/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 
  ack : [o * o] --> o 
  div : [o * o] --> o 
  false : [] --> 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(minus(X, Y), Z) => minus(X, plus(Y, Z)) 
  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)) 
  plus(s(X), Y) => s(plus(Y, X)) 
  zero(s(X)) => false 
  zero(0) => true 
  p(s(X)) => X 
  p(0) => 0 
  div(X, Y) => quot(X, Y, 0) 
  quot(s(X), s(Y), Z) => quot(minus(p(ack(0, X)), Y), s(Y), s(Z)) 
  quot(0, s(X), Y) => Y 
  ack(0, X) => s(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))