/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 
  head : [o] --> o 
  ifPlus : [o * o * o * o] --> o 
  ifSum : [o * o * o * o] --> o 
  isempty : [o] --> o 
  le : [o * o] --> o 
  nil : [] --> o 
  plus : [o * o] --> o 
  plusIter : [o * o * o] --> o 
  s : [o] --> o 
  sum : [o] --> o 
  sumIter : [o * o] --> o 
  tail : [o] --> o 
  true : [] --> o 

  plus(X, Y) => plusIter(X, Y, 0) 
  plusIter(X, Y, Z) => ifPlus(le(X, Z), X, Y, Z) 
  ifPlus(true, X, Y, Z) => Y 
  ifPlus(false, X, Y, Z) => plusIter(X, s(Y), s(Z)) 
  le(s(X), 0) => false 
  le(0, X) => true 
  le(s(X), s(Y)) => le(X, Y) 
  sum(X) => sumIter(X, 0) 
  sumIter(X, Y) => ifSum(isempty(X), X, Y, plus(Y, head(X))) 
  ifSum(true, X, Y, Z) => Y 
  ifSum(false, X, Y, Z) => sumIter(tail(X), Z) 
  isempty(nil) => true 
  isempty(cons(X, Y)) => false 
  head(nil) => error 
  head(cons(X, Y)) => X 
  tail(nil) => nil 
  tail(cons(X, Y)) => Y 
  a => b 
  a => c