/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 5 ↦ 4, 4 ↦ 5 },
it remains to prove termination of the 96-rule system
{ 0 0 1 1 1 2 0 1 1 3 2 1 ⟶ 3 4 4 5 3 3 0 4 0 5 1 4 5 0 3 1 ,
  0 0 5 1 1 3 1 5 1 1 3 1 ⟶ 3 4 4 4 2 5 4 0 4 2 4 2 0 4 1 0 5 ,
  0 1 0 5 2 2 0 3 5 1 1 4 ⟶ 5 0 1 4 5 3 1 2 3 4 3 4 0 1 ,
  0 1 2 2 2 2 2 5 3 0 5 0 ⟶ 4 4 4 2 2 5 4 3 4 3 3 3 4 0 4 4 0 2 ,
  0 1 2 5 1 4 3 5 2 1 2 1 ⟶ 0 4 2 3 4 4 2 1 0 5 4 3 1 1 4 ,
  0 1 3 1 1 2 2 5 2 4 0 2 ⟶ 2 4 5 4 3 4 1 3 5 3 3 4 4 4 2 4 5 ,
  0 2 1 5 1 5 2 2 1 5 1 1 ⟶ 2 3 3 4 4 5 3 4 4 2 3 0 2 0 0 0 ,
  0 2 3 3 2 0 1 5 5 5 0 5 ⟶ 4 1 3 4 4 0 3 2 1 5 4 4 4 4 1 4 3 3 ,
  0 2 5 0 3 4 1 3 0 2 2 0 ⟶ 0 5 0 4 4 4 4 4 5 1 3 3 4 4 2 4 0 ,
  0 3 3 1 1 1 5 1 0 2 1 2 ⟶ 4 1 2 4 2 4 1 4 0 0 1 4 5 3 4 4 ,
  0 5 1 1 2 2 2 2 0 1 5 5 ⟶ 5 0 0 4 0 0 4 1 4 0 2 3 0 4 2 2 3 ,
  0 5 1 3 1 5 5 5 5 1 0 2 ⟶ 5 5 2 3 0 1 1 0 3 4 3 1 0 2 ,
  0 5 5 5 5 0 0 1 2 4 2 4 ⟶ 4 4 4 3 0 5 0 0 1 4 4 2 5 3 3 4 4 1 ,
  0 5 4 2 0 3 0 1 5 4 1 1 ⟶ 0 1 0 4 3 3 0 3 4 4 4 0 0 3 3 4 ,
  0 4 1 2 4 5 5 2 0 1 1 2 ⟶ 0 4 5 4 3 5 4 5 3 3 3 2 3 3 4 5 2 ,
  0 4 3 5 5 5 0 2 5 0 2 1 ⟶ 3 4 3 3 4 5 5 3 4 4 2 3 4 3 4 0 ,
  0 4 5 1 2 0 0 2 0 5 2 3 ⟶ 4 4 5 4 3 4 2 2 3 3 3 3 4 4 0 2 ,
  0 4 5 2 2 1 3 1 1 1 3 1 ⟶ 5 3 4 0 2 0 1 4 0 2 4 3 3 4 5 4 4 3 ,
  1 0 0 5 5 5 0 1 2 1 4 0 ⟶ 3 4 0 2 1 0 4 3 4 3 3 2 1 4 4 ,
  1 0 1 4 0 1 0 5 2 0 1 2 ⟶ 3 2 4 4 3 5 3 4 5 4 4 3 1 0 2 ,
  1 2 1 5 1 2 1 3 5 3 5 5 ⟶ 2 2 5 0 0 0 0 4 3 0 1 2 5 4 ,
  1 3 2 2 4 1 1 2 1 2 4 0 ⟶ 4 4 4 1 4 5 4 1 5 4 4 4 3 5 4 3 4 0 ,
  1 3 3 2 2 3 1 4 1 5 0 2 ⟶ 5 3 3 4 4 5 4 1 4 4 4 0 4 3 2 ,
  1 3 5 5 0 2 2 0 2 1 2 2 ⟶ 1 3 1 4 3 3 4 4 4 4 0 5 3 2 5 ,
  1 5 0 2 5 0 2 1 0 1 1 5 ⟶ 4 0 4 3 0 3 4 4 3 3 0 2 3 5 ,
  1 5 1 5 5 5 5 1 5 1 4 2 ⟶ 3 4 0 5 3 4 5 4 0 4 3 2 1 4 0 4 4 ,
  1 5 3 2 0 2 5 3 1 1 1 1 ⟶ 5 5 4 3 5 4 4 5 0 5 4 0 4 4 ,
  1 5 5 5 0 2 2 3 2 5 2 2 ⟶ 1 5 4 4 4 4 3 4 1 4 0 0 4 2 4 3 4 ,
  2 0 0 1 5 1 4 3 1 3 2 4 ⟶ 3 5 5 0 4 1 0 5 4 3 3 0 0 0 0 4 ,
  2 0 1 3 2 0 4 0 5 5 1 5 ⟶ 5 4 4 3 4 0 5 3 4 4 4 0 1 3 2 3 3 0 ,
  2 0 2 0 1 3 5 1 2 0 1 4 ⟶ 4 4 3 4 2 3 0 3 3 4 3 4 4 3 3 ,
