/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 
  a : [] --> o 
  b : [] --> o 
  c : [] --> o 
  div : [o * o * o] --> o 
  divisible : [o * o] --> o 
  false : [] --> o 
  ge : [o * o] --> o 
  if : [o * o * o * o * o] --> o 
  if2 : [o * o * o * o * o] --> o 
  ifTimes : [o * o * o] --> o 
  lcm : [o * o] --> o 
  lcmIter : [o * o * o * o] --> o 
  or : [o * o] --> o 
  p : [o] --> o 
  plus : [o * o] --> o 
  s : [o] --> o 
  times : [o * o] --> o 
  true : [] --> o 

  lcm(X, Y) => lcmIter(X, Y, 0, times(X, Y)) 
  lcmIter(X, Y, Z, U) => if(or(ge(0, X), ge(Z, U)), X, Y, Z, U) 
  if(true, X, Y, Z, U) => Z 
  if(false, X, Y, Z, U) => if2(divisible(Z, Y), X, Y, Z, U) 
  if2(true, X, Y, Z, U) => Z 
  if2(false, X, Y, Z, U) => lcmIter(X, Y, plus(X, Z), U) 
  plus(0, X) => X 
  plus(s(X), Y) => s(plus(X, Y)) 
  times(X, Y) => ifTimes(ge(0, X), X, Y) 
  ifTimes(true, X, Y) => 0 
  ifTimes(false, X, Y) => plus(Y, times(Y, p(X))) 
  p(s(X)) => X 
  p(0) => s(s(0)) 
  ge(X, 0) => true 
  ge(0, s(X)) => false 
  ge(s(X), s(Y)) => ge(X, Y) 
  or(true, X) => true 
  or(false, X) => X 
  divisible(0, s(X)) => true 
  divisible(s(X), s(Y)) => div(s(X), s(Y), s(Y)) 
  div(X, Y, 0) => divisible(X, Y) 
  div(0, X, s(Y)) => false 
  div(s(X), Y, s(Z)) => div(X, Y, Z) 
  a => b 
  a => c