YES

After renaming modulo { 0->0, 1->1 }, 
it remains to prove termination of the 32-rule system
{ 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 1 0 1 1 1 0 -> 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 ,
  0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 1 0 1 1 1 1 -> 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 1 ,
  0 0 1 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 -> 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 ,
  0 0 1 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 -> 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 ,
  0 0 1 1 0 0 1 0 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 -> 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 ,
  0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 1 1 -> 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 0 0 1 0 1 0 0 1 1 0 1 ,
  0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 -> 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 ,
  0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 1 1 0 1 0 0 -> 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 1 0 0 ,
  0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 1 0 0 1 -> 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 ,
  0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 1 0 0 1 -> 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 0 1 1 ,
  0 1 0 0 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 0 0 1 0 1 1 -> 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 ,
  0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1 0 0 0 1 0 0 0 0 -> 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 ,
  0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1 0 0 0 1 0 0 0 0 -> 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 ,
  0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 -> 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 ,
  0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 0 -> 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 ,
  0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 -> 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 1 1 0 0 1 1 1 1 1 ,
  0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 -> 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 0 1 0 0 0 1 ,
  0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 1 1 -> 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 ,
  0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 0 1 1 0 1 -> 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 0 1 1 ,
  0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 0 1 1 1 0 -> 0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 0 1 0 0 0 1 ,
  0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 0 -> 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 ,
  0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 0 -> 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 ,
  0 1 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 0 0 0 1 1 0 0 -> 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 ,
  0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 1 -> 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 ,
  0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 0 0 -> 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 ,
  0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 0 0 -> 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 ,
  0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 0 1 -> 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 ,
  0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 0 1 -> 1 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 0 1 1 1 0 1 0 1 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 0 1 1 ,
  0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 0 1 -> 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 ,
  0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 1 0 1 0 -> 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 ,
  0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 -> 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 ,
  0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 1 1 0 0 0 0 -> 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 }


Applying sparse 2-tiling [Hofbauer/Geser/Waldmann, FSCD 2019].