  2 0 2 1 1 1 3 5 5 2 2 0 ⟶ 4 4 0 1 5 0 3 0 4 3 3 4 5 4 5 5 0 3 ,
  2 0 2 4 2 2 0 3 1 4 0 5 ⟶ 4 0 4 5 4 2 4 1 2 2 3 4 4 4 3 ,
  2 0 5 1 3 5 2 4 5 1 1 3 ⟶ 2 2 3 4 0 0 5 2 0 5 3 4 4 4 5 4 0 ,
  2 1 0 0 5 5 4 2 0 2 1 1 ⟶ 3 4 1 0 1 4 4 5 4 0 5 2 4 2 5 4 4 5 ,
  2 1 1 1 0 5 1 3 0 5 0 3 ⟶ 5 3 0 2 4 0 4 2 1 3 4 3 4 1 ,
  2 1 1 5 1 5 5 0 3 1 1 0 ⟶ 3 2 4 4 4 5 3 4 3 3 4 4 1 5 1 3 ,
  2 1 3 4 1 3 1 3 1 3 1 2 ⟶ 0 4 1 4 0 2 4 1 3 5 5 0 4 5 3 4 5 ,
  2 2 1 1 5 2 4 2 5 2 0 3 ⟶ 3 5 5 5 4 2 2 2 2 5 0 4 5 4 ,
  2 2 1 3 1 1 2 0 1 3 5 5 ⟶ 2 5 5 0 0 0 2 4 4 4 3 4 1 3 4 0 5 ,
  2 2 1 5 5 0 4 2 0 5 2 5 ⟶ 3 4 0 2 4 1 3 2 3 3 4 4 4 0 0 5 ,
  2 2 2 1 5 5 3 3 4 1 5 1 ⟶ 1 4 5 4 4 4 3 4 4 4 2 1 0 1 0 4 1 ,
  2 2 4 2 4 4 0 5 0 1 2 0 ⟶ 1 2 4 5 0 4 5 3 0 4 4 0 4 4 ,
  2 3 1 3 5 1 2 1 2 1 0 1 ⟶ 2 2 5 5 0 3 3 2 5 4 0 1 5 4 4 ,
  2 3 2 1 4 1 1 2 5 1 5 1 ⟶ 3 3 0 4 5 4 4 0 0 0 2 3 3 1 5 4 0 ,
  2 3 2 3 5 2 2 3 4 2 5 5 ⟶ 4 0 3 0 4 4 1 2 5 3 4 4 4 5 0 4 ,
  2 3 2 5 0 0 5 1 3 0 5 1 ⟶ 5 4 4 1 0 0 1 0 4 1 4 4 3 3 4 4 4 0 ,
  2 3 3 5 1 3 2 1 5 1 5 3 ⟶ 4 1 1 4 0 0 0 4 1 0 3 4 2 2 ,
  2 5 2 0 5 5 2 2 3 3 1 0 ⟶ 4 4 4 0 2 4 1 4 3 4 2 5 5 1 5 4 3 ,
  2 5 3 5 1 0 5 2 0 1 4 2 ⟶ 0 0 4 3 5 4 3 5 4 5 0 3 0 2 ,
  2 5 4 5 1 2 0 4 5 1 0 3 ⟶ 4 3 4 3 3 3 4 4 5 3 2 1 4 1 0 ,
  2 4 1 5 5 1 3 5 1 3 2 0 ⟶ 2 4 0 4 3 5 4 3 3 2 1 3 0 5 5 ,
  3 0 5 1 5 2 0 5 1 1 0 0 ⟶ 4 4 4 0 3 2 3 2 1 0 5 3 4 4 0 4 4 2 ,
  3 0 5 3 4 2 1 5 5 0 0 1 ⟶ 4 4 3 0 0 4 5 0 4 1 3 2 4 3 ,
  3 1 5 4 1 1 5 1 4 1 3 1 ⟶ 3 4 3 0 3 4 4 3 5 3 4 4 3 0 1 0 ,
  3 2 0 3 1 5 1 2 1 1 5 5 ⟶ 1 4 2 0 4 1 3 4 5 3 4 3 0 4 2 4 2 ,
  3 2 0 5 2 3 0 3 3 0 5 5 ⟶ 3 5 5 0 2 4 4 0 4 3 2 3 5 4 3 3 ,
  3 2 2 2 0 5 4 2 2 4 3 5 ⟶ 1 4 2 3 1 1 0 1 0 5 3 1 4 3 ,
  3 2 5 2 4 0 3 2 0 2 2 4 ⟶ 5 4 0 0 2 2 4 0 4 0 4 1 0 2 4 ,
  3 3 1 2 3 5 5 4 5 1 3 1 ⟶ 5 0 5 4 2 1 4 4 0 5 3 1 4 3 4 4 ,
  3 3 3 5 0 0 1 5 3 2 0 3 ⟶ 3 4 3 4 1 0 2 4 4 4 2 3 3 5 3 ,
  3 5 1 0 3 5 2 2 3 2 1 3 ⟶ 4 5 4 0 4 4 1 3 0 0 2 5 1 1 ,
  3 5 2 1 1 5 5 1 3 3 5 2 ⟶ 5 0 5 2 1 1 4 4 5 5 4 0 4 0 ,
