1 -1 -1  -2    4        0 0 1 0   -1
   *  2 -1  2  -1    0        0 0 0 1   -2
   * ------------------------------------------------------------------- */
  rhs = {Integer(1), Integer(-2), Integer(4), Integer(0)};
  lhs = {{Integer(1), Integer(1), Integer(2), Integer(0)},
         {Integer(2), Integer(-1), Integer(0), Integer(1)},
         {Integer(1), Integer(-1), Integer(-1), Integer(-2)},
         {Integer(2), Integer(-1), Integer(2), Integer(-1)}};
  std::cout << "matrix 3, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);
}

TEST_F(TestPPWhiteBVGauss, elim_unique_zero1)
{
  std::vector<Integer> rhs;
  std::vector<std::vector<Integer>> lhs;

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs   modulo 11
   *  --^--   ^        --^--   ^
   *  0 4 5   2   -->  1 0 0   4
   *  1 1 1   5        0 1 0   3
   *  3 2 5   8        0 0 1   9
   * ------------------------------------------------------------------- */
  rhs = {Integer(2), Integer(5), Integer(8)};
  lhs = {{Integer(0), Integer(4), Integer(5)},
         {Integer(1), Integer(1), Integer(1)},
         {Integer(3), Integer(2), Integer(5)}};
  std::cout << "matrix 4, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs   modulo 11
   *  --^--   ^        --^--   ^
   *  1 1 1   5   -->  1 0 0   4
   *  0 4 5   2        0 1 0   3
   *  3 2 5   8        0 0 1   9
   * ------------------------------------------------------------------- */
  rhs = {Integer(5), Integer(2), Integer(8)};
  lhs = {{Integer(1), Integer(1), Integer(1)},
         {Integer(0), Integer(4), Integer(5)},
         {Integer(3), Integer(2), Integer(5)}};
  std::cout << "matrix 5, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs   modulo 11
   *  --^--   ^        --^--   ^
   *  1 1 1   5   -->  1 0 0   4
   *  3 2 5   8        0 1 0   9
   *  0 4 5   2        0 0 1   3
   * ------------------------------------------------------------------- */
  rhs = {Integer(5), Integer(8), Integer(2)};
  lhs = {{Integer(1), Integer(1), Integer(1)},
         {Integer(3), Integer(2), Integer(5)},
         {Integer(0), Integer(4), Integer(5)}};
  std::cout << "matrix 6, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);
}

TEST_F(TestPPWhiteBVGauss, elim_unique_zero2)
{
  std::vector<Integer> rhs;
  std::vector<std::vector<Integer>> lhs;

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs   modulo 11
   *  --^--   ^        --^--   ^
   *  0 0 5   2        1 0 0   10
   *  1 1 1   5   -->  0 1 0   10
   *  3 2 5   8        0 0 1   7
   * ------------------------------------------------------------------- */
  rhs = {Integer(2), Integer(5), Integer(8)};
  lhs = {{Integer(0), Integer(0), Integer(5)},
         {Integer(1), Integer(1), Integer(1)},
         {Integer(3), Integer(2), Integer(5)}};
  std::cout << "matrix 7, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs   modulo 11
   *  --^--   ^        --^--   ^
   *  1 1 1   5   -->  1 0 0   10
   *  0 0 5   2        0 1 0   10
   *  3 2 5   8        0 0 1   7
   * ------------------------------------------------------------------- */
  rhs = {Integer(5), Integer(2), Integer(8)};
  lhs = {{Integer(1), Integer(1), Integer(1)},
         {Integer(0), Integer(0), Integer(5)},
         {Integer(3), Integer(2), Integer(5)}};
  std::cout << "matrix 8, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs   modulo 11
   *  --^--   ^        --^--   ^
   *  1 1 1   5   -->  1 0 0   10
   *  3 2 5   8        0 1 0   10
   *  0 0 5   2        0 0 1    7
   * ------------------------------------------------------------------- */
  rhs = {Integer(5), Integer(8), Integer(2)};
  lhs = {{Integer(1), Integer(1), Integer(1)},
         {Integer(3), Integer(2), Integer(5)},
         {Integer(0), Integer(0), Integer(5)}};
  std::cout << "matrix 9, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);
}

TEST_F(TestPPWhiteBVGauss, elim_unique_zero3)
{
  std::vector<Integer> rhs;
  std::vector<std::vector<Integer>> lhs;

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs   modulo 7
   *  --^--   ^        --^--   ^
   *  2 0 6   4        1 0 0   3
   *  0 0 0   0   -->  0 0 0   0
   *  4 0 6   3        0 0 1   2
   * ------------------------------------------------------------------- */
  rhs = {Integer(4), Integer(0), Integer(3)};
  lhs = {{Integer(2), Integer(0), Integer(6)},
         {Integer(0), Integer(0), Integer(0)},
         {Integer(4), Integer(0), Integer(6)}};
  std::cout << "matrix 10, modulo 7" << std::endl;
  testGaussElimX(Integer(7), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs   modulo 7
   *  --^--   ^        --^--   ^
   *  2 6 0   4        1 0 0   3
   *  0 0 0   0   -->  0 0 0   0
   *  4 6 0   3        0 0 1   2
   * ------------------------------------------------------------------- */
  rhs = {Integer(4), Integer(0), Integer(3)};
  lhs = {{Integer(2), Integer(6), Integer(0)},
         {Integer(0), Integer(0), Integer(0)},
         {Integer(4), Integer(6), Integer(0)}};
  std::cout << "matrix 11, modulo 7" << std::endl;
  testGaussElimX(Integer(7), rhs, lhs, BVGauss::Result::UNIQUE);
}

TEST_F(TestPPWhiteBVGauss, elim_unique_zero4)
{
  std::vector<Integer> rhs, resrhs;
  std::vector<std::vector<Integer>> lhs, reslhs;

  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo 11
   *  --^--   ^
   *  0 1 1   5
   *  0 0 0   0
   *  0 0 5   2
   * ------------------------------------------------------------------- */
  rhs = {Integer(5), Integer(0), Integer(2)};
  lhs = {{Integer(0), Integer(1), Integer(1)},
         {Integer(0), Integer(0), Integer(0)},
         {Integer(0), Integer(0), Integer(5)}};
  std::cout << "matrix 12, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo 11
   *  --^--   ^
   *  0 1 1   5
   *  0 3 5   8
   *  0 0 0   0
   * ------------------------------------------------------------------- */
  rhs = {Integer(5), Integer(8), Integer(0)};
  lhs = {{Integer(0), Integer(1), Integer(1)},
         {Integer(0), Integer(3), Integer(5)},
         {Integer(0), Integer(0), Integer(0)}};
  std::cout << "matrix 13, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo 11
   *  --^--   ^
   *  0 0 0   0
   *  0 3 5   8
   *  0 0 5   2
   * ------------------------------------------------------------------- */
  rhs = {Integer(0), Integer(8), Integer(2)};
  lhs = {{Integer(0), Integer(0), Integer(0)},
         {Integer(0), Integer(3), Integer(5)},
         {Integer(0), Integer(0), Integer(5)}};
  std::cout << "matrix 14, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo 11
   *  --^--   ^
   *  1 0 1   5
   *  0 0 0   0
   *  4 0 5   2
   * ------------------------------------------------------------------- */
  rhs = {Integer(5), Integer(0), Integer(2)};
  lhs = {{Integer(1), Integer(0), Integer(1)},
         {Integer(0), Integer(0), Integer(0)},
         {Integer(4), Integer(0), Integer(5)}};
  std::cout << "matrix 15, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo 11
   *  --^--   ^
   *  1 0 1   5
   *  2 0 5   8
   *  0 0 0   0
   * ------------------------------------------------------------------- */
  rhs = {Integer(5), Integer(8), Integer(0)};
  lhs = {{Integer(1), Integer(0), Integer(1)},
         {Integer(2), Integer(0), Integer(5)},
         {Integer(0), Integer(0), Integer(0)}};
  std::cout << "matrix 16, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo 11
   *  --^--   ^
   *  0 0 0   0
   *  2 0 5   8
   *  4 0 5   2
   * ------------------------------------------------------------------- */
  rhs = {Integer(0), Integer(8), Integer(2)};
  lhs = {{Integer(0), Integer(0), Integer(0)},
         {Integer(2), Integer(0), Integer(5)},
         {Integer(4), Integer(0), Integer(5)}};
  std::cout << "matrix 17, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo 11
   *  --^--   ^
   *  1 1 0   5
   *  0 0 0   0
   *  4 0 0   2
   * ------------------------------------------------------------------- */
  rhs = {Integer(5), Integer(0), Integer(2)};
  lhs = {{Integer(1), Integer(1), Integer(0)},
         {Integer(0), Integer(0), Integer(0)},
         {Integer(4), Integer(0), Integer(0)}};
  std::cout << "matrix 18, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo 11
   *  --^--   ^
   *  1 1 0   5
   *  2 3 0   8
   *  0 0 0   0
   * ------------------------------------------------------------------- */
  rhs = {Integer(5), Integer(8), Integer(0)};
  lhs = {{Integer(1), Integer(1), Integer(0)},
         {Integer(2), Integer(3), Integer(0)},
         {Integer(0), Integer(0), Integer(0)}};
  std::cout << "matrix 18, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo 11
   *  --^--   ^
   *  0 0 0   0
   *  2 3 0   8
   *  4 0 0   2
   * ------------------------------------------------------------------- */
  rhs = {Integer(0), Integer(8), Integer(2)};
  lhs = {{Integer(0), Integer(0), Integer(0)},
         {Integer(2), Integer(3), Integer(0)},
         {Integer(4), Integer(0), Integer(0)}};
  std::cout << "matrix 19, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *     lhs    rhs  modulo 2
   *  ----^---   ^
   *  2  4   6   18     0 0 0   0
   *  4  5   6   24  =  0 1 0   0
   *  2  7  12   30     0 1 0   0
   * ------------------------------------------------------------------- */
  rhs = {Integer(18), Integer(24), Integer(30)};
  lhs = {{Integer(2), Integer(4), Integer(6)},
         {Integer(4), Integer(5), Integer(6)},
         {Integer(2), Integer(7), Integer(12)}};
  std::cout << "matrix 20, modulo 2" << std::endl;
  resrhs = {Integer(0), Integer(0), Integer(0)};
  reslhs = {{Integer(0), Integer(1), Integer(0)},
            {Integer(0), Integer(0), Integer(0)},
            {Integer(0), Integer(0), Integer(0)}};
  testGaussElimX(
      Integer(2), rhs, lhs, BVGauss::Result::UNIQUE, &resrhs, &reslhs);
}

TEST_F(TestPPWhiteBVGauss, elim_unique_partial)
{
  std::vector<Integer> rhs;
  std::vector<std::vector<Integer>> lhs;

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs   modulo 7
   *  --^--   ^        --^--   ^
   *  2 0 6   4        1 0 0   3
   *  4 0 6   3        0 0 1   2
   * ------------------------------------------------------------------- */
  rhs = {Integer(4), Integer(3)};
  lhs = {{Integer(2), Integer(0), Integer(6)},
         {Integer(4), Integer(0), Integer(6)}};
  std::cout << "matrix 21, modulo 7" << std::endl;
  testGaussElimX(Integer(7), rhs, lhs, BVGauss::Result::UNIQUE);

