/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 
  f : [] --> o 
  false : [] --> o 
  g : [] --> o 
  h : [] --> o 
  half : [o] --> o 
  if : [o * o * o * o] --> o 
  inc : [o] --> o 
  le : [o * o] --> o 
  logIter : [o * o] --> o 
  logZeroError : [] --> o 
  logarithm : [o] --> o 
  s : [o] --> o 
  true : [] --> o 

  half(0) => 0 
  half(s(0)) => 0 
  half(s(s(X))) => s(half(X)) 
  le(0, X) => true 
  le(s(X), 0) => false 
  le(s(X), s(Y)) => le(X, Y) 
  inc(s(X)) => s(inc(X)) 
  inc(0) => s(0) 
  logarithm(X) => logIter(X, 0) 
  logIter(X, Y) => if(le(s(0), X), le(s(s(0)), X), half(X), inc(Y)) 
  if(false, X, Y, Z) => logZeroError 
  if(true, false, X, s(Y)) => Y 
  if(true, true, X, Y) => logIter(X, Y) 
  f => g 
  f => h