/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 
  c : [] --> o 
  d : [] --> o 
  div : [o * o] --> o 
  div2 : [o * o * o] --> o 
  divZeroError : [] --> o 
  false : [] --> o 
  if1 : [o * o * o * o * o * o] --> o 
  if2 : [o * o * o * o * o] --> o 
  ifPlus : [o * o * o * o] --> o 
  inc : [o] --> o 
  le : [o * o] --> o 
  minus : [o * o] --> o 
  plus : [o * o] --> o 
  plusIter : [o * o * o] --> o 
  s : [o] --> o 
  true : [] --> o 

  div(X, Y) => div2(X, Y, 0) 
  div2(X, Y, Z) => if1(le(Y, 0), le(Y, X), X, Y, plus(Z, 0), inc(Z)) 
  if1(true, X, Y, Z, U, V) => divZeroError 
  if1(false, X, Y, Z, U, V) => if2(X, Y, Z, U, V) 
  if2(true, X, Y, Z, U) => div2(minus(X, Y), Y, U) 
  if2(false, X, Y, Z, U) => Z 
  inc(0) => 0 
  inc(s(X)) => s(inc(X)) 
  le(s(X), 0) => false 
  le(0, X) => true 
  le(s(X), s(Y)) => le(X, Y) 
  minus(X, 0) => X 
  minus(0, X) => 0 
  minus(s(X), s(Y)) => minus(X, Y) 
  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)) 
  a => c 
  a => d