/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.

  !plus : [o * o] --> o 
  !times : [o * o] --> o 
  0 : [] --> o 
  False : [] --> o 
  True : [] --> o 
  d : [o * o] --> o 
  gcd : [o * o] --> o 
  gt : [o * o] --> o 
  is!6220NzNat : [o] --> o 
  lt : [o * o] --> o 
  p : [o] --> o 
  quot : [o * o] --> o 
  s : [o] --> o 
  u!622001 : [o] --> o 
  u!622002 : [o * o] --> o 
  u!62201 : [o * o * o] --> o 
  u!622011 : [o * o * o] --> o 
  u!62202 : [o] --> o 
  u!622021 : [o * o * o] --> o 
  u!62203 : [o * o * o] --> o 
  u!622031 : [o * o * o * o] --> o 
  u!62204 : [o] --> o 

  p(s(X)) => X 
  !plus(X, 0) => X 
  !plus(s(X), s(Y)) => s(s(!plus(X, Y))) 
  !times(X, 0) => 0 
  !times(s(X), s(Y)) => s(!plus(X, !plus(Y, !times(X, Y)))) 
  gt(0, X) => False 
  gt(X, 0) => u!62204(is!6220NzNat(X)) 
  u!62204(True) => True 
  is!6220NzNat(0) => False 
  is!6220NzNat(s(X)) => True 
  gt(s(X), s(Y)) => gt(X, Y) 
  lt(X, Y) => gt(Y, X) 
  d(0, X) => X 
  d(s(X), s(Y)) => d(X, Y) 
  quot(X, Y) => u!622011(is!6220NzNat(Y), X, Y) 
  u!622011(True, X, Y) => u!62201(gt(X, Y), X, Y) 
  u!62201(True, X, Y) => s(quot(d(X, Y), Y)) 
  quot(X, X) => u!622001(is!6220NzNat(X)) 
  u!622001(True) => s(0) 
  quot(X, Y) => u!622021(is!6220NzNat(Y), Y, X) 
  u!622021(True, X, Y) => u!62202(gt(X, Y)) 
  u!62202(True) => 0 
  gcd(0, X) => 0 
  gcd(X, X) => u!622002(is!6220NzNat(X), X) 
  u!622002(True, X) => X 
  gcd(X, Y) => u!622031(is!6220NzNat(X), is!6220NzNat(Y), X, Y) 
  u!622031(True, True, X, Y) => u!62203(gt(X, Y), X, Y) 
  u!62203(True, X, Y) => gcd(d(X, Y), Y)