/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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 
  1 : [] --> o 
  c : [] --> o 
  d : [] --> o 
  f0 : [o * o * o] --> o 
  f1 : [o * o * o] --> o 
  f2 : [o * o * o] --> o 
  false : [] --> o 
  ge : [o * o] --> o 
  ifPlus : [o * o * o] --> o 
  ifTimes : [o * o * o * o * o] --> o 
  inc : [o] --> o 
  isZero : [o] --> o 
  p : [o] --> o 
  plus : [o * o] --> o 
  s : [o] --> o 
  times : [o * o] --> o 
  timesIter : [o * o * o * o] --> o 
  true : [] --> o 

  plus(X, Y) => ifPlus(isZero(X), X, inc(Y)) 
  ifPlus(true, X, Y) => p(Y) 
  ifPlus(false, X, Y) => plus(p(X), Y) 
  times(X, Y) => timesIter(0, X, Y, 0) 
  timesIter(X, Y, Z, U) => ifTimes(ge(X, Y), X, Y, Z, U) 
  ifTimes(true, X, Y, Z, U) => U 
  ifTimes(false, X, Y, Z, U) => timesIter(inc(X), Y, Z, plus(U, Z)) 
  isZero(0) => true 
  isZero(s(0)) => false 
  isZero(s(s(X))) => isZero(s(X)) 
  inc(0) => s(0) 
  inc(s(X)) => s(inc(X)) 
  inc(X) => s(X) 
  p(0) => 0 
  p(s(X)) => X 
  p(s(s(X))) => s(p(s(X))) 
  ge(X, 0) => true 
  ge(0, s(X)) => false 
  ge(s(X), s(Y)) => ge(X, Y) 
  f0(0, X, Y) => f1(Y, X, Y) 
  f1(X, Y, Z) => f2(X, Y, Z) 
  f2(X, 1, Y) => f0(X, Y, Y) 
  f0(X, Y, Z) => d 
  f1(X, Y, Z) => c