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs   modulo 7
   *  --^--   ^        --^--   ^
   *  2 6 0   4        1 0 0   3
   *  4 6 0   3        0 1 0   2
   * ------------------------------------------------------------------- */
  rhs = {Integer(4), Integer(3)};
  lhs = {{Integer(2), Integer(6), Integer(0)},
         {Integer(4), Integer(6), Integer(0)}};
  std::cout << "matrix 22, modulo 7" << std::endl;
  testGaussElimX(Integer(7), rhs, lhs, BVGauss::Result::UNIQUE);
}

TEST_F(TestPPWhiteBVGauss, elim_none)
{
  std::vector<Integer> rhs;
  std::vector<std::vector<Integer>> lhs;

  /* -------------------------------------------------------------------
   *   lhs     rhs       modulo 9
   *  --^---    ^
   *  2 4  6   18   -->  not coprime (no inverse)
   *  4 5  6   24
   *  3 1 -2    4
   * ------------------------------------------------------------------- */
  rhs = {Integer(18), Integer(24), Integer(4)};
  lhs = {{Integer(2), Integer(4), Integer(6)},
         {Integer(4), Integer(5), Integer(6)},
         {Integer(3), Integer(1), Integer(-2)}};
  std::cout << "matrix 23, modulo 9" << std::endl;
  testGaussElimX(Integer(9), rhs, lhs, BVGauss::Result::INVALID);

  /* -------------------------------------------------------------------
   *     lhs    rhs       modulo 59
   *  ----^---   ^
   *  1 -2  -6   12   --> no solution
   *  2  4  12  -17
   *  1 -4 -12   22
   * ------------------------------------------------------------------- */
  rhs = {Integer(12), Integer(-17), Integer(22)};
  lhs = {{Integer(1), Integer(-2), Integer(-6)},
         {Integer(2), Integer(4), Integer(12)},
         {Integer(1), Integer(-4), Integer(-12)}};
  std::cout << "matrix 24, modulo 59" << std::endl;
  testGaussElimX(Integer(59), rhs, lhs, BVGauss::Result::NONE);

  /* -------------------------------------------------------------------
   *     lhs    rhs       modulo 9
   *  ----^---   ^
   *  2  4   6   18   --> not coprime (no inverse)
   *  4  5   6   24
   *  2  7  12   30
   * ------------------------------------------------------------------- */
  rhs = {Integer(18), Integer(24), Integer(30)};
  lhs = {{Integer(2), Integer(4), Integer(6)},
         {Integer(4), Integer(5), Integer(6)},
         {Integer(2), Integer(7), Integer(12)}};
  std::cout << "matrix 25, modulo 9" << std::endl;
  testGaussElimX(Integer(9), rhs, lhs, BVGauss::Result::INVALID);
}

TEST_F(TestPPWhiteBVGauss, elim_none_zero)
{
  std::vector<Integer> rhs;
  std::vector<std::vector<Integer>> lhs;

  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo 11
   *  --^--   ^
   *  0 1 1   5
   *  0 3 5   8
   *  0 0 5   2
   * ------------------------------------------------------------------- */
  rhs = {Integer(5), Integer(8), Integer(2)};
  lhs = {{Integer(0), Integer(1), Integer(1)},
         {Integer(0), Integer(3), Integer(5)},
         {Integer(0), Integer(0), Integer(5)}};
  std::cout << "matrix 26, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::NONE);

  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo 11
   *  --^--   ^
   *  1 0 1   5
   *  2 0 5   8
   *  4 0 5   2
   * ------------------------------------------------------------------- */
  rhs = {Integer(5), Integer(8), Integer(2)};
  lhs = {{Integer(1), Integer(0), Integer(1)},
         {Integer(2), Integer(0), Integer(5)},
         {Integer(4), Integer(0), Integer(5)}};
  std::cout << "matrix 27, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::NONE);

  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo 11
   *  --^--   ^
   *  1 1 0   5
   *  2 3 0   8
   *  4 0 0   2
   * ------------------------------------------------------------------- */
  rhs = {Integer(5), Integer(8), Integer(2)};
  lhs = {{Integer(1), Integer(1), Integer(0)},
         {Integer(2), Integer(3), Integer(0)},
         {Integer(4), Integer(0), Integer(0)}};
  std::cout << "matrix 28, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::NONE);
}

TEST_F(TestPPWhiteBVGauss, elim_partial1)
{
  std::vector<Integer> rhs, resrhs;
  std::vector<std::vector<Integer>> lhs, reslhs;

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs  modulo 11
   *  --^--   ^        --^--   ^
   *  1 0 9   7   -->  1 0 9   7
   *  0 1 3   9        0 1 3   9
   * ------------------------------------------------------------------- */
  rhs = {Integer(7), Integer(9)};
  lhs = {{Integer(1), Integer(0), Integer(9)},
         {Integer(0), Integer(1), Integer(3)}};
  std::cout << "matrix 29, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::PARTIAL);

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs  modulo 11
   *  --^--   ^        --^--   ^
   *  1 3 0   7   -->  1 3 0   7
   *  0 0 1   9        0 0 1   9
   * ------------------------------------------------------------------- */
  rhs = {Integer(7), Integer(9)};
  lhs = {{Integer(1), Integer(3), Integer(0)},
         {Integer(0), Integer(0), Integer(1)}};
  std::cout << "matrix 30, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::PARTIAL);

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs  modulo 11
   *  --^--   ^        --^--   ^
   *  1 1 1   5   -->  1 0 9   7
   *  2 3 5   8        0 1 3   9
   * ------------------------------------------------------------------- */
  rhs = {Integer(5), Integer(8)};
  lhs = {{Integer(1), Integer(1), Integer(1)},
         {Integer(2), Integer(3), Integer(5)}};
  std::cout << "matrix 31, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::PARTIAL);

  /* -------------------------------------------------------------------
   *     lhs    rhs  modulo { 3, 5, 7, 11, 17, 31, 59 }
   *  ----^---   ^
   *  2  4   6   18
   *  4  5   6   24
   *  2  7  12   30
   * ------------------------------------------------------------------- */
  rhs = {Integer(18), Integer(24), Integer(30)};
  lhs = {{Integer(2), Integer(4), Integer(6)},
         {Integer(4), Integer(5), Integer(6)},
         {Integer(2), Integer(7), Integer(12)}};
  std::cout << "matrix 32, modulo 3" << std::endl;
  resrhs = {Integer(0), Integer(0), Integer(0)};
  reslhs = {{Integer(1), Integer(2), Integer(0)},
            {Integer(0), Integer(0), Integer(0)},
            {Integer(0), Integer(0), Integer(0)}};
  testGaussElimX(
      Integer(3), rhs, lhs, BVGauss::Result::PARTIAL, &resrhs, &reslhs);
  resrhs = {Integer(1), Integer(4), Integer(0)};
  std::cout << "matrix 32, modulo 5" << std::endl;
  reslhs = {{Integer(1), Integer(0), Integer(4)},
            {Integer(0), Integer(1), Integer(2)},
            {Integer(0), Integer(0), Integer(0)}};
  testGaussElimX(
      Integer(5), rhs, lhs, BVGauss::Result::PARTIAL, &resrhs, &reslhs);
  std::cout << "matrix 32, modulo 7" << std::endl;
  reslhs = {{Integer(1), Integer(0), Integer(6)},
            {Integer(0), Integer(1), Integer(2)},
            {Integer(0), Integer(0), Integer(0)}};
  testGaussElimX(
      Integer(7), rhs, lhs, BVGauss::Result::PARTIAL, &resrhs, &reslhs);
  std::cout << "matrix 32, modulo 11" << std::endl;
  reslhs = {{Integer(1), Integer(0), Integer(10)},
            {Integer(0), Integer(1), Integer(2)},
            {Integer(0), Integer(0), Integer(0)}};
  testGaussElimX(
      Integer(11), rhs, lhs, BVGauss::Result::PARTIAL, &resrhs, &reslhs);
  std::cout << "matrix 32, modulo 17" << std::endl;
  reslhs = {{Integer(1), Integer(0), Integer(16)},
            {Integer(0), Integer(1), Integer(2)},
            {Integer(0), Integer(0), Integer(0)}};
  testGaussElimX(
      Integer(17), rhs, lhs, BVGauss::Result::PARTIAL, &resrhs, &reslhs);
  std::cout << "matrix 32, modulo 59" << std::endl;
  reslhs = {{Integer(1), Integer(0), Integer(58)},
            {Integer(0), Integer(1), Integer(2)},
            {Integer(0), Integer(0), Integer(0)}};
  testGaussElimX(
      Integer(59), rhs, lhs, BVGauss::Result::PARTIAL, &resrhs, &reslhs);

  /* -------------------------------------------------------------------
   *     lhs    rhs        lhs   rhs   modulo 3
   *  ----^---   ^        --^--   ^
   *   4  6 2   18   -->  1 0 2   0
   *   5  6 4   24        0 0 0   0
   *   7 12 2   30        0 0 0   0
   * ------------------------------------------------------------------- */
  rhs = {Integer(18), Integer(24), Integer(30)};
  lhs = {{Integer(4), Integer(6), Integer(2)},
         {Integer(5), Integer(6), Integer(4)},
         {Integer(7), Integer(12), Integer(2)}};
  std::cout << "matrix 33, modulo 3" << std::endl;
  resrhs = {Integer(0), Integer(0), Integer(0)};
  reslhs = {{Integer(1), Integer(0), Integer(2)},
            {Integer(0), Integer(0), Integer(0)},
            {Integer(0), Integer(0), Integer(0)}};
  testGaussElimX(
      Integer(3), rhs, lhs, BVGauss::Result::PARTIAL, &resrhs, &reslhs);
}

TEST_F(TestPPWhiteBVGauss, elim_partial2)
{
  std::vector<Integer> rhs;
  std::vector<std::vector<Integer>> lhs;

  /* -------------------------------------------------------------------
   *    lhs    rhs  -->    lhs    rhs  modulo 11
   *  ---^---   ^        ---^---   ^
   *  x y z w            x y z w
   *  1 2 0 6   2        1 2 0 0   1
   *  0 0 2 2   2        0 0 1 0   10
   *  0 0 0 1   2        0 0 0 1   2
   * ------------------------------------------------------------------- */
  rhs = {Integer(2), Integer(2), Integer(2)};
  lhs = {{Integer(1), Integer(2), Integer(6), Integer(0)},
         {Integer(0), Integer(0), Integer(2), Integer(2)},
         {Integer(0), Integer(0), Integer(1), Integer(0)}};
  std::cout << "matrix 34, modulo 11" << std::endl;
  testGaussElimX(Integer(11), rhs, lhs, BVGauss::Result::PARTIAL);
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_unique1)
{
  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo 11
   *  --^--   ^
   *  1 1 1   5
   *  2 3 5   8
   *  4 0 5   2
   * ------------------------------------------------------------------- */

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(
                  kind::BITVECTOR_ADD, d_x_mul_one, d_y_mul_one),
              d_z_mul_one),
          d_p),
      d_five);

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(
                  kind::BITVECTOR_ADD, d_x_mul_two, d_y_mul_three),
              d_z_mul_five),
          d_p),
      d_eight);

  Node eq3 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD, d_x_mul_four, d_z_mul_five),
          d_p),
      d_two);

  std::vector<Node> eqs = {eq1, eq2, eq3};
  std::unordered_map<Node, Node> res;
  BVGauss::Result ret = BVGauss::gaussElimRewriteForUrem(eqs, res);
  ASSERT_EQ(ret, BVGauss::Result::UNIQUE);
  ASSERT_EQ(res.size(), 3);
  ASSERT_EQ(res[d_x], d_three32);
  ASSERT_EQ(res[d_y], d_four32);
  ASSERT_EQ(res[d_z], d_nine32);
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_unique2)
{
  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo 11
   *  --^--   ^
   *  1 1 1   5
   *  2 3 5   8
   *  4 0 5   2
   * ------------------------------------------------------------------- */

