/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 
  a : [] --> o 
  ack : [o * o] --> o 
  b : [] --> o 
  c : [] --> o 
  double : [o] --> o 
  false : [] --> o 
  isZero : [o] --> o 
  p : [o] --> o 
  permute : [o * o * o] --> o 
  plus : [o * o] --> o 
  s : [o] --> o 
  true : [] --> o 

  double(X) => permute(X, X, a) 
  permute(X, Y, a) => permute(isZero(X), X, b) 
  permute(false, X, b) => permute(ack(X, X), p(X), c) 
  permute(true, X, b) => 0 
  permute(X, Y, c) => s(s(permute(Y, X, a))) 
  p(0) => 0 
  p(s(X)) => X 
  ack(0, X) => plus(X, s(0)) 
  ack(s(X), 0) => ack(X, s(0)) 
  ack(s(X), s(Y)) => ack(X, ack(s(X), Y)) 
  plus(0, X) => X 
  plus(s(X), Y) => plus(X, s(Y)) 
  plus(X, s(s(Y))) => s(plus(s(X), Y)) 
  plus(X, s(0)) => s(X) 
  plus(X, 0) => X 
  isZero(0) => true 
  isZero(s(X)) => false