  3 5 2 2 0 5 2 2 1 2 5 2 ⟶ 2 2 0 1 5 4 2 2 3 4 4 3 3 5 ,
  3 5 5 5 2 1 4 2 5 1 4 2 ⟶ 3 0 0 1 4 4 3 5 0 4 1 0 4 3 4 5 4 4 ,
  5 0 0 1 0 5 1 3 1 2 2 5 ⟶ 5 4 0 2 0 0 4 2 4 0 4 0 3 3 0 ,
  5 0 2 1 1 1 5 3 0 3 5 5 ⟶ 1 4 4 1 0 2 5 4 4 5 0 4 2 3 4 ,
  5 0 2 2 2 2 4 5 5 2 5 0 ⟶ 4 0 3 3 4 4 2 5 4 0 5 0 2 4 2 4 ,
  5 0 5 1 2 5 4 5 0 1 5 3 ⟶ 4 2 3 3 4 0 1 3 5 4 5 4 5 4 5 4 ,
  5 1 1 2 0 2 3 0 3 5 4 5 ⟶ 5 1 4 3 4 1 4 4 5 2 3 3 4 3 4 3 3 ,
  5 1 1 2 3 2 5 2 5 3 5 3 ⟶ 1 4 2 4 3 4 0 2 4 0 5 3 4 2 3 5 4 4 ,
  5 1 1 3 5 5 1 2 1 3 1 2 ⟶ 2 4 4 4 3 3 0 0 2 3 3 0 3 4 2 5 4 3 ,
  5 1 2 1 5 2 5 2 1 2 0 1 ⟶ 5 1 5 4 2 1 1 5 2 5 4 1 4 4 0 ,
  5 1 3 5 5 5 3 3 3 5 2 2 ⟶ 5 5 3 5 0 2 5 4 4 0 3 3 4 2 3 0 ,
  5 1 5 2 2 0 5 4 2 0 5 4 ⟶ 0 5 2 2 5 4 4 4 3 3 3 4 1 5 ,
  5 1 5 2 3 1 3 5 3 2 4 2 ⟶ 3 3 5 4 4 5 3 3 3 3 0 5 2 1 4 ,
  5 2 0 0 4 3 2 0 5 1 3 4 ⟶ 2 4 3 3 5 3 1 3 0 3 3 4 4 4 4 4 ,
  5 2 0 2 5 2 0 0 0 1 2 4 ⟶ 4 2 1 3 2 3 4 3 2 5 4 5 3 5 4 4 ,
  5 2 0 3 2 2 0 3 2 5 2 3 ⟶ 2 1 4 2 2 1 4 4 5 4 0 0 0 2 ,
  5 2 1 0 5 3 2 1 2 5 2 3 ⟶ 0 3 4 0 4 4 4 4 3 4 5 0 3 4 4 3 5 ,
  5 2 1 1 2 2 0 2 2 0 3 1 ⟶ 1 2 4 4 3 1 0 4 5 0 4 0 2 3 0 5 0 4 ,
  5 2 2 0 2 2 0 4 2 1 0 4 ⟶ 3 5 4 4 4 5 0 3 5 3 5 4 4 0 2 4 3 3 ,
  5 2 2 3 1 5 1 1 2 3 5 5 ⟶ 1 0 0 5 3 5 0 1 5 4 3 2 5 0 ,
  5 2 5 0 3 1 3 1 3 2 2 3 ⟶ 5 4 1 0 1 3 5 4 4 5 4 2 5 5 4 4 4 2 ,
  5 3 1 1 2 5 0 3 1 5 3 0 ⟶ 2 4 3 4 4 2 3 0 3 4 4 2 3 5 1 ,
  5 5 2 2 0 5 2 0 3 1 5 2 ⟶ 2 5 4 1 4 3 3 3 1 0 1 0 1 5 4 4 ,
  5 5 5 5 1 0 5 1 3 2 3 2 ⟶ 1 3 0 5 0 0 4 4 4 1 3 4 4 1 0 1 5 4 ,
  5 4 0 0 2 2 0 5 3 0 5 5 ⟶ 5 4 4 5 3 5 4 3 0 0 3 5 4 4 4 1 5 ,
  4 1 2 3 1 3 1 3 0 5 2 5 ⟶ 0 3 2 4 4 5 4 4 3 4 4 5 4 4 5 3 4 ,
  4 1 4 2 2 1 1 2 0 3 2 2 ⟶ 0 2 4 3 4 4 5 1 0 4 1 4 4 3 3 4 4 4 ,
  4 2 0 5 2 2 1 2 4 5 1 2 ⟶ 5 4 4 4 1 3 0 5 0 5 5 4 4 4 0 5 ,
  4 2 0 4 0 1 2 0 0 2 0 5 ⟶ 0 3 3 5 3 4 1 4 4 2 3 0 1 3 ,
  4 3 0 2 2 5 1 2 5 4 1 0 ⟶ 0 4 1 4 0 2 4 2 4 3 4 1 4 4 ,
  4 3 2 1 5 2 1 2 1 1 5 3 ⟶ 5 4 0 4 3 3 0 4 4 0 4 4 3 4 1 4 1 3 ,
  4 5 2 2 2 1 1 4 3 2 2 1 ⟶ 0 5 0 4 4 0 4 3 0 2 4 5 2 4 4 ,
  4 4 1 2 2 0 3 4 1 1 5 3 ⟶ 0 4 0 3 4 5 4 0 1 0 5 0 4 0 }

