/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 
  divides : [o * o] --> o 
  eq : [o * o] --> o 
  false : [] --> o 
  if : [o * o * o] --> o 
  p : [o] --> o 
  plus : [o * o] --> o 
  pr : [o * o] --> o 
  prime : [o] --> o 
  quot : [o * o * o] --> o 
  s : [o] --> o 
  times : [o * o] --> o 
  true : [] --> o 

  p(0) => 0 
  p(s(X)) => X 
  plus(X, 0) => X 
  plus(0, X) => X 
  plus(s(X), Y) => s(plus(X, Y)) 
  plus(s(X), Y) => s(plus(p(s(X)), Y)) 
  plus(X, s(Y)) => s(plus(X, p(s(Y)))) 
  times(0, X) => 0 
  times(s(0), X) => X 
  times(s(X), Y) => plus(Y, times(X, Y)) 
  div(0, X) => 0 
  div(X, Y) => quot(X, Y, Y) 
  quot(0, s(X), Y) => 0 
  quot(s(X), s(Y), Z) => quot(X, Y, Z) 
  quot(X, 0, s(Y)) => s(div(X, s(Y))) 
  div(div(X, Y), Z) => div(X, times(Y, Z)) 
  eq(0, 0) => true 
  eq(s(X), 0) => false 
  eq(0, s(X)) => false 
  eq(s(X), s(Y)) => eq(X, Y) 
  divides(X, Y) => eq(Y, times(div(Y, X), X)) 
  prime(s(s(X))) => pr(s(s(X)), s(X)) 
  pr(X, s(0)) => true 
  pr(X, s(s(Y))) => if(divides(s(s(Y)), X), X, s(Y)) 
  if(true, X, Y) => false 
  if(false, X, Y) => pr(X, Y)