/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 
  false : [] --> o 
  if : [o * o * o * o] --> o 
  minus : [o * o] --> o 
  p : [o] --> o 
  plus : [o * o] --> o 
  quot : [o * o * o] --> o 
  s : [o] --> o 
  true : [] --> o 
  zero : [o] --> o 

  minus(0, X) => 0 
  minus(X, 0) => X 
  minus(s(X), s(Y)) => minus(X, Y) 
  plus(0, X) => X 
  plus(s(X), Y) => plus(X, s(Y)) 
  zero(s(X)) => false 
  zero(0) => true 
  p(s(X)) => X 
  div(X, Y) => quot(X, Y, 0) 
  quot(X, Y, Z) => if(zero(X), X, Y, plus(Z, s(0))) 
  if(true, X, Y, Z) => p(Z) 
  if(false, X, s(Y), Z) => quot(minus(X, s(Y)), s(Y), Z)