  Node zextop6 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(6));

  Node p = d_nodeManager->mkNode(
      zextop6,
      bv::utils::mkConcat(bv::utils::mkZero(6),
                          d_nodeManager->mkNode(kind::BITVECTOR_ADD,
                                                bv::utils::mkConst(20, 7),
                                                bv::utils::mkConst(20, 4))));

  Node x_mul_one = d_nodeManager->mkNode(
      kind::BITVECTOR_MULT,
      d_nodeManager->mkNode(kind::BITVECTOR_SUB, d_five, d_four),
      d_x);
  Node y_mul_one = d_nodeManager->mkNode(
      kind::BITVECTOR_MULT,
      d_nodeManager->mkNode(kind::BITVECTOR_UREM, d_one, d_five),
      d_y);
  Node z_mul_one =
      d_nodeManager->mkNode(kind::BITVECTOR_MULT, bv::utils::mkOne(32), d_z);

  Node x_mul_two = d_nodeManager->mkNode(
      kind::BITVECTOR_MULT,
      d_nodeManager->mkNode(
          kind::BITVECTOR_SHL, bv::utils::mkOne(32), bv::utils::mkOne(32)),
      d_x);
  Node y_mul_three =
      d_nodeManager->mkNode(kind::BITVECTOR_MULT,
                            d_nodeManager->mkNode(kind::BITVECTOR_LSHR,
                                                  bv::utils::mkOnes(32),
                                                  bv::utils::mkConst(32, 30)),
                            d_y);
  Node z_mul_five = d_nodeManager->mkNode(
      kind::BITVECTOR_MULT,
      bv::utils::mkExtract(
          d_nodeManager->mkNode(
              zextop6,
              d_nodeManager->mkNode(kind::BITVECTOR_ADD, d_three, d_two)),
          31,
          0),
      d_z);

  Node x_mul_four = d_nodeManager->mkNode(
      kind::BITVECTOR_MULT,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UDIV,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(kind::BITVECTOR_MULT,
                                    bv::utils::mkConst(32, 4),
                                    bv::utils::mkConst(32, 5)),
              bv::utils::mkConst(32, 4)),
          bv::utils::mkConst(32, 6)),
      d_x);

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(kind::BITVECTOR_ADD, x_mul_one, y_mul_one),
              z_mul_one),
          p),
      d_five);

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(
                  kind::BITVECTOR_ADD, x_mul_two, y_mul_three),
              z_mul_five),
          p),
      d_eight);

  Node eq3 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(kind::BITVECTOR_ADD, x_mul_four, z_mul_five),
          d_p),
      d_two);

  std::vector<Node> eqs = {eq1, eq2, eq3};
  std::unordered_map<Node, Node> res;
  BVGauss::Result ret = BVGauss::gaussElimRewriteForUrem(eqs, res);
  ASSERT_EQ(ret, BVGauss::Result::UNIQUE);
  ASSERT_EQ(res.size(), 3);
  ASSERT_EQ(res[d_x], d_three32);
  ASSERT_EQ(res[d_y], d_four32);
  ASSERT_EQ(res[d_z], d_nine32);
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_partial1a)
{
  std::unordered_map<Node, Node> res;
  BVGauss::Result ret;

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs  modulo 11
   *  --^--   ^        --^--   ^
   *  1 0 9   7   -->  1 0 9   7
   *  0 1 3   9        0 1 3   9
   * ------------------------------------------------------------------- */

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(kind::BITVECTOR_ADD, d_x_mul_one, d_z_mul_nine),
          d_p),
      d_seven);

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD, d_y_mul_one, d_z_mul_three),
          d_p),
      d_nine);

  std::vector<Node> eqs = {eq1, eq2};
  ret = BVGauss::gaussElimRewriteForUrem(eqs, res);
  ASSERT_EQ(ret, BVGauss::Result::PARTIAL);
  ASSERT_EQ(res.size(), 2);

  Node x1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_seven32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_two32)),
      d_p);
  Node y1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_nine32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_eight32)),
      d_p);

  Node x2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_two32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_three32)),
      d_p);
  Node z2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_three32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_seven32)),
      d_p);

  Node y3 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_three32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_four32)),
      d_p);
  Node z3 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_two32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_six32)),
      d_p);

  /* result depends on order of variables in matrix */
  if (res.find(d_x) == res.end())
  {
    /*
     *  y z x           y z x
     *  0 9 1  7   -->  1 0 7  3
     *  1 3 0  9        0 1 5  2
     *
     *  z y x           z y x
     *  9 0 1  7   -->  1 0 5  2
     *  3 1 0  9        0 1 7  3
     */
    ASSERT_EQ(res[d_y], y3);
    ASSERT_EQ(res[d_z], z3);
  }
  else if (res.find(d_y) == res.end())
  {
    /*
     *  x z y           x z y
     *  1 9 0  7   -->  1 0 8  2
     *  0 3 1  9        0 1 4  3
     *
     *  z x y           z x y
     *  9 1 0  7   -->  1 0 4  3
     *  3 0 1  9        0 1 8  2
     */
    ASSERT_EQ(res[d_x], x2);
    ASSERT_EQ(res[d_z], z2);
  }
  else
  {
    ASSERT_EQ(res.find(d_z), res.end());
    /*
     *  x y z           x y z
     *  1 0 9  7   -->  1 0 9  7
     *  0 1 3  9        0 1 3  9
     *
     *  y x z           y x z
     *  0 1 9  7   -->  1 0 3  9
     *  1 0 3  9        0 1 9  7
     */
    ASSERT_EQ(res[d_x], x1);
    ASSERT_EQ(res[d_y], y1);
  }
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_partial1b)
{
  std::unordered_map<Node, Node> res;
  BVGauss::Result ret;

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs  modulo 11
   *  --^--   ^        --^--   ^
   *  1 0 9   7   -->  1 0 9   7
   *  0 1 3   9        0 1 3   9
   * ------------------------------------------------------------------- */

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(kind::BITVECTOR_ADD, d_x, d_z_mul_nine),
          d_p),
      d_seven);

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(kind::BITVECTOR_ADD, d_y, d_z_mul_three),
          d_p),
      d_nine);

  std::vector<Node> eqs = {eq1, eq2};
  ret = BVGauss::gaussElimRewriteForUrem(eqs, res);
  ASSERT_EQ(ret, BVGauss::Result::PARTIAL);
  ASSERT_EQ(res.size(), 2);

  Node x1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_seven32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_two32)),
      d_p);
  Node y1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_nine32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_eight32)),
      d_p);

  Node x2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_two32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_three32)),
      d_p);
  Node z2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_three32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_seven32)),
      d_p);

  Node y3 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_three32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_four32)),
      d_p);
  Node z3 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_two32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_six32)),
      d_p);

  /* result depends on order of variables in matrix */
  if (res.find(d_x) == res.end())
  {
    /*
     *  y z x           y z x
     *  0 9 1  7   -->  1 0 7  3
     *  1 3 0  9        0 1 5  2
     *
     *  z y x           z y x
     *  9 0 1  7   -->  1 0 5  2
     *  3 1 0  9        0 1 7  3
     */
    ASSERT_EQ(res[d_y], y3);
    ASSERT_EQ(res[d_z], z3);
  }
  else if (res.find(d_y) == res.end())
  {
    /*
     *  x z y           x z y
     *  1 9 0  7   -->  1 0 8  2
     *  0 3 1  9        0 1 4  3
     *
     *  z x y           z x y
     *  9 1 0  7   -->  1 0 4  3
     *  3 0 1  9        0 1 8  2
     */
    ASSERT_EQ(res[d_x], x2);
    ASSERT_EQ(res[d_z], z2);
  }
  else
  {
    ASSERT_EQ(res.find(d_z), res.end());
    /*
     *  x y z           x y z
     *  1 0 9  7   -->  1 0 9  7
     *  0 1 3  9        0 1 3  9
     *
     *  y x z           y x z
     *  0 1 9  7   -->  1 0 3  9
     *  1 0 3  9        0 1 9  7
     */
    ASSERT_EQ(res[d_x], x1);
    ASSERT_EQ(res[d_y], y1);
  }
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_partial2)
{
  std::unordered_map<Node, Node> res;
  BVGauss::Result ret;

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs  modulo 11
   *  --^--   ^        --^--   ^
   *  1 3 0   7   -->  1 3 0   7
   *  0 0 1   9        0 0 1   9
   * ------------------------------------------------------------------- */

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD, d_x_mul_one, d_y_mul_three),
          d_p),
      d_seven);

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(kind::BITVECTOR_UREM, d_z_mul_one, d_p),
      d_nine);

  std::vector<Node> eqs = {eq1, eq2};
  ret = BVGauss::gaussElimRewriteForUrem(eqs, res);
  ASSERT_EQ(ret, BVGauss::Result::PARTIAL);
  ASSERT_EQ(res.size(), 2);

  Node x1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_seven32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_eight32)),
      d_p);
  Node y2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_six32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_seven32)),
      d_p);

  /* result depends on order of variables in matrix */
  if (res.find(d_x) == res.end())
  {
    /*
     *  x y z           x y z
     *  1 3 0  7   -->  1 3 0  7
     *  0 0 1  9        0 0 1  9
     *
     *  x z y           x z y
     *  1 0 3  7   -->  1 0 3  7
     *  0 1 0  9        0 1 0  9
     *
     *  z x y           z x y
     *  0 1 3  7   -->  1 0 0  9
     *  1 0 0  9        0 1 3  7
     */
    ASSERT_EQ(res[d_y], y2);
    ASSERT_EQ(res[d_z], d_nine32);
  }
  else if (res.find(d_y) == res.end())
  {
    /*
     *  z y x           z y x
     *  0 3 1  7   -->  1 0 0  9
     *  1 0 0  9        0 1 4  6
     *
     *  y x z           y x z
     *  3 1 0  7   -->  1 4 0  6
     *  0 0 1  9        0 0 1  9
     *
     *  y z x           y z x
     *  3 0 1  7   -->  1 0 4  6
     *  0 1 0  9        0 1 0  9
     */
    ASSERT_EQ(res[d_x], x1);
    ASSERT_EQ(res[d_z], d_nine32);
  }
  else
  {
    ASSERT_TRUE(false);
  }
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_partial3)
{
  std::unordered_map<Node, Node> res;
  BVGauss::Result ret;

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs  modulo 11
   *  --^--   ^        --^--   ^
   *  1 1 1   5   -->  1 0 9   7
   *  2 3 5   8        0 1 3   9
   * ------------------------------------------------------------------- */

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(kind::BITVECTOR_ADD, d_x_mul_one, d_y),
              d_z_mul_one),
          d_p),
      d_five);

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(
                  kind::BITVECTOR_ADD, d_x_mul_two, d_y_mul_three),
              d_z_mul_five),
          d_p),
      d_eight);

  std::vector<Node> eqs = {eq1, eq2};
  ret = BVGauss::gaussElimRewriteForUrem(eqs, res);
  ASSERT_EQ(ret, BVGauss::Result::PARTIAL);
  ASSERT_EQ(res.size(), 2);

  Node x1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_seven32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_two32)),
      d_p);
  Node y1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_nine32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_eight32)),
      d_p);
  Node x2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_two32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_three32)),
      d_p);
  Node z2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_three32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_seven32)),
      d_p);
  Node y3 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_three32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_four32)),
      d_p);
  Node z3 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_two32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_six32)),
      d_p);