The system was reversed.

After renaming modulo the bijection { 1 ↦ 0, 2 ↦ 1, 3 ↦ 2, 0 ↦ 3, 5 ↦ 4, 4 ↦ 5 },
it remains to prove termination of the 96-rule system
{ 0 1 2 0 0 3 1 0 0 0 3 3 ⟶ 0 2 3 4 5 0 4 3 5 3 2 2 4 5 5 2 ,
  0 2 0 0 4 0 2 0 0 4 3 3 ⟶ 4 3 0 5 3 1 5 1 5 3 5 4 1 5 5 5 2 ,
  5 0 0 4 2 3 1 1 4 3 0 3 ⟶ 0 3 5 2 5 2 1 0 2 4 5 0 3 4 ,
  3 4 3 2 4 1 1 1 1 1 0 3 ⟶ 1 3 5 5 3 5 2 2 2 5 2 5 4 1 1 5 5 5 ,
  0 1 0 1 4 2 5 0 4 1 0 3 ⟶ 5 0 0 2 5 4 3 0 1 5 5 2 1 5 3 ,
  1 3 5 1 4 1 1 0 0 2 0 3 ⟶ 4 5 1 5 5 5 2 2 4 2 0 5 2 5 4 5 1 ,
  0 0 4 0 1 1 4 0 4 0 1 3 ⟶ 3 3 3 1 3 2 1 5 5 2 4 5 5 2 2 1 ,
  4 3 4 4 4 0 3 1 2 2 1 3 ⟶ 2 2 5 0 5 5 5 5 4 0 1 2 3 5 5 2 0 5 ,
  3 1 1 3 2 0 5 2 3 4 1 3 ⟶ 3 5 1 5 5 2 2 0 4 5 5 5 5 5 3 4 3 ,
  1 0 1 3 0 4 0 0 0 2 2 3 ⟶ 5 5 2 4 5 0 3 3 5 0 5 1 5 1 0 5 ,
  4 4 0 3 1 1 1 1 0 0 4 3 ⟶ 2 1 1 5 3 2 1 3 5 0 5 3 3 5 3 3 4 ,
  1 3 0 4 4 4 4 0 2 0 4 3 ⟶ 1 3 0 2 5 2 3 0 0 3 2 1 4 4 ,
  5 1 5 1 0 3 3 4 4 4 4 3 ⟶ 0 5 5 2 2 4 1 5 5 0 3 3 4 3 2 5 5 5 ,
  0 0 5 4 0 3 2 3 1 5 4 3 ⟶ 5 2 2 3 3 5 5 5 2 3 2 2 5 3 0 3 ,
  1 0 0 3 1 4 4 5 1 0 5 3 ⟶ 1 4 5 2 2 1 2 2 2 4 5 4 2 5 4 5 3 ,
  0 1 3 4 1 3 4 4 4 2 5 3 ⟶ 3 5 2 5 2 1 5 5 2 4 4 5 2 2 5 2 ,
  2 1 4 3 1 3 3 1 0 4 5 3 ⟶ 1 3 5 5 2 2 2 2 1 1 5 2 5 4 5 5 ,
  0 2 0 0 0 2 0 1 1 4 5 3 ⟶ 2 5 5 4 5 2 2 5 1 3 5 0 3 1 3 5 2 4 ,
  3 5 0 1 0 3 4 4 4 3 3 0 ⟶ 5 5 0 1 2 2 5 2 5 3 0 1 3 5 2 ,
  1 0 3 1 4 3 0 3 5 0 3 0 ⟶ 1 3 0 2 5 5 4 5 2 4 2 5 5 1 2 ,
  4 4 2 4 2 0 1 0 4 0 1 0 ⟶ 5 4 1 0 3 2 5 3 3 3 3 4 1 1 ,
  3 5 1 0 1 0 0 5 1 1 2 0 ⟶ 3 5 2 5 4 2 5 5 5 4 0 5 4 5 0 5 5 5 ,
