/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.

  !minus : [o * o] --> o 
  !plus : [o * o] --> o 
  !times : [o * o] --> o 
  0 : [] --> o 
  f : [o * o * o] --> o 
  false : [] --> o 
  half : [o] --> o 
  if : [o * o * o] --> o 
  odd : [o] --> o 
  pow : [o * o] --> o 
  s : [o] --> o 
  true : [] --> o 

  !minus(X, 0) => X 
  !minus(s(X), s(Y)) => !minus(X, Y) 
  !times(X, 0) => 0 
  !times(X, s(Y)) => !plus(!times(X, Y), X) 
  if(true, X, Y) => X 
  if(false, X, Y) => Y 
  odd(0) => false 
  odd(s(0)) => true 
  odd(s(s(X))) => odd(X) 
  half(0) => 0 
  half(s(0)) => 0 
  half(s(s(X))) => s(half(X)) 
  if(true, X, Y) => true 
  if(false, X, Y) => false 
  pow(X, Y) => f(X, Y, s(0)) 
  f(X, 0, Y) => Y 
  f(X, s(Y), Z) => if(odd(s(Y)), f(X, Y, !times(X, Z)), f(!times(X, X), half(s(Y)), Z))