  /* result depends on order of variables in matrix */
  if (res.find(d_x) == res.end())
  {
    /*
     *  y z x           y z x
     *  1 1 1  5   -->  1 0 7  3
     *  3 5 2  8        0 1 5  2
     *
     *  z y x           z y x
     *  1 1 1  5   -->  1 0 5  2
     *  5 3 2  8        0 1 7  3
     */
    ASSERT_EQ(res[d_y], y3);
    ASSERT_EQ(res[d_z], z3);
  }
  else if (res.find(d_y) == res.end())
  {
    /*
     *  x z y           x z y
     *  1 1 1  5   -->  1 0 8  2
     *  2 5 3  8        0 1 4  3
     *
     *  z x y           z x y
     *  1 1 1  5   -->  1 0 4  3
     *  5 2 3  9        0 1 8  2
     */
    ASSERT_EQ(res[d_x], x2);
    ASSERT_EQ(res[d_z], z2);
  }
  else
  {
    ASSERT_EQ(res.find(d_z), res.end());
    /*
     *  x y z           x y z
     *  1 1 1  5   -->  1 0 9  7
     *  2 3 5  8        0 1 3  9
     *
     *  y x z           y x z
     *  1 1 1  5   -->  1 0 3  9
     *  3 2 5  8        0 1 9  7
     */
    ASSERT_EQ(res[d_x], x1);
    ASSERT_EQ(res[d_y], y1);
  }
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_partial4)
{
  std::unordered_map<Node, Node> res;
  BVGauss::Result ret;

  /* -------------------------------------------------------------------
   *     lhs    rhs          lhs    rhs  modulo 11
   *  ----^---   ^         ---^---   ^
   *  2  4   6   18   -->  1 0 10    1
   *  4  5   6   24        0 1  2    4
   *  2  7  12   30        0 0  0    0
   * ------------------------------------------------------------------- */

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(
                  kind::BITVECTOR_ADD, d_x_mul_two, d_y_mul_four),
              d_z_mul_six),
          d_p),
      d_eighteen);

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(
                  kind::BITVECTOR_ADD, d_x_mul_four, d_y_mul_five),
              d_z_mul_six),
          d_p),
      d_twentyfour);

  Node eq3 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(
                  kind::BITVECTOR_ADD, d_x_mul_two, d_y_mul_seven),
              d_z_mul_twelve),
          d_p),
      d_thirty);

  std::vector<Node> eqs = {eq1, eq2, eq3};
  ret = BVGauss::gaussElimRewriteForUrem(eqs, res);
  ASSERT_EQ(ret, BVGauss::Result::PARTIAL);
  ASSERT_EQ(res.size(), 2);

  Node x1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_one32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_one32)),
      d_p);
  Node y1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_four32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_nine32)),
      d_p);
  Node x2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_three32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_five32)),
      d_p);
  Node z2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_two32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_five32)),
      d_p);
  Node y3 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_six32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_nine32)),
      d_p);
  Node z3 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_ten32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_one32)),
      d_p);

  /* result depends on order of variables in matrix */
  if (res.find(d_x) == res.end())
  {
    /*
     *  y  z x           y z  x
     *  4  6 2  18  -->  1 0  2   6
     *  5  6 4  24       0 1 10  10
     *  7 12 2  30       0 0  0   0
     *
     *  z  y x           z y  x
     *  6  4 2  18  -->  1 0 10  10
     *  6  5 4  24       0 1  2   6
     * 12 12 2  30       0 0  0   0
     *
     */
    ASSERT_EQ(res[d_y], y3);
    ASSERT_EQ(res[d_z], z3);
  }
  else if (res.find(d_y) == res.end())
  {
    /*
     *  x  z y           x z y
     *  2  6 4  18  -->  1 0 6  3
     *  4  6 5  24       0 1 6  2
     *  2 12 7  30       0 0 0  0
     *
     *  z x  y           z  x y
     *  6 2  4  18  -->  1  0 6  2
     *  6 4  5  24       0  1 6  3
     * 12 2 12  30       0  0 0  0
     *
     */
    ASSERT_EQ(res[d_x], x2);
    ASSERT_EQ(res[d_z], z2);
  }
  else
  {
    ASSERT_EQ(res.find(d_z), res.end());
    /*
     *  x y  z           x y  z
     *  2 4  6  18  -->  1 0 10  1
     *  4 5  6  24       0 1  2  4
     *  2 7 12  30       0 0  0  0
     *
     *  y x  z            y x  z
     *  4 2  6  18   -->  1 0  2 49
     *  5 4  6  24        0 1 10  1
     *  7 2 12  30        0 0  0  0
     */
    ASSERT_EQ(res[d_x], x1);
    ASSERT_EQ(res[d_y], y1);
  }
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_partial5)
{
  std::unordered_map<Node, Node> res;
  BVGauss::Result ret;

  /* -------------------------------------------------------------------
   *     lhs    rhs         lhs   rhs  modulo 3
   *  ----^---   ^         --^--   ^
   *  2  4   6   18   -->  1 2 0   0
   *  4  5   6   24        0 0 0   0
   *  2  7  12   30        0 0 0   0
   * ------------------------------------------------------------------- */

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(
                  kind::BITVECTOR_ADD, d_x_mul_two, d_y_mul_four),
              d_z_mul_six),
          d_three),
      d_eighteen);

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(
                  kind::BITVECTOR_ADD, d_x_mul_four, d_y_mul_five),
              d_z_mul_six),
          d_three),
      d_twentyfour);

  Node eq3 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(
                  kind::BITVECTOR_ADD, d_x_mul_two, d_y_mul_seven),
              d_z_mul_twelve),
          d_three),
      d_thirty);

  std::vector<Node> eqs = {eq1, eq2, eq3};
  ret = BVGauss::gaussElimRewriteForUrem(eqs, res);
  ASSERT_EQ(ret, BVGauss::Result::PARTIAL);
  ASSERT_EQ(res.size(), 1);

  Node x1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_one32),
      d_three);
  Node y2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_one32),
      d_three);

  /* result depends on order of variables in matrix */
  if (res.find(d_x) == res.end())
  {
    /*
     *  y x  z           y x z
     *  4 2  6  18  -->  1 2 0 0
     *  5 4  6  24       0 0 0 0
     *  7 2 12  30       0 0 0 0
     *
     *  y  z x            y z x
     *  4  6 2  18  -->  1 0 2  0
     *  5  6 4  24       0 0 0  0
     *  7 12 2  30       0 0 0  0
     *
     *  z  y x           z y x
     *  6  4 2  18  -->  0 1 2  0
     *  6  5 4  24       0 0 0  0
     * 12 12 2  30       0 0 0  0
     *
     */
    ASSERT_EQ(res[d_y], y2);
  }
  else if (res.find(d_y) == res.end())
  {
    /*
     *  x y  z           x y z
     *  2 4  6  18  -->  1 2 0  0
     *  4 5  6  24       0 0 0  0
     *  2 7 12  30       0 0 0  0
     *
     *  x  z y           x z y
     *  2  6 4  18  -->  1 0 2  0
     *  4  6 5  24       0 0 0  0
     *  2 12 7  30       0 0 0  0
     *
     *  z x  y           z  x y
     *  6 2  4  18  -->  0  1 2  0
     *  6 4  5  24       0  0 0  0
     * 12 2 12  30       0  0 0  0
     *
     */
    ASSERT_EQ(res[d_x], x1);
  }
  else
  {
    ASSERT_TRUE(false);
  }
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_partial6)
{
  std::unordered_map<Node, Node> res;
  BVGauss::Result ret;

  /* -------------------------------------------------------------------
   *    lhs    rhs  -->    lhs    rhs  modulo 11
   *  ---^---   ^        ---^---   ^
   *  x y z w            x y z w
   *  1 2 0 6   2        1 2 0 6   2
   *  0 0 2 2   2        0 0 1 1   1
   *  0 0 0 1   2        0 0 0 1   2
   * ------------------------------------------------------------------- */

  Node y_mul_two = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_two);
  Node z_mul_two = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_two);
  Node w = bv::utils::mkConcat(
      d_zero, d_nodeManager->mkVar("w", d_nodeManager->mkBitVectorType(16)));
  Node w_mul_six = d_nodeManager->mkNode(kind::BITVECTOR_MULT, w, d_six);
  Node w_mul_two = d_nodeManager->mkNode(kind::BITVECTOR_MULT, w, d_two);

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(
                  kind::BITVECTOR_ADD, d_x_mul_one, y_mul_two),
              w_mul_six),
          d_p),
      d_two);

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(kind::BITVECTOR_ADD, z_mul_two, w_mul_two),
          d_p),
      d_two);

  Node eq3 = d_nodeManager->mkNode(
      kind::EQUAL, d_nodeManager->mkNode(kind::BITVECTOR_UREM, w, d_p), d_two);

  std::vector<Node> eqs = {eq1, eq2, eq3};
  ret = BVGauss::gaussElimRewriteForUrem(eqs, res);
  ASSERT_EQ(ret, BVGauss::Result::PARTIAL);
  ASSERT_EQ(res.size(), 3);

  Node x1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_one32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_nine32)),
      d_p);
  Node z1 = d_ten32;
  Node w1 = d_two32;

  Node y2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_six32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_five32)),
      d_p);
  Node z2 = d_ten32;
  Node w2 = d_two32;

  /* result depends on order of variables in matrix */
  if (res.find(d_x) == res.end())
  {
    ASSERT_EQ(res[d_y], y2);
    ASSERT_EQ(res[d_z], z2);
    ASSERT_EQ(res[w], w2);
  }
  else if (res.find(d_y) == res.end())
  {
    ASSERT_EQ(res[d_x], x1);
    ASSERT_EQ(res[d_z], z1);
    ASSERT_EQ(res[w], w1);
  }
  else
  {
    ASSERT_TRUE(false);
  }
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_with_expr_partial)
{
  std::unordered_map<Node, Node> res;
  BVGauss::Result ret;

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs  modulo 11
   *  --^--   ^        --^--   ^
   *  1 0 9   7   -->  1 0 9   7
   *  0 1 3   9        0 1 3   9
   * ------------------------------------------------------------------- */

  Node zero = bv::utils::mkZero(8);
  Node xx = d_nodeManager->mkVar("xx", d_nodeManager->mkBitVectorType(8));
  Node yy = d_nodeManager->mkVar("yy", d_nodeManager->mkBitVectorType(8));
  Node zz = d_nodeManager->mkVar("zz", d_nodeManager->mkBitVectorType(8));

  Node x = bv::utils::mkConcat(
      d_zero,
      bv::utils::mkConcat(
          zero, bv::utils::mkExtract(bv::utils::mkConcat(zero, xx), 7, 0)));
  Node y = bv::utils::mkConcat(
      d_zero,
      bv::utils::mkConcat(
          zero, bv::utils::mkExtract(bv::utils::mkConcat(zero, yy), 7, 0)));
  Node z = bv::utils::mkConcat(
      d_zero,
      bv::utils::mkConcat(
          zero, bv::utils::mkExtract(bv::utils::mkConcat(zero, zz), 7, 0)));

  Node x_mul_one = d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, d_one32);
  Node nine_mul_z = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_nine32, z);
  Node one_mul_y = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_one, y);
  Node z_mul_three = d_nodeManager->mkNode(kind::BITVECTOR_MULT, z, d_three);

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(kind::BITVECTOR_ADD, x_mul_one, nine_mul_z),
          d_p),
      d_seven);