After renaming modulo { (0,0)->0, (0,1)->1, (1,0)->2, (1,1)->3, (0,3)->4, (2,0)->5, (1,3)->6, (2,1)->7 },
it remains to prove termination of the 288-rule system
{ 0 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 0 -> 0 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 0 ,
  0 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 1 -> 0 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 1 ,
  0 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 4 -> 0 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 4 ,
  2 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 0 -> 2 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 0 ,
  2 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 1 -> 2 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 1 ,
  2 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 4 -> 2 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 4 ,
  5 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 0 -> 5 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 0 ,
  5 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 1 -> 5 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 1 ,
  5 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 4 -> 5 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 4 ,
  0 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 3 2 -> 0 0 0 0 0 0 0 1 3 3 3 3 2 1 2 0 1 3 2 1 2 0 0 1 2 0 1 3 3 2 0 0 1 2 1 2 1 3 2 0 1 2 0 0 1 2 0 1 3 2 0 1 3 2 1 2 0 1 2 0 1 3 2 0 1 2 0 0 0 1 3 2 0 0 0 0 1 2 1 3 2 1 2 ,
  0 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 3 3 -> 0 0 0 0 0 0 0 1 3 3 3 3 2 1 2 0 1 3 2 1 2 0 0 1 2 0 1 3 3 2 0 0 1 2 1 2 1 3 2 0 1 2 0 0 1 2 0 1 3 2 0 1 3 2 1 2 0 1 2 0 1 3 2 0 1 2 0 0 0 1 3 2 0 0 0 0 1 2 1 3 2 1 3 ,
  0 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 3 6 -> 0 0 0 0 0 0 0 1 3 3 3 3 2 1 2 0 1 3 2 1 2 0 0 1 2 0 1 3 3 2 0 0 1 2 1 2 1 3 2 0 1 2 0 0 1 2 0 1 3 2 0 1 3 2 1 2 0 1 2 0 1 3 2 0 1 2 0 0 0 1 3 2 0 0 0 0 1 2 1 3 2 1 6 ,
  2 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 3 2 -> 2 0 0 0 0 0 0 1 3 3 3 3 2 1 2 0 1 3 2 1 2 0 0 1 2 0 1 3 3 2 0 0 1 2 1 2 1 3 2 0 1 2 0 0 1 2 0 1 3 2 0 1 3 2 1 2 0 1 2 0 1 3 2 0 1 2 0 0 0 1 3 2 0 0 0 0 1 2 1 3 2 1 2 ,
  2 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 3 3 -> 2 0 0 0 0 0 0 1 3 3 3 3 2 1 2 0 1 3 2 1 2 0 0 1 2 0 1 3 3 2 0 0 1 2 1 2 1 3 2 0 1 2 0 0 1 2 0 1 3 2 0 1 3 2 1 2 0 1 2 0 1 3 2 0 1 2 0 0 0 1 3 2 0 0 0 0 1 2 1 3 2 1 3 ,
  2 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 3 6 -> 2 0 0 0 0 0 0 1 3 3 3 3 2 1 2 0 1 3 2 1 2 0 0 1 2 0 1 3 3 2 0 0 1 2 1 2 1 3 2 0 1 2 0 0 1 2 0 1 3 2 0 1 3 2 1 2 0 1 2 0 1 3 2 0 1 2 0 0 0 1 3 2 0 0 0 0 1 2 1 3 2 1 6 ,
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  2 1 2 0 1 3 2 1 2 1 3 3 3 3 2 1 2 1 2 0 0 0 0 0 0 1 2 1 2 0 1 2 1 3 2 1 2 1 3 2 0 1 3 2 1 2 0 1 2 0 1 2 0 1 2 1 3 3 3 2 1 2 1 3 3 3 3 2 1 2 1 3 3 3 2 1 3 2 0 0 0 4 -> 3 2 1 3 3 3 3 2 0 1 2 0 0 1 2 1 3 3 2 1 2 1 3 3 2 0 0 1 2 1 3 2 1 3 2 1 2 0 1 3 2 1 2 1 2 0 0 1 3 2 0 0 0 1 2 1 2 0 0 0 0 0 1 3 3 3 2 1 3 2 1 2 0 0 0 0 0 0 0 1 2 1 2 0 4 ,
  5 1 2 0 1 3 2 1 2 1 3 3 3 3 2 1 2 1 2 0 0 0 0 0 0 1 2 1 2 0 1 2 1 3 2 1 2 1 3 2 0 1 3 2 1 2 0 1 2 0 1 2 0 1 2 1 3 3 3 2 1 2 1 3 3 3 3 2 1 2 1 3 3 3 2 1 3 2 0 0 0 0 -> 7 2 1 3 3 3 3 2 0 1 2 0 0 1 2 1 3 3 2 1 2 1 3 3 2 0 0 1 2 1 3 2 1 3 2 1 2 0 1 3 2 1 2 1 2 0 0 1 3 2 0 0 0 1 2 1 2 0 0 0 0 0 1 3 3 3 2 1 3 2 1 2 0 0 0 0 0 0 0 1 2 1 2 0 0 ,
  5 1 2 0 1 3 2 1 2 1 3 3 3 3 2 1 2 1 2 0 0 0 0 0 0 1 2 1 2 0 1 2 1 3 2 1 2 1 3 2 0 1 3 2 1 2 0 1 2 0 1 2 0 1 2 1 3 3 3 2 1 2 1 3 3 3 3 2 1 2 1 3 3 3 2 1 3 2 0 0 0 1 -> 7 2 1 3 3 3 3 2 0 1 2 0 0 1 2 1 3 3 2 1 2 1 3 3 2 0 0 1 2 1 3 2 1 3 2 1 2 0 1 3 2 1 2 1 2 0 0 1 3 2 0 0 0 1 2 1 2 0 0 0 0 0 1 3 3 3 2 1 3 2 1 2 0 0 0 0 0 0 0 1 2 1 2 0 1 ,
  5 1 2 0 1 3 2 1 2 1 3 3 3 3 2 1 2 1 2 0 0 0 0 0 0 1 2 1 2 0 1 2 1 3 2 1 2 1 3 2 0 1 3 2 1 2 0 1 2 0 1 2 0 1 2 1 3 3 3 2 1 2 1 3 3 3 3 2 1 2 1 3 3 3 2 1 3 2 0 0 0 4 -> 7 2 1 3 3 3 3 2 0 1 2 0 0 1 2 1 3 3 2 1 2 1 3 3 2 0 0 1 2 1 3 2 1 3 2 1 2 0 1 3 2 1 2 1 2 0 0 1 3 2 0 0 0 1 2 1 2 0 0 0 0 0 1 3 3 3 2 1 3 2 1 2 0 0 0 0 0 0 0 1 2 1 2 0 4 }


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

0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 12-rule system
{ 0 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 0 -> 0 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 0 ,
  0 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 1 -> 0 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 1 ,
  0 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 4 -> 0 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 4 ,
  2 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 0 -> 2 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 0 ,
  2 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 1 -> 2 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 1 ,
  2 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 4 -> 2 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 4 ,
  5 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 0 -> 5 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 0 ,
  5 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 1 -> 5 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 1 ,
  5 0 1 2 1 3 2 0 0 0 1 2 1 3 2 1 2 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 2 0 0 0 0 0 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 3 2 0 0 1 2 0 1 3 2 1 3 3 2 4 -> 5 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 3 2 0 0 0 1 3 2 0 1 3 2 0 1 2 1 2 0 1 2 0 4 ,
  0 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 2 0 0 0 0 1 3 2 1 3 3 3 2 0 1 3 3 2 0 -> 0 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 2 0 0 0 0 1 3 2 1 3 3 3 2 0 1 2 0 0 1 2 ,
  2 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 2 0 0 0 0 1 3 2 1 3 3 3 2 0 1 3 3 2 0 -> 2 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 2 0 0 0 0 1 3 2 1 3 3 3 2 0 1 2 0 0 1 2 ,
  5 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 2 0 0 0 0 1 3 2 1 3 3 3 2 0 1 3 3 2 0 -> 5 1 2 0 1 3 2 0 1 3 2 0 0 1 2 0 0 1 2 0 1 2 1 3 3 3 2 1 2 0 1 3 2 0 0 1 2 0 1 3 3 2 0 0 0 1 2 1 3 2 1 3 2 1 3 2 1 2 0 1 2 0 1 2 0 0 0 0 1 3 2 1 3 3 3 2 0 1 2 0 0 1 2 }


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

0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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

The system is trivially terminating.