  1 3 4 0 5 0 2 1 1 2 2 0 ⟶ 1 2 5 3 5 5 5 0 5 4 5 5 2 2 4 ,
  1 1 0 1 3 1 1 3 4 4 2 0 ⟶ 4 1 2 4 3 5 5 5 5 2 2 5 0 2 0 ,
  4 0 0 3 0 1 3 4 1 3 4 0 ⟶ 4 2 1 3 2 2 5 5 2 3 2 5 3 5 ,
  1 5 0 4 0 4 4 4 4 0 4 0 ⟶ 5 5 3 5 0 1 2 5 3 5 4 5 2 4 3 5 2 ,
  0 0 0 0 2 4 1 3 1 2 4 0 ⟶ 5 5 3 5 4 3 4 5 5 4 2 5 4 4 ,
  1 1 4 1 2 1 1 3 4 4 4 0 ⟶ 5 2 5 1 5 3 3 5 0 5 2 5 5 5 5 4 0 ,
  5 1 2 0 2 5 0 4 0 3 3 1 ⟶ 5 3 3 3 3 2 2 5 4 3 0 5 3 4 4 2 ,
  4 0 4 4 3 5 3 1 2 0 3 1 ⟶ 3 2 2 1 2 0 3 5 5 5 2 4 3 5 2 5 5 4 ,
  5 0 3 1 0 4 2 0 3 1 3 1 ⟶ 2 2 5 5 2 5 2 2 3 2 1 5 2 5 5 ,
  3 1 1 4 4 2 0 0 0 1 3 1 ⟶ 2 3 4 4 5 4 5 2 2 5 3 2 3 4 0 3 5 5 ,
  4 3 5 0 2 3 1 1 5 1 3 1 ⟶ 2 5 5 5 2 1 1 0 5 1 5 4 5 3 5 ,
  2 0 0 4 5 1 4 2 0 4 3 1 ⟶ 3 5 4 5 5 5 2 4 3 1 4 3 3 5 2 1 1 ,
  0 0 1 3 1 5 4 4 3 3 0 1 ⟶ 4 5 5 4 1 5 1 4 3 5 4 5 5 0 3 0 5 2 ,
  2 3 4 3 2 0 4 3 0 0 0 1 ⟶ 0 5 2 5 2 0 1 5 3 5 1 3 2 4 ,
  3 0 0 2 3 4 4 0 4 0 0 1 ⟶ 2 0 4 0 5 5 2 2 5 2 4 5 5 5 1 2 ,
  1 0 2 0 2 0 2 0 5 2 0 1 ⟶ 4 5 2 4 5 3 4 4 2 0 5 1 3 5 0 5 3 ,
  2 3 1 4 1 5 1 4 0 0 1 1 ⟶ 5 4 5 3 4 1 1 1 1 5 4 4 4 2 ,
  4 4 2 0 3 1 0 0 2 0 1 1 ⟶ 4 3 5 2 0 5 2 5 5 5 1 3 3 3 4 4 1 ,
  4 1 4 3 1 5 3 4 4 0 1 1 ⟶ 4 3 3 5 5 5 2 2 1 2 0 5 1 3 5 2 ,
  0 4 0 5 2 2 4 4 0 1 1 1 ⟶ 0 5 3 0 3 0 1 5 5 5 2 5 5 5 4 5 0 ,
  3 1 0 3 4 3 5 5 1 5 1 1 ⟶ 5 5 3 5 5 3 2 4 5 3 4 5 1 0 ,
  0 3 0 1 0 1 0 4 2 0 2 1 ⟶ 5 5 4 0 3 5 4 1 2 2 3 4 4 1 1 ,
  0 4 0 4 1 0 0 5 0 1 2 1 ⟶ 3 5 4 0 2 2 1 3 3 3 5 5 4 5 3 2 2 ,
  4 4 1 5 2 1 1 4 2 1 2 1 ⟶ 5 3 4 5 5 5 2 4 1 0 5 5 3 2 3 5 ,
  0 4 3 2 0 4 3 3 4 1 2 1 ⟶ 3 5 5 5 2 2 5 5 0 5 3 0 3 3 0 5 5 4 ,