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(kind::BITVECTOR_ADD, one_mul_y, z_mul_three),
          d_p),
      d_nine);

  std::vector<Node> eqs = {eq1, eq2};
  ret = BVGauss::gaussElimRewriteForUrem(eqs, res);
  ASSERT_EQ(ret, BVGauss::Result::PARTIAL);
  ASSERT_EQ(res.size(), 2);

  x = Rewriter::rewrite(x);
  y = Rewriter::rewrite(y);
  z = Rewriter::rewrite(z);

  Node x1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_seven32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, z, d_two32)),
      d_p);
  Node y1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_nine32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, z, d_eight32)),
      d_p);

  Node x2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_two32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, y, d_three32)),
      d_p);
  Node z2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_three32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, y, d_seven32)),
      d_p);

  Node y3 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_three32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, d_four32)),
      d_p);
  Node z3 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_two32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, d_six32)),
      d_p);

  /* result depends on order of variables in matrix */
  if (res.find(x) == res.end())
  {
    /*
     *  y z x           y z x
     *  0 9 1  7   -->  1 0 7  3
     *  1 3 0  9        0 1 5  2
     *
     *  z y x           z y x
     *  9 0 1  7   -->  1 0 5  2
     *  3 1 0  9        0 1 7  3
     */
    ASSERT_EQ(res[Rewriter::rewrite(y)], y3);
    ASSERT_EQ(res[Rewriter::rewrite(z)], z3);
  }
  else if (res.find(y) == res.end())
  {
    /*
     *  x z y           x z y
     *  1 9 0  7   -->  1 0 8  2
     *  0 3 1  9        0 1 4  3
     *
     *  z x y           z x y
     *  9 1 0  7   -->  1 0 4  3
     *  3 0 1  9        0 1 8  2
     */
    ASSERT_EQ(res[x], x2);
    ASSERT_EQ(res[z], z2);
  }
  else
  {
    ASSERT_EQ(res.find(z), res.end());
    /*
     *  x y z           x y z
     *  1 0 9  7   -->  1 0 9  7
     *  0 1 3  9        0 1 3  9
     *
     *  y x z           y x z
     *  0 1 9  7   -->  1 0 3  9
     *  1 0 3  9        0 1 9  7
     */
    ASSERT_EQ(res[x], x1);
    ASSERT_EQ(res[y], y1);
  }
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_nary_partial)
{
  std::unordered_map<Node, Node> res;
  BVGauss::Result ret;

  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs  modulo 11
   *  --^--   ^        --^--   ^
   *  1 0 9   7   -->  1 0 9   7
   *  0 1 3   9        0 1 3   9
   * ------------------------------------------------------------------- */

  Node zero = bv::utils::mkZero(8);
  Node xx = d_nodeManager->mkVar("xx", d_nodeManager->mkBitVectorType(8));
  Node yy = d_nodeManager->mkVar("yy", d_nodeManager->mkBitVectorType(8));
  Node zz = d_nodeManager->mkVar("zz", d_nodeManager->mkBitVectorType(8));

  Node x = bv::utils::mkConcat(
      d_zero,
      bv::utils::mkConcat(
          zero,
          bv::utils::mkExtract(
              d_nodeManager->mkNode(kind::BITVECTOR_CONCAT, zero, xx), 7, 0)));
  Node y = bv::utils::mkConcat(
      d_zero,
      bv::utils::mkConcat(
          zero,
          bv::utils::mkExtract(
              d_nodeManager->mkNode(kind::BITVECTOR_CONCAT, zero, yy), 7, 0)));
  Node z = bv::utils::mkConcat(
      d_zero,
      bv::utils::mkConcat(
          zero,
          bv::utils::mkExtract(
              d_nodeManager->mkNode(kind::BITVECTOR_CONCAT, zero, zz), 7, 0)));

  NodeBuilder nbx(d_nodeManager.get(), kind::BITVECTOR_MULT);
  nbx << d_x << d_one << x;
  Node x_mul_one_mul_xx = nbx.constructNode();
  NodeBuilder nby(d_nodeManager.get(), kind::BITVECTOR_MULT);
  nby << d_y << y << d_one;
  Node y_mul_yy_mul_one = nby.constructNode();
  NodeBuilder nbz(d_nodeManager.get(), kind::BITVECTOR_MULT);
  nbz << d_three << d_z << z;
  Node three_mul_z_mul_zz = nbz.constructNode();
  NodeBuilder nbz2(d_nodeManager.get(), kind::BITVECTOR_MULT);
  nbz2 << d_z << d_nine << z;
  Node z_mul_nine_mul_zz = nbz2.constructNode();

  Node x_mul_xx = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, x);
  Node y_mul_yy = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, y);
  Node z_mul_zz = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, z);

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD, x_mul_one_mul_xx, z_mul_nine_mul_zz),
          d_p),
      d_seven);

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD, y_mul_yy_mul_one, three_mul_z_mul_zz),
          d_p),
      d_nine);

  std::vector<Node> eqs = {eq1, eq2};
  ret = BVGauss::gaussElimRewriteForUrem(eqs, res);
  ASSERT_EQ(ret, BVGauss::Result::PARTIAL);
  ASSERT_EQ(res.size(), 2);

  x_mul_xx = Rewriter::rewrite(x_mul_xx);
  y_mul_yy = Rewriter::rewrite(y_mul_yy);
  z_mul_zz = Rewriter::rewrite(z_mul_zz);

  Node x1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_seven32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, z_mul_zz, d_two32)),
      d_p);
  Node y1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_nine32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, z_mul_zz, d_eight32)),
      d_p);

  Node x2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_two32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, y_mul_yy, d_three32)),
      d_p);
  Node z2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_three32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, y_mul_yy, d_seven32)),
      d_p);

  Node y3 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_three32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, x_mul_xx, d_four32)),
      d_p);
  Node z3 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(
          kind::BITVECTOR_ADD,
          d_two32,
          d_nodeManager->mkNode(kind::BITVECTOR_MULT, x_mul_xx, d_six32)),
      d_p);

  /* result depends on order of variables in matrix */
  if (res.find(x_mul_xx) == res.end())
  {
    /*
     *  y z x           y z x
     *  0 9 1  7   -->  1 0 7  3
     *  1 3 0  9        0 1 5  2
     *
     *  z y x           z y x
     *  9 0 1  7   -->  1 0 5  2
     *  3 1 0  9        0 1 7  3
     */
    ASSERT_EQ(res[y_mul_yy], y3);
    ASSERT_EQ(res[z_mul_zz], z3);
  }
  else if (res.find(y_mul_yy) == res.end())
  {
    /*
     *  x z y           x z y
     *  1 9 0  7   -->  1 0 8  2
     *  0 3 1  9        0 1 4  3
     *
     *  z x y           z x y
     *  9 1 0  7   -->  1 0 4  3
     *  3 0 1  9        0 1 8  2
     */
    ASSERT_EQ(res[x_mul_xx], x2);
    ASSERT_EQ(res[z_mul_zz], z2);
  }
  else
  {
    ASSERT_EQ(res.find(z_mul_zz), res.end());
    /*
     *  x y z           x y z
     *  1 0 9  7   -->  1 0 9  7
     *  0 1 3  9        0 1 3  9
     *
     *  y x z           y x z
     *  0 1 9  7   -->  1 0 3  9
     *  1 0 3  9        0 1 9  7
     */
    ASSERT_EQ(res[x_mul_xx], x1);
    ASSERT_EQ(res[y_mul_yy], y1);
  }
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_not_invalid1)
{
  std::unordered_map<Node, Node> res;
  BVGauss::Result ret;

  /* -------------------------------------------------------------------
   * 3x / 2z = 4  modulo 11
   * 2x % 5y = 2
   * y O z = 5
   * ------------------------------------------------------------------- */

  Node n1 = d_nodeManager->mkNode(
      kind::BITVECTOR_UDIV,
      d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_three, d_x),
      d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_two, d_y));
  Node n2 = d_nodeManager->mkNode(
      kind::BITVECTOR_UREM,
      d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_two, d_x),
      d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_five, d_y));

  Node n3 = bv::utils::mkConcat(
      d_zero,
      bv::utils::mkExtract(
          d_nodeManager->mkNode(kind::BITVECTOR_CONCAT, d_y, d_z), 15, 0));

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(kind::BITVECTOR_UREM, n1, d_p),
      d_four);

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL, d_nodeManager->mkNode(kind::BITVECTOR_UREM, n2, d_p), d_two);

  Node eq3 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(kind::BITVECTOR_UREM, n3, d_p),
      d_five);

  std::vector<Node> eqs = {eq1, eq2, eq3};
  ret = BVGauss::gaussElimRewriteForUrem(eqs, res);
  ASSERT_EQ(ret, BVGauss::Result::UNIQUE);
  ASSERT_EQ(res.size(), 3);

  ASSERT_EQ(res[n1], d_four32);
  ASSERT_EQ(res[n2], d_two32);
  ASSERT_EQ(res[n3], d_five32);
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_not_invalid2)
{
  std::unordered_map<Node, Node> res;
  BVGauss::Result ret;

  /* -------------------------------------------------------------------
   * x*y = 4  modulo 11
   * x*y*z = 2
   * 2*x*y + 2*z = 9
   * ------------------------------------------------------------------- */

  Node zero32 = bv::utils::mkZero(32);

  Node x = bv::utils::mkConcat(
      zero32, d_nodeManager->mkVar("x", d_nodeManager->mkBitVectorType(16)));
  Node y = bv::utils::mkConcat(
      zero32, d_nodeManager->mkVar("y", d_nodeManager->mkBitVectorType(16)));
  Node z = bv::utils::mkConcat(
      zero32, d_nodeManager->mkVar("z", d_nodeManager->mkBitVectorType(16)));

  Node n1 = d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, y);
  Node n2 =
      d_nodeManager->mkNode(kind::BITVECTOR_MULT,
                            d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, y),
                            z);
  Node n3 = d_nodeManager->mkNode(
      kind::BITVECTOR_ADD,
      d_nodeManager->mkNode(kind::BITVECTOR_MULT,
                            d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, y),
                            bv::utils::mkConcat(d_zero, d_two)),
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConcat(d_zero, d_two), z));

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM, n1, bv::utils::mkConcat(d_zero, d_p)),
      bv::utils::mkConcat(d_zero, d_four));

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM, n2, bv::utils::mkConcat(d_zero, d_p)),
      bv::utils::mkConcat(d_zero, d_two));

  Node eq3 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM, n3, bv::utils::mkConcat(d_zero, d_p)),
      bv::utils::mkConcat(d_zero, d_nine));

  std::vector<Node> eqs = {eq1, eq2, eq3};
  ret = BVGauss::gaussElimRewriteForUrem(eqs, res);
  ASSERT_EQ(ret, BVGauss::Result::UNIQUE);
  ASSERT_EQ(res.size(), 3);

  n1 = Rewriter::rewrite(n1);
  n2 = Rewriter::rewrite(n2);
  z = Rewriter::rewrite(z);

  ASSERT_EQ(res[n1], bv::utils::mkConst(48, 4));
  ASSERT_EQ(res[n2], bv::utils::mkConst(48, 2));

  Integer twoxy = (res[n1].getConst<BitVector>().getValue() * Integer(2))
                      .euclidianDivideRemainder(Integer(48));
  Integer twoz = (res[z].getConst<BitVector>().getValue() * Integer(2))
                     .euclidianDivideRemainder(Integer(48));
  Integer r = (twoxy + twoz).euclidianDivideRemainder(Integer(11));
  ASSERT_EQ(r, Integer(9));
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_for_urem_invalid)
{
  std::unordered_map<Node, Node> res;
  BVGauss::Result ret;

