/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 
  eq : [o * o] --> o 
  f : [] --> o 
  false : [] --> o 
  g : [] --> o 
  h : [] --> o 
  ifPlus : [o * o * o * o] --> o 
  ifTimes : [o * o * o * o * o] --> o 
  inc : [o] --> o 
  minus : [o * o] --> o 
  plus : [o * o] --> o 
  s : [o] --> o 
  times : [o * o] --> o 
  timesIter : [o * o * o] --> o 
  true : [] --> o 

  inc(s(X)) => s(inc(X)) 
  inc(0) => s(0) 
  plus(X, Y) => ifPlus(eq(X, 0), minus(X, s(0)), X, inc(X)) 
  ifPlus(false, X, Y, Z) => plus(X, Z) 
  ifPlus(true, X, Y, Z) => Y 
  minus(s(X), s(Y)) => minus(X, Y) 
  minus(0, X) => 0 
  minus(X, 0) => X 
  minus(X, X) => 0 
  eq(s(X), s(Y)) => eq(X, Y) 
  eq(0, s(X)) => false 
  eq(s(X), 0) => false 
  eq(0, 0) => true 
  eq(X, X) => true 
  times(X, Y) => timesIter(X, Y, 0) 
  timesIter(X, Y, Z) => ifTimes(eq(X, 0), minus(X, s(0)), Y, Z, plus(Y, Z)) 
  ifTimes(true, X, Y, Z, U) => Z 
  ifTimes(false, X, Y, Z, U) => timesIter(X, Y, U) 
  f => g 
  f => h