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


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MAYBE
We consider the system theBenchmark.

We are asked to determine termination of the following first-order TRS.

  0 : [] --> o 
  div : [o * o * o] --> o 
  div!6220by!6220zero : [] --> o 
  false : [] --> o 
  ge : [o * o] --> o 
  id!6220inc : [o] --> o 
  if : [o * o * o * o * o] --> o 
  minus : [o * o] --> o 
  quot : [o * o] --> o 
  s : [o] --> o 
  true : [] --> o 

  ge(X, 0) => true 
  ge(0, s(X)) => false 
  ge(s(X), s(Y)) => ge(X, Y) 
  minus(X, 0) => X 
  minus(0, X) => 0 
  minus(s(X), s(Y)) => minus(X, Y) 
  id!6220inc(X) => X 
  id!6220inc(X) => s(X) 
  quot(X, Y) => div(X, Y, 0) 
  div(X, Y, Z) => if(ge(Y, s(0)), ge(X, Y), X, Y, Z) 
  if(false, X, Y, Z, U) => div!6220by!6220zero 
  if(true, false, X, Y, Z) => Z 
  if(true, true, X, Y, Z) => div(minus(X, Y), Y, id!6220inc(Z))