  /* -------------------------------------------------------------------
   * x*y = 4  modulo 11
   * x*y*z = 2
   * 2*x*y = 9
   * ------------------------------------------------------------------- */

  Node zero32 = bv::utils::mkZero(32);

  Node x = bv::utils::mkConcat(
      zero32, d_nodeManager->mkVar("x", d_nodeManager->mkBitVectorType(16)));
  Node y = bv::utils::mkConcat(
      zero32, d_nodeManager->mkVar("y", d_nodeManager->mkBitVectorType(16)));
  Node z = bv::utils::mkConcat(
      zero32, d_nodeManager->mkVar("z", d_nodeManager->mkBitVectorType(16)));

  Node n1 = d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, y);
  Node n2 =
      d_nodeManager->mkNode(kind::BITVECTOR_MULT,
                            d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, y),
                            z);
  Node n3 =
      d_nodeManager->mkNode(kind::BITVECTOR_MULT,
                            d_nodeManager->mkNode(kind::BITVECTOR_MULT, x, y),
                            bv::utils::mkConcat(d_zero, d_two));

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM, n1, bv::utils::mkConcat(d_zero, d_p)),
      bv::utils::mkConcat(d_zero, d_four));

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM, n2, bv::utils::mkConcat(d_zero, d_p)),
      bv::utils::mkConcat(d_zero, d_two));

  Node eq3 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM, n3, bv::utils::mkConcat(d_zero, d_p)),
      bv::utils::mkConcat(d_zero, d_nine));

  std::vector<Node> eqs = {eq1, eq2, eq3};
  ret = BVGauss::gaussElimRewriteForUrem(eqs, res);
  ASSERT_EQ(ret, BVGauss::Result::INVALID);
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_unique1)
{
  /* -------------------------------------------------------------------
   *   lhs   rhs  modulo 11
   *  --^--   ^
   *  1 1 1   5
   *  2 3 5   8
   *  4 0 5   2
   * ------------------------------------------------------------------- */

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(
                  kind::BITVECTOR_ADD, d_x_mul_one, d_y_mul_one),
              d_z_mul_one),
          d_p),
      d_five);

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(
                  kind::BITVECTOR_ADD, d_x_mul_two, d_y_mul_three),
              d_z_mul_five),
          d_p),
      d_eight);

  Node eq3 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD, d_x_mul_four, d_z_mul_five),
          d_p),
      d_two);

  Node a = d_nodeManager->mkNode(
      kind::AND, d_nodeManager->mkNode(kind::AND, eq1, eq2), eq3);

  AssertionPipeline apipe;
  apipe.push_back(a);
  passes::BVGauss bgauss(nullptr, "bv-gauss-unit");
  std::unordered_map<Node, Node> res;
  PreprocessingPassResult pres = bgauss.applyInternal(&apipe);
  ASSERT_EQ(pres, PreprocessingPassResult::NO_CONFLICT);
  Node resx = d_nodeManager->mkNode(
      kind::EQUAL, d_x, d_nodeManager->mkConst<BitVector>(BitVector(32, 3u)));
  Node resy = d_nodeManager->mkNode(
      kind::EQUAL, d_y, d_nodeManager->mkConst<BitVector>(BitVector(32, 4u)));
  Node resz = d_nodeManager->mkNode(
      kind::EQUAL, d_z, d_nodeManager->mkConst<BitVector>(BitVector(32, 9u)));
  ASSERT_EQ(apipe.size(), 4);
  ASSERT_NE(std::find(apipe.begin(), apipe.end(), resx), apipe.end());
  ASSERT_NE(std::find(apipe.begin(), apipe.end(), resy), apipe.end());
  ASSERT_NE(std::find(apipe.begin(), apipe.end(), resz), apipe.end());
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_unique2)
{
  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs   modulo 11
   *  --^--   ^        --^--   ^
   *  1 1 1   5        1 0 0   3
   *  2 3 5   8        0 1 0   4
   *  4 0 5   2        0 0 1   9
   *
   *   lhs   rhs        lhs   rhs   modulo 7
   *  --^--   ^        --^--   ^
   *  2 6 0   4        1 0 0   3
   *  4 6 0   3        0 1 0   2
   * ------------------------------------------------------------------- */

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(
                  kind::BITVECTOR_ADD, d_x_mul_one, d_y_mul_one),
              d_z_mul_one),
          d_p),
      d_five);

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nodeManager->mkNode(
                  kind::BITVECTOR_ADD, d_x_mul_two, d_y_mul_three),
              d_z_mul_five),
          d_p),
      d_eight);

  Node eq3 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD, d_x_mul_four, d_z_mul_five),
          d_p),
      d_two);

  Node y_mul_six = d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_six);

  Node eq4 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(kind::BITVECTOR_ADD, d_x_mul_two, y_mul_six),
          d_seven),
      d_four);

  Node eq5 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(kind::BITVECTOR_ADD, d_x_mul_four, y_mul_six),
          d_seven),
      d_three);

  Node a = d_nodeManager->mkNode(
      kind::AND, d_nodeManager->mkNode(kind::AND, eq1, eq2), eq3);

  AssertionPipeline apipe;
  apipe.push_back(a);
  apipe.push_back(eq4);
  apipe.push_back(eq5);
  passes::BVGauss bgauss(nullptr, "bv-gauss-unit");
  std::unordered_map<Node, Node> res;
  PreprocessingPassResult pres = bgauss.applyInternal(&apipe);
  ASSERT_EQ(pres, PreprocessingPassResult::NO_CONFLICT);
  Node resx1 = d_nodeManager->mkNode(
      kind::EQUAL, d_x, d_nodeManager->mkConst<BitVector>(BitVector(32, 3u)));
  Node resx2 = d_nodeManager->mkNode(
      kind::EQUAL, d_x, d_nodeManager->mkConst<BitVector>(BitVector(32, 3u)));
  Node resy1 = d_nodeManager->mkNode(
      kind::EQUAL, d_y, d_nodeManager->mkConst<BitVector>(BitVector(32, 4u)));
  Node resy2 = d_nodeManager->mkNode(
      kind::EQUAL, d_y, d_nodeManager->mkConst<BitVector>(BitVector(32, 2u)));
  Node resz = d_nodeManager->mkNode(
      kind::EQUAL, d_z, d_nodeManager->mkConst<BitVector>(BitVector(32, 9u)));
  ASSERT_EQ(apipe.size(), 8);
  ASSERT_NE(std::find(apipe.begin(), apipe.end(), resx1), apipe.end());
  ASSERT_NE(std::find(apipe.begin(), apipe.end(), resx2), apipe.end());
  ASSERT_NE(std::find(apipe.begin(), apipe.end(), resy1), apipe.end());
  ASSERT_NE(std::find(apipe.begin(), apipe.end(), resy2), apipe.end());
  ASSERT_NE(std::find(apipe.begin(), apipe.end(), resz), apipe.end());
}

TEST_F(TestPPWhiteBVGauss, elim_rewrite_partial)
{
  /* -------------------------------------------------------------------
   *   lhs   rhs        lhs   rhs  modulo 11
   *  --^--   ^        --^--   ^
   *  1 0 9   7   -->  1 0 9   7
   *  0 1 3   9        0 1 3   9
   * ------------------------------------------------------------------- */

  Node eq1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(kind::BITVECTOR_ADD, d_x_mul_one, d_z_mul_nine),
          d_p),
      d_seven);

  Node eq2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD, d_y_mul_one, d_z_mul_three),
          d_p),
      d_nine);

  AssertionPipeline apipe;
  apipe.push_back(eq1);
  apipe.push_back(eq2);
  passes::BVGauss bgauss(nullptr, "bv-gauss-unit");
  std::unordered_map<Node, Node> res;
  PreprocessingPassResult pres = bgauss.applyInternal(&apipe);
  ASSERT_EQ(pres, PreprocessingPassResult::NO_CONFLICT);
  ASSERT_EQ(apipe.size(), 4);

  Node resx1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_x,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_seven32,
              d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_two32)),
          d_p));
  Node resy1 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_y,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_nine32,
              d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_z, d_eight32)),
          d_p));

  Node resx2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_x,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_two32,
              d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_three32)),
          d_p));
  Node resz2 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_z,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_three32,
              d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_y, d_seven32)),
          d_p));

  Node resy3 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_y,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_three32,
              d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_four32)),
          d_p));
  Node resz3 = d_nodeManager->mkNode(
      kind::EQUAL,
      d_z,
      d_nodeManager->mkNode(
          kind::BITVECTOR_UREM,
          d_nodeManager->mkNode(
              kind::BITVECTOR_ADD,
              d_two32,
              d_nodeManager->mkNode(kind::BITVECTOR_MULT, d_x, d_six32)),
          d_p));

  bool fx1 = std::find(apipe.begin(), apipe.end(), resx1) != apipe.end();
  bool fy1 = std::find(apipe.begin(), apipe.end(), resy1) != apipe.end();
  bool fx2 = std::find(apipe.begin(), apipe.end(), resx2) != apipe.end();
  bool fz2 = std::find(apipe.begin(), apipe.end(), resz2) != apipe.end();
  bool fy3 = std::find(apipe.begin(), apipe.end(), resy3) != apipe.end();
  bool fz3 = std::find(apipe.begin(), apipe.end(), resz3) != apipe.end();

  /* result depends on order of variables in matrix */
  ASSERT_TRUE((fx1 && fy1) || (fx2 && fz2) || (fy3 && fz3));
}

TEST_F(TestPPWhiteBVGauss, get_min_bw1)
{
  ASSERT_EQ(BVGauss::getMinBwExpr(bv::utils::mkConst(32, 11)), 4);

  ASSERT_EQ(BVGauss::getMinBwExpr(d_p), 4);
  ASSERT_EQ(BVGauss::getMinBwExpr(d_x), 16);

  Node extp = bv::utils::mkExtract(d_p, 4, 0);
  ASSERT_EQ(BVGauss::getMinBwExpr(extp), 4);
  Node extx = bv::utils::mkExtract(d_x, 4, 0);
  ASSERT_EQ(BVGauss::getMinBwExpr(extx), 5);

  Node zextop8 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(8));
  Node zextop16 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(16));
  Node zextop32 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(32));
  Node zextop40 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(40));

  Node zext40p = d_nodeManager->mkNode(zextop8, d_p);
  ASSERT_EQ(BVGauss::getMinBwExpr(zext40p), 4);
  Node zext40x = d_nodeManager->mkNode(zextop8, d_x);
  ASSERT_EQ(BVGauss::getMinBwExpr(zext40x), 16);

  Node zext48p = d_nodeManager->mkNode(zextop16, d_p);
  ASSERT_EQ(BVGauss::getMinBwExpr(zext48p), 4);
  Node zext48x = d_nodeManager->mkNode(zextop16, d_x);
  ASSERT_EQ(BVGauss::getMinBwExpr(zext48x), 16);

  Node p8 = d_nodeManager->mkConst<BitVector>(BitVector(8, 11u));
  Node x8 = d_nodeManager->mkVar("x8", d_nodeManager->mkBitVectorType(8));

  Node zext48p8 = d_nodeManager->mkNode(zextop40, p8);
  ASSERT_EQ(BVGauss::getMinBwExpr(zext48p8), 4);
  Node zext48x8 = d_nodeManager->mkNode(zextop40, x8);
  ASSERT_EQ(BVGauss::getMinBwExpr(zext48x8), 8);

