/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 
  cons : [o * o] --> o 
  gcd : [o * o] --> o 
  max : [o * o] --> o 
  min : [o * o] --> o 
  minus : [o * o] --> o 
  s : [o] --> o 
  transform : [o] --> o 

  min(X, 0) => 0 
  min(0, X) => 0 
  min(s(X), s(Y)) => s(min(X, Y)) 
  max(X, 0) => X 
  max(0, X) => X 
  max(s(X), s(Y)) => s(max(X, Y)) 
  minus(X, 0) => X 
  minus(s(X), s(Y)) => s(minus(X, Y)) 
  gcd(s(X), s(Y)) => gcd(minus(max(X, Y), min(X, transform(Y))), s(min(X, Y))) 
  transform(X) => s(s(X)) 
  transform(cons(X, Y)) => cons(cons(X, X), X) 
  transform(cons(X, Y)) => Y 
  transform(s(X)) => s(s(transform(X))) 
  cons(X, Y) => Y 
  cons(X, cons(Y, s(Z))) => cons(Y, X) 
  cons(cons(X, Y), s(Z)) => transform(X)