  2 4 0 4 0 1 2 0 4 2 2 1 ⟶ 1 1 5 2 3 0 5 3 3 3 5 0 0 5 ,
  3 0 2 2 1 1 4 4 3 1 4 1 ⟶ 2 5 4 0 4 4 1 5 2 5 0 5 1 3 5 5 5 ,
  1 5 0 3 1 4 3 0 4 2 4 1 ⟶ 1 3 2 3 4 5 4 2 5 4 2 5 3 3 ,
  2 3 0 4 5 3 1 0 4 5 4 1 ⟶ 3 0 5 0 1 2 4 5 5 2 2 2 5 2 5 ,
  3 1 2 0 4 2 0 4 4 0 5 1 ⟶ 4 4 3 2 0 1 2 2 5 4 2 5 3 5 1 ,
  3 3 0 0 4 3 1 4 0 4 3 2 ⟶ 1 5 5 3 5 5 2 4 3 0 1 2 1 2 3 5 5 5 ,
  0 3 3 4 4 0 1 5 2 4 3 2 ⟶ 2 5 1 2 0 5 3 4 5 3 3 2 5 5 ,
  0 2 0 5 0 4 0 0 5 4 0 2 ⟶ 3 0 3 2 5 5 2 4 2 5 5 2 3 2 5 2 ,
  4 4 0 0 1 0 4 0 2 3 1 2 ⟶ 1 5 1 5 3 2 5 2 4 5 2 0 5 3 1 5 0 ,
  4 4 3 2 2 3 2 1 4 3 1 2 ⟶ 2 2 5 4 2 1 2 5 3 5 5 1 3 4 4 2 ,
  4 2 5 1 1 5 4 3 1 1 1 2 ⟶ 2 5 0 2 4 3 0 3 0 0 2 1 5 0 ,
  5 1 1 3 1 2 3 5 1 4 1 2 ⟶ 5 1 3 0 5 3 5 3 5 1 1 3 3 5 4 ,
  0 2 0 4 5 4 4 2 1 0 2 2 ⟶ 5 5 2 5 0 2 4 3 5 5 0 1 5 4 3 4 ,
  2 3 1 2 4 0 3 3 4 2 2 2 ⟶ 2 4 2 2 1 5 5 5 1 3 0 5 2 5 2 ,
  2 0 1 2 1 1 4 2 3 0 4 2 ⟶ 0 0 4 1 3 3 2 0 5 5 3 5 4 5 ,
  1 4 2 2 0 4 4 0 0 1 4 2 ⟶ 3 5 3 5 4 4 5 5 0 0 1 4 3 4 ,
  1 4 1 0 1 1 4 3 1 1 4 2 ⟶ 4 2 2 5 5 2 1 1 5 4 0 3 1 1 ,
  1 5 0 4 1 5 0 1 4 4 4 2 ⟶ 5 5 4 5 2 5 3 0 5 3 4 2 5 5 0 3 3 2 ,
  4 1 1 0 2 0 4 3 0 3 3 4 ⟶ 3 2 2 3 5 3 5 1 5 3 3 1 3 5 4 ,
  4 4 2 3 2 4 0 0 0 1 3 4 ⟶ 5 2 1 5 3 4 5 5 4 1 3 0 5 5 0 ,
  3 4 1 4 4 5 1 1 1 1 3 4 ⟶ 5 1 5 1 3 4 3 5 4 1 5 5 2 2 3 5 ,
  2 4 0 3 4 5 4 1 0 4 3 4 ⟶ 5 4 5 4 5 4 5 4 2 0 3 5 2 2 1 5 ,
  4 5 4 2 3 2 1 3 1 0 0 4 ⟶ 2 2 5 2 5 2 2 1 4 5 5 0 5 2 5 0 4 ,
  2 4 2 4 1 4 1 2 1 0 0 4 ⟶ 5 5 4 2 1 5 2 4 3 5 1 3 5 2 5 1 5 0 ,
  1 0 2 0 1 0 4 4 2 0 0 4 ⟶ 2 5 4 1 5 2 3 2 2 1 3 3 2 2 5 5 5 1 ,
  0 3 1 0 1 4 1 4 0 1 0 4 ⟶ 3 5 5 0 5 4 1 4 0 0 1 5 4 0 4 ,