  Node mult1p = d_nodeManager->mkNode(kind::BITVECTOR_MULT, extp, extp);
  ASSERT_EQ(BVGauss::getMinBwExpr(mult1p), 5);
  Node mult1x = d_nodeManager->mkNode(kind::BITVECTOR_MULT, extx, extx);
  ASSERT_EQ(BVGauss::getMinBwExpr(mult1x), 0);

  Node mult2p = d_nodeManager->mkNode(kind::BITVECTOR_MULT, zext40p, zext40p);
  ASSERT_EQ(BVGauss::getMinBwExpr(mult2p), 7);
  Node mult2x = d_nodeManager->mkNode(kind::BITVECTOR_MULT, zext40x, zext40x);
  ASSERT_EQ(BVGauss::getMinBwExpr(mult2x), 32);

  NodeBuilder nbmult3p(kind::BITVECTOR_MULT);
  nbmult3p << zext48p << zext48p << zext48p;
  Node mult3p = nbmult3p;
  ASSERT_EQ(BVGauss::getMinBwExpr(mult3p), 11);
  NodeBuilder nbmult3x(kind::BITVECTOR_MULT);
  nbmult3x << zext48x << zext48x << zext48x;
  Node mult3x = nbmult3x;
  ASSERT_EQ(BVGauss::getMinBwExpr(mult3x), 48);

  NodeBuilder nbmult4p(kind::BITVECTOR_MULT);
  nbmult4p << zext48p << zext48p8 << zext48p;
  Node mult4p = nbmult4p;
  ASSERT_EQ(BVGauss::getMinBwExpr(mult4p), 11);
  NodeBuilder nbmult4x(kind::BITVECTOR_MULT);
  nbmult4x << zext48x << zext48x8 << zext48x;
  Node mult4x = nbmult4x;
  ASSERT_EQ(BVGauss::getMinBwExpr(mult4x), 40);

  Node concat1p = bv::utils::mkConcat(d_p, zext48p);
  ASSERT_EQ(BVGauss::getMinBwExpr(concat1p), 52);
  Node concat1x = bv::utils::mkConcat(d_x, zext48x);
  ASSERT_EQ(BVGauss::getMinBwExpr(concat1x), 64);

  Node concat2p = bv::utils::mkConcat(bv::utils::mkZero(16), zext48p);
  ASSERT_EQ(BVGauss::getMinBwExpr(concat2p), 4);
  Node concat2x = bv::utils::mkConcat(bv::utils::mkZero(16), zext48x);
  ASSERT_EQ(BVGauss::getMinBwExpr(concat2x), 16);

  Node udiv1p = d_nodeManager->mkNode(kind::BITVECTOR_UDIV, zext48p, zext48p);
  ASSERT_EQ(BVGauss::getMinBwExpr(udiv1p), 1);
  Node udiv1x = d_nodeManager->mkNode(kind::BITVECTOR_UDIV, zext48x, zext48x);
  ASSERT_EQ(BVGauss::getMinBwExpr(udiv1x), 48);

  Node udiv2p = d_nodeManager->mkNode(kind::BITVECTOR_UDIV, zext48p, zext48p8);
  ASSERT_EQ(BVGauss::getMinBwExpr(udiv2p), 1);
  Node udiv2x = d_nodeManager->mkNode(kind::BITVECTOR_UDIV, zext48x, zext48x8);
  ASSERT_EQ(BVGauss::getMinBwExpr(udiv2x), 48);

  Node urem1p = d_nodeManager->mkNode(kind::BITVECTOR_UREM, zext48p, zext48p);
  ASSERT_EQ(BVGauss::getMinBwExpr(urem1p), 1);
  Node urem1x = d_nodeManager->mkNode(kind::BITVECTOR_UREM, zext48x, zext48x);
  ASSERT_EQ(BVGauss::getMinBwExpr(urem1x), 1);

  Node urem2p = d_nodeManager->mkNode(kind::BITVECTOR_UREM, zext48p, zext48p8);
  ASSERT_EQ(BVGauss::getMinBwExpr(urem2p), 1);
  Node urem2x = d_nodeManager->mkNode(kind::BITVECTOR_UREM, zext48x, zext48x8);
  ASSERT_EQ(BVGauss::getMinBwExpr(urem2x), 16);

  Node urem3p = d_nodeManager->mkNode(kind::BITVECTOR_UREM, zext48p8, zext48p);
  ASSERT_EQ(BVGauss::getMinBwExpr(urem3p), 1);
  Node urem3x = d_nodeManager->mkNode(kind::BITVECTOR_UREM, zext48x8, zext48x);
  ASSERT_EQ(BVGauss::getMinBwExpr(urem3x), 8);

  Node add1p = d_nodeManager->mkNode(kind::BITVECTOR_ADD, extp, extp);
  ASSERT_EQ(BVGauss::getMinBwExpr(add1p), 5);
  Node add1x = d_nodeManager->mkNode(kind::BITVECTOR_ADD, extx, extx);
  ASSERT_EQ(BVGauss::getMinBwExpr(add1x), 0);

  Node add2p = d_nodeManager->mkNode(kind::BITVECTOR_ADD, zext40p, zext40p);
  ASSERT_EQ(BVGauss::getMinBwExpr(add2p), 5);
  Node add2x = d_nodeManager->mkNode(kind::BITVECTOR_ADD, zext40x, zext40x);
  ASSERT_EQ(BVGauss::getMinBwExpr(add2x), 17);

  Node add3p = d_nodeManager->mkNode(kind::BITVECTOR_ADD, zext48p8, zext48p);
  ASSERT_EQ(BVGauss::getMinBwExpr(add3p), 5);
  Node add3x = d_nodeManager->mkNode(kind::BITVECTOR_ADD, zext48x8, zext48x);
  ASSERT_EQ(BVGauss::getMinBwExpr(add3x), 17);

  NodeBuilder nbadd4p(kind::BITVECTOR_ADD);
  nbadd4p << zext48p << zext48p << zext48p;
  Node add4p = nbadd4p;
  ASSERT_EQ(BVGauss::getMinBwExpr(add4p), 6);
  NodeBuilder nbadd4x(kind::BITVECTOR_ADD);
  nbadd4x << zext48x << zext48x << zext48x;
  Node add4x = nbadd4x;
  ASSERT_EQ(BVGauss::getMinBwExpr(add4x), 18);

  NodeBuilder nbadd5p(kind::BITVECTOR_ADD);
  nbadd5p << zext48p << zext48p8 << zext48p;
  Node add5p = nbadd5p;
  ASSERT_EQ(BVGauss::getMinBwExpr(add5p), 6);
  NodeBuilder nbadd5x(kind::BITVECTOR_ADD);
  nbadd5x << zext48x << zext48x8 << zext48x;
  Node add5x = nbadd5x;
  ASSERT_EQ(BVGauss::getMinBwExpr(add5x), 18);

  NodeBuilder nbadd6p(kind::BITVECTOR_ADD);
  nbadd6p << zext48p << zext48p << zext48p << zext48p;
  Node add6p = nbadd6p;
  ASSERT_EQ(BVGauss::getMinBwExpr(add6p), 6);
  NodeBuilder nbadd6x(kind::BITVECTOR_ADD);
  nbadd6x << zext48x << zext48x << zext48x << zext48x;
  Node add6x = nbadd6x;
  ASSERT_EQ(BVGauss::getMinBwExpr(add6x), 18);

  Node not1p = d_nodeManager->mkNode(kind::BITVECTOR_NOT, zext40p);
  ASSERT_EQ(BVGauss::getMinBwExpr(not1p), 40);
  Node not1x = d_nodeManager->mkNode(kind::BITVECTOR_NOT, zext40x);
  ASSERT_EQ(BVGauss::getMinBwExpr(not1x), 40);
}

TEST_F(TestPPWhiteBVGauss, get_min_bw2)
{
  /* ((_ zero_extend 5)
   *     ((_ extract 7 0) ((_ zero_extend 15) d_p)))  */
  Node zextop5 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(5));
  Node zextop15 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(15));
  Node zext1 = d_nodeManager->mkNode(zextop15, d_p);
  Node ext = bv::utils::mkExtract(zext1, 7, 0);
  Node zext2 = d_nodeManager->mkNode(zextop5, ext);
  ASSERT_EQ(BVGauss::getMinBwExpr(zext2), 4);
}

TEST_F(TestPPWhiteBVGauss, get_min_bw3a)
{
  /* ((_ zero_extend 5)
   *     (bvudiv ((_ extract 4 0) ((_ zero_extend 5) (bvudiv x z)))
   *             ((_ extract 4 0) z)))  */
  Node x = d_nodeManager->mkVar("x", d_nodeManager->mkBitVectorType(16));
  Node y = d_nodeManager->mkVar("y", d_nodeManager->mkBitVectorType(16));
  Node z = d_nodeManager->mkVar("z", d_nodeManager->mkBitVectorType(16));
  Node zextop5 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(5));
  Node udiv1 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV, x, y);
  Node zext1 = d_nodeManager->mkNode(zextop5, udiv1);
  Node ext1 = bv::utils::mkExtract(zext1, 4, 0);
  Node ext2 = bv::utils::mkExtract(z, 4, 0);
  Node udiv2 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV, ext1, ext2);
  Node zext2 = bv::utils::mkConcat(bv::utils::mkZero(5), udiv2);
  ASSERT_EQ(BVGauss::getMinBwExpr(zext2), 5);
}

TEST_F(TestPPWhiteBVGauss, get_min_bw3b)
{
  /* ((_ zero_extend 5)
   *     (bvudiv ((_ extract 4 0) ((_ zero_extend 5) (bvudiv x z)))
   *             ((_ extract 4 0) z)))  */
  Node zextop5 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(5));
  Node udiv1 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV, d_x, d_y);
  Node zext1 = d_nodeManager->mkNode(zextop5, udiv1);
  Node ext1 = bv::utils::mkExtract(zext1, 4, 0);
  Node ext2 = bv::utils::mkExtract(d_z, 4, 0);
  Node udiv2 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV, ext1, ext2);
  Node zext2 = bv::utils::mkConcat(bv::utils::mkZero(5), udiv2);
  ASSERT_EQ(BVGauss::getMinBwExpr(zext2), 5);
}

TEST_F(TestPPWhiteBVGauss, get_min_bw4a)
{
  /* (bvadd
   *     ((_ zero_extend 5)
   *         (bvudiv ((_ extract 4 0) ((_ zero_extend 5) (bvudiv x y)))
   *                 ((_ extract 4 0) z)))
   *     ((_ zero_extend 7)
   *         (bvudiv ((_ extract 2 0) ((_ zero_extend 5) (bvudiv x y)))
   *                 ((_ extract 2 0) z)))  */
  Node x = d_nodeManager->mkVar("x", d_nodeManager->mkBitVectorType(16));
  Node y = d_nodeManager->mkVar("y", d_nodeManager->mkBitVectorType(16));
  Node z = d_nodeManager->mkVar("z", d_nodeManager->mkBitVectorType(16));
  Node zextop5 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(5));
  Node zextop7 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(7));

  Node udiv1 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV, x, y);
  Node zext1 = d_nodeManager->mkNode(zextop5, udiv1);

  Node ext1_1 = bv::utils::mkExtract(zext1, 4, 0);
  Node ext2_1 = bv::utils::mkExtract(z, 4, 0);
  Node udiv2_1 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV, ext1_1, ext2_1);
  Node zext2_1 = bv::utils::mkConcat(bv::utils::mkZero(5), udiv2_1);

  Node ext1_2 = bv::utils::mkExtract(zext1, 2, 0);
  Node ext2_2 = bv::utils::mkExtract(z, 2, 0);
  Node udiv2_2 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV, ext1_2, ext2_2);
  Node zext2_2 = d_nodeManager->mkNode(zextop7, udiv2_2);

