/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 
  and : [o * o] --> o 
  false : [] --> o 
  greaterZero : [o] --> o 
  minus : [o * o] --> o 
  minusT : [o * o] --> o 
  neg : [o] --> o 
  negate : [o] --> o 
  notZero : [o] --> o 
  plusNat : [o * o] --> o 
  pos : [o] --> o 
  s : [o] --> o 
  true : [] --> o 
  while : [o * o * o] --> o 

  notZero(pos(s(X))) => true 
  notZero(neg(s(X))) => true 
  notZero(neg(0)) => false 
  notZero(pos(0)) => false 
  greaterZero(pos(s(X))) => true 
  greaterZero(pos(0)) => false 
  greaterZero(neg(X)) => false 
  and(false, false) => false 
  and(false, true) => false 
  and(true, false) => false 
  and(true, true) => true 
  minusT(0, X) => neg(X) 
  minusT(X, 0) => pos(X) 
  minusT(s(X), s(Y)) => minusT(X, Y) 
  plusNat(0, X) => X 
  plusNat(s(X), Y) => plusNat(X, s(Y)) 
  negate(pos(X)) => neg(X) 
  negate(neg(X)) => pos(X) 
  minus(pos(X), pos(Y)) => minusT(X, Y) 
  minus(neg(X), neg(Y)) => negate(minusT(X, Y)) 
  minus(pos(X), neg(Y)) => pos(plusNat(X, Y)) 
  minus(neg(X), pos(Y)) => neg(plusNat(X, Y)) 
  while(true, X, Y) => while(and(notZero(Y), greaterZero(X)), minus(X, Y), Y)