  1 1 4 2 2 2 4 4 4 2 0 4 ⟶ 3 2 1 5 2 2 3 5 5 4 1 3 4 2 4 4 ,
  5 4 3 1 5 4 3 1 1 4 0 4 ⟶ 4 0 5 2 2 2 5 5 5 4 1 1 4 3 ,
  1 5 1 2 4 2 0 2 1 4 0 4 ⟶ 5 0 1 4 3 2 2 2 2 4 5 5 4 2 2 ,
  5 2 0 4 3 1 2 5 3 3 1 4 ⟶ 5 5 5 5 5 2 2 3 2 0 2 4 2 2 5 1 ,
  5 1 0 3 3 3 1 4 1 3 1 4 ⟶ 5 5 4 2 4 5 4 1 2 5 2 1 2 0 1 5 ,
  2 1 4 1 2 3 1 1 2 3 1 4 ⟶ 1 3 3 3 5 4 5 5 0 1 1 5 0 1 ,
  2 1 4 1 0 1 2 4 3 0 1 4 ⟶ 4 2 5 5 2 3 4 5 2 5 5 5 5 3 5 2 3 ,
  0 2 3 1 1 3 1 1 0 0 1 4 ⟶ 5 3 4 3 2 1 3 5 3 4 5 3 0 2 5 5 1 0 ,
  5 3 0 1 5 3 1 1 3 1 1 4 ⟶ 2 2 5 1 3 5 5 4 2 4 2 3 4 5 5 5 4 2 ,
  4 4 2 1 0 0 4 0 2 1 1 4 ⟶ 3 4 1 2 5 4 0 3 4 2 4 3 3 0 ,
  2 1 1 2 0 2 0 2 3 4 1 4 ⟶ 1 5 5 5 4 4 1 5 4 5 5 4 2 0 3 0 5 4 ,
  3 2 4 0 2 3 4 1 0 0 2 4 ⟶ 0 4 2 1 5 5 2 3 2 1 5 5 2 5 1 ,
  1 4 0 2 3 1 4 3 1 1 4 4 ⟶ 5 5 4 0 3 0 3 0 2 2 2 5 0 5 4 1 ,
  1 2 1 2 0 4 3 0 4 4 4 4 ⟶ 5 4 0 3 0 5 5 2 0 5 5 5 3 3 4 3 2 0 ,
  4 4 3 2 4 3 1 1 3 3 5 4 ⟶ 4 0 5 5 5 4 2 3 3 2 5 4 2 4 5 5 4 ,
  4 1 4 3 2 0 2 0 2 1 0 5 ⟶ 5 2 4 5 5 4 5 5 2 5 5 4 5 5 1 2 3 ,
  1 1 2 3 1 0 0 1 1 5 0 5 ⟶ 5 5 5 2 2 5 5 0 5 3 0 4 5 5 2 5 1 3 ,
  1 0 4 5 1 0 1 1 4 3 1 5 ⟶ 4 3 5 5 5 4 4 3 4 3 2 0 5 5 5 4 ,
  4 3 1 3 3 1 0 3 5 3 1 5 ⟶ 2 0 3 2 1 5 5 0 5 2 4 2 2 3 ,
  3 0 5 4 1 0 4 1 1 3 2 5 ⟶ 5 5 0 5 2 5 1 5 1 3 5 0 5 3 ,
  2 4 0 0 1 0 1 4 0 1 2 5 ⟶ 2 0 5 0 5 2 5 5 3 5 5 3 2 2 5 3 5 4 ,
  0 1 1 2 5 0 0 1 1 1 4 5 ⟶ 5 5 1 4 5 1 3 2 5 3 5 5 3 4 3 ,
  2 4 0 0 5 2 3 1 1 0 5 5 ⟶ 3 5 3 4 3 0 3 5 4 5 2 3 5 3 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 ↦ ⎛     ⎞
    ⎜ 1 7 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