  Node plus = d_nodeManager->mkNode(kind::BITVECTOR_ADD, zext2_1, zext2_2);

  ASSERT_EQ(BVGauss::getMinBwExpr(plus), 6);
}

TEST_F(TestPPWhiteBVGauss, get_min_bw4b)
{
  /* (bvadd
   *     ((_ zero_extend 5)
   *         (bvudiv ((_ extract 4 0) ((_ zero_extend 5) (bvudiv x y)))
   *                 ((_ extract 4 0) z)))
   *     ((_ zero_extend 7)
   *         (bvudiv ((_ extract 2 0) ((_ zero_extend 5) (bvudiv x y)))
   *                 ((_ extract 2 0) z)))  */
  Node zextop5 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(5));
  Node zextop7 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(7));

  Node udiv1 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV, d_x, d_y);
  Node zext1 = d_nodeManager->mkNode(zextop5, udiv1);

  Node ext1_1 = bv::utils::mkExtract(zext1, 4, 0);
  Node ext2_1 = bv::utils::mkExtract(d_z, 4, 0);
  Node udiv2_1 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV, ext1_1, ext2_1);
  Node zext2_1 = bv::utils::mkConcat(bv::utils::mkZero(5), udiv2_1);

  Node ext1_2 = bv::utils::mkExtract(zext1, 2, 0);
  Node ext2_2 = bv::utils::mkExtract(d_z, 2, 0);
  Node udiv2_2 = d_nodeManager->mkNode(kind::BITVECTOR_UDIV, ext1_2, ext2_2);
  Node zext2_2 = d_nodeManager->mkNode(zextop7, udiv2_2);

  Node plus = d_nodeManager->mkNode(kind::BITVECTOR_ADD, zext2_1, zext2_2);

  ASSERT_EQ(BVGauss::getMinBwExpr(plus), 6);
}

TEST_F(TestPPWhiteBVGauss, get_min_bw5a)
{
  /* (bvadd
   *   (bvadd
   *     (bvadd
   *       (bvadd
   *         (bvadd
   *           (bvadd
   *             (bvadd (bvmul (_ bv86 13)
   *                           ((_ zero_extend 5)
   *                             ((_ extract 7 0) ((_ zero_extend 15) x))))
   *                    (bvmul (_ bv41 13)
   *                           ((_ zero_extend 5)
   *                             ((_ extract 7 0) ((_ zero_extend 15) y)))))
   *             (bvmul (_ bv37 13)
   *                    ((_ zero_extend 5)
   *                      ((_ extract 7 0) ((_ zero_extend 15) z)))))
   *           (bvmul (_ bv170 13)
   *                  ((_ zero_extend 5)
   *                    ((_ extract 7 0) ((_ zero_extend 15) u)))))
   *         (bvmul (_ bv112 13)
   *                ((_ zero_extend 5)
   *                  ((_ extract 7 0) ((_ zero_extend 15) v)))))
   *       (bvmul (_ bv195 13) ((_ zero_extend 5) ((_ extract 15 8) s))))
   *     (bvmul (_ bv124 13) ((_ zero_extend 5) ((_ extract 7 0) s))))
   *   (bvmul (_ bv83 13)
   *          ((_ zero_extend 5) ((_ extract 7 0) ((_ zero_extend 15) w)))))
   */
  Node x = bv::utils::mkVar(1);
  Node y = bv::utils::mkVar(1);
  Node z = bv::utils::mkVar(1);
  Node u = bv::utils::mkVar(1);
  Node v = bv::utils::mkVar(1);
  Node w = bv::utils::mkVar(1);
  Node s = bv::utils::mkVar(16);

  Node zextop5 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(5));
  Node zextop15 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(15));

  Node zext15x = d_nodeManager->mkNode(zextop15, x);
  Node zext15y = d_nodeManager->mkNode(zextop15, y);
  Node zext15z = d_nodeManager->mkNode(zextop15, z);
  Node zext15u = d_nodeManager->mkNode(zextop15, u);
  Node zext15v = d_nodeManager->mkNode(zextop15, v);
  Node zext15w = d_nodeManager->mkNode(zextop15, w);

  Node ext7x = bv::utils::mkExtract(zext15x, 7, 0);
  Node ext7y = bv::utils::mkExtract(zext15y, 7, 0);
  Node ext7z = bv::utils::mkExtract(zext15z, 7, 0);
  Node ext7u = bv::utils::mkExtract(zext15u, 7, 0);
  Node ext7v = bv::utils::mkExtract(zext15v, 7, 0);
  Node ext7w = bv::utils::mkExtract(zext15w, 7, 0);
  Node ext7s = bv::utils::mkExtract(s, 7, 0);
  Node ext15s = bv::utils::mkExtract(s, 15, 8);

  Node xx = bv::utils::mkConcat(bv::utils::mkZero(5), ext7x);
  Node yy = bv::utils::mkConcat(bv::utils::mkZero(5), ext7y);
  Node zz = bv::utils::mkConcat(bv::utils::mkZero(5), ext7z);
  Node uu = bv::utils::mkConcat(bv::utils::mkZero(5), ext7u);
  Node vv = bv::utils::mkConcat(bv::utils::mkZero(5), ext7v);
  Node ww = bv::utils::mkConcat(bv::utils::mkZero(5), ext7w);
  Node s7 = bv::utils::mkConcat(bv::utils::mkZero(5), ext7s);
  Node s15 = bv::utils::mkConcat(bv::utils::mkZero(5), ext15s);

  Node plus1 = d_nodeManager->mkNode(
      kind::BITVECTOR_ADD,
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(13, 86), xx),
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(13, 41), yy));
  Node plus2 = d_nodeManager->mkNode(
      kind::BITVECTOR_ADD,
      plus1,
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(13, 37), zz));
  Node plus3 = d_nodeManager->mkNode(
      kind::BITVECTOR_ADD,
      plus2,
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(13, 170), uu));
  Node plus4 = d_nodeManager->mkNode(
      kind::BITVECTOR_ADD,
      plus3,
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(13, 112), uu));
  Node plus5 = d_nodeManager->mkNode(
      kind::BITVECTOR_ADD,
      plus4,
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(13, 195), s15));
  Node plus6 = d_nodeManager->mkNode(
      kind::BITVECTOR_ADD,
      plus5,
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(13, 124), s7));
  Node plus7 = d_nodeManager->mkNode(
      kind::BITVECTOR_ADD,
      plus6,
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(13, 83), ww));

  ASSERT_EQ(BVGauss::getMinBwExpr(plus7), 0);
}

TEST_F(TestPPWhiteBVGauss, get_min_bw5b)
{
  /* (bvadd
   *   (bvadd
   *     (bvadd
   *       (bvadd
   *         (bvadd
   *           (bvadd
   *             (bvadd (bvmul (_ bv86 20)
   *                           ((_ zero_extend 12)
   *                             ((_ extract 7 0) ((_ zero_extend 15) x))))
   *                    (bvmul (_ bv41 20)
   *                           ((_ zero_extend 12)
   *                             ((_ extract 7 0) ((_ zero_extend 15) y)))))
   *             (bvmul (_ bv37 20)
   *                    ((_ zero_extend 12)
   *                      ((_ extract 7 0) ((_ zero_extend 15) z)))))
   *           (bvmul (_ bv170 20)
   *                  ((_ zero_extend 12)
   *                    ((_ extract 7 0) ((_ zero_extend 15) u)))))
   *         (bvmul (_ bv112 20)
   *                ((_ zero_extend 12)
   *                  ((_ extract 7 0) ((_ zero_extend 15) v)))))
   *       (bvmul (_ bv195 20) ((_ zero_extend 12) ((_ extract 15 8) s))))
   *     (bvmul (_ bv124 20) ((_ zero_extend 12) ((_ extract 7 0) s))))
   *   (bvmul (_ bv83 20)
   *          ((_ zero_extend 12) ((_ extract 7 0) ((_ zero_extend 15) w)))))
   */
  Node x = bv::utils::mkVar(1);
  Node y = bv::utils::mkVar(1);
  Node z = bv::utils::mkVar(1);
  Node u = bv::utils::mkVar(1);
  Node v = bv::utils::mkVar(1);
  Node w = bv::utils::mkVar(1);
  Node s = bv::utils::mkVar(16);

  Node zextop15 =
      d_nodeManager->mkConst<BitVectorZeroExtend>(BitVectorZeroExtend(15));

  Node zext15x = d_nodeManager->mkNode(zextop15, x);
  Node zext15y = d_nodeManager->mkNode(zextop15, y);
  Node zext15z = d_nodeManager->mkNode(zextop15, z);
  Node zext15u = d_nodeManager->mkNode(zextop15, u);
  Node zext15v = d_nodeManager->mkNode(zextop15, v);
  Node zext15w = d_nodeManager->mkNode(zextop15, w);

  Node ext7x = bv::utils::mkExtract(zext15x, 7, 0);
  Node ext7y = bv::utils::mkExtract(zext15y, 7, 0);
  Node ext7z = bv::utils::mkExtract(zext15z, 7, 0);
  Node ext7u = bv::utils::mkExtract(zext15u, 7, 0);
  Node ext7v = bv::utils::mkExtract(zext15v, 7, 0);
  Node ext7w = bv::utils::mkExtract(zext15w, 7, 0);
  Node ext7s = bv::utils::mkExtract(s, 7, 0);
  Node ext15s = bv::utils::mkExtract(s, 15, 8);

  Node xx = bv::utils::mkConcat(bv::utils::mkZero(12), ext7x);
  Node yy = bv::utils::mkConcat(bv::utils::mkZero(12), ext7y);
  Node zz = bv::utils::mkConcat(bv::utils::mkZero(12), ext7z);
  Node uu = bv::utils::mkConcat(bv::utils::mkZero(12), ext7u);
  Node vv = bv::utils::mkConcat(bv::utils::mkZero(12), ext7v);
  Node ww = bv::utils::mkConcat(bv::utils::mkZero(12), ext7w);
  Node s7 = bv::utils::mkConcat(bv::utils::mkZero(12), ext7s);
  Node s15 = bv::utils::mkConcat(bv::utils::mkZero(12), ext15s);

  Node plus1 = d_nodeManager->mkNode(
      kind::BITVECTOR_ADD,
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(20, 86), xx),
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(20, 41), yy));
  Node plus2 = d_nodeManager->mkNode(
      kind::BITVECTOR_ADD,
      plus1,
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(20, 37), zz));
  Node plus3 = d_nodeManager->mkNode(
      kind::BITVECTOR_ADD,
      plus2,
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(20, 170), uu));
  Node plus4 = d_nodeManager->mkNode(
      kind::BITVECTOR_ADD,
      plus3,
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(20, 112), uu));
  Node plus5 = d_nodeManager->mkNode(
      kind::BITVECTOR_ADD,
      plus4,
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(20, 195), s15));
  Node plus6 = d_nodeManager->mkNode(
      kind::BITVECTOR_ADD,
      plus5,
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(20, 124), s7));
  Node plus7 = d_nodeManager->mkNode(
      kind::BITVECTOR_ADD,
      plus6,
      d_nodeManager->mkNode(
          kind::BITVECTOR_MULT, bv::utils::mkConst(20, 83), ww));

  ASSERT_EQ(BVGauss::getMinBwExpr(plus7), 19);
  ASSERT_EQ(BVGauss::getMinBwExpr(Rewriter::rewrite(plus7)), 17);
}
}  // namespace test
}  // namespace cvc5

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