/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 
  b : [] --> o 
  c : [] --> o 
  cons : [o * o] --> o 
  error : [] --> o 
  false : [] --> o 
  ge : [o * o] --> o 
  head : [o] --> o 
  ifProd : [o * o * o] --> o 
  ifTimes : [o * o * o * o * o] --> o 
  isempty : [o] --> o 
  nil : [] --> o 
  plus : [o * o] --> o 
  prod : [o] --> o 
  prodIter : [o * o] --> o 
  s : [o] --> o 
  tail : [o] --> o 
  times : [o * o] --> o 
  timesIter : [o * o * o * o] --> o 
  true : [] --> o 

  prod(X) => prodIter(X, s(0)) 
  prodIter(X, Y) => ifProd(isempty(X), X, Y) 
  ifProd(true, X, Y) => Y 
  ifProd(false, X, Y) => prodIter(tail(X), times(Y, head(X))) 
  plus(0, X) => X 
  plus(s(X), Y) => s(plus(X, Y)) 
  times(X, Y) => timesIter(X, Y, 0, 0) 
  timesIter(X, Y, Z, U) => ifTimes(ge(U, X), X, Y, Z, U) 
  ifTimes(true, X, Y, Z, U) => Z 
  ifTimes(false, X, Y, Z, U) => timesIter(X, Y, plus(Y, Z), s(U)) 
  isempty(nil) => true 
  isempty(cons(X, Y)) => false 
  head(nil) => error 
  head(cons(X, Y)) => X 
  tail(nil) => nil 
  tail(cons(X, Y)) => Y 
  ge(X, 0) => true 
  ge(0, s(X)) => false 
  ge(s(X), s(Y)) => ge(X, Y) 
  a => b 
  a => c