1 ↦ ⎛     ⎞
    ⎜ 1 9 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

2 ↦ ⎛     ⎞
    ⎜ 1 3 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

3 ↦ ⎛     ⎞
    ⎜ 1 3 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

4 ↦ ⎛     ⎞
    ⎜ 1 6 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

5 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

After renaming modulo the bijection { 1 ↦ 0, 3 ↦ 1, 0 ↦ 2, 4 ↦ 3, 2 ↦ 4, 5 ↦ 5 },
it remains to prove termination of the 3-rule system
{ 0 1 2 3 3 3 3 2 4 2 3 1 ⟶ 0 1 2 4 5 4 1 2 2 1 4 0 3 3 ,
  3 3 1 4 4 1 4 0 3 1 0 4 ⟶ 4 4 5 3 4 0 4 5 1 5 5 0 1 3 3 4 ,
  4 0 0 4 2 4 2 4 1 3 0 3 ⟶ 0 5 5 5 3 3 0 5 3 5 5 3 4 2 1 2 5 3 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 13:

0 ↦ ⎛                           ⎞
    ⎜ 1 0 1 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                           ⎠

1 ↦ ⎛                           ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 1 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                           ⎠

2 ↦ ⎛                           ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 1 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 1 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 1 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                           ⎠

3 ↦ ⎛                           ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 1 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 1 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 1 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 1 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 1 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                           ⎠

4 ↦ ⎛                           ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 1 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                           ⎠

5 ↦ ⎛                           ⎞
    ⎜ 1 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 1 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎜ 0 0 0 0 0 0 0 0 0 0 0 0 0 ⎟
    ⎝                           ⎠

After renaming modulo the bijection { 3 ↦ 0, 1 ↦ 1, 4 ↦ 2, 0 ↦ 3, 5 ↦ 4, 2 ↦ 5 },
it remains to prove termination of the 2-rule system
{ 0 0 1 2 2 1 2 3 0 1 3 2 ⟶ 2 2 4 0 2 3 2 4 1 4 4 3 1 0 0 2 ,
  2 3 3 2 5 2 5 2 1 0 3 0 ⟶ 3 4 4 4 0 0 3 4 0 4 4 0 2 5 1 5 4 0 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

1 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

2 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

3 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

4 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

5 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

After renaming modulo the bijection { 0 ↦ 0, 1 ↦ 1, 2 ↦ 2, 3 ↦ 3, 4 ↦ 4 },
it remains to prove termination of the 1-rule system
{ 0 0 1 2 2 1 2 3 0 1 3 2 ⟶ 2 2 4 0 2 3 2 4 1 4 4 3 1 0 0 2 }

The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

1 ↦ ⎛     ⎞
    ⎜ 1 1 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

2 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

3 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

4 ↦ ⎛     ⎞
    ⎜ 1 0 ⎟
    ⎜ 0 1 ⎟
    ⎝     ⎠

After renaming modulo the bijection {  },
it remains to prove termination of the 0-rule system
{ }

The system is trivially terminating.