/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 
  false : [] --> o 
  if : [o * o * o * o] --> o 
  if2 : [o * o * o] --> o 
  inc : [o] --> o 
  le : [o * o] --> o 
  log : [o] --> o 
  log!6220undefined : [] --> o 
  log2 : [o * o] --> o 
  minus : [o * o] --> o 
  quot : [o * o] --> o 
  s : [o] --> o 
  true : [] --> o 

  le(0, X) => true 
  le(s(X), 0) => false 
  le(s(X), s(Y)) => le(X, Y) 
  inc(0) => 0 
  inc(s(X)) => s(inc(X)) 
  minus(0, X) => 0 
  minus(X, 0) => X 
  minus(s(X), s(Y)) => minus(X, Y) 
  quot(0, s(X)) => 0 
  quot(s(X), s(Y)) => s(quot(minus(X, Y), s(Y))) 
  log(X) => log2(X, 0) 
  log2(X, Y) => if(le(X, 0), le(X, s(0)), X, inc(Y)) 
  if(true, X, Y, Z) => log!6220undefined 
  if(false, X, Y, Z) => if2(X, Y, Z) 
  if2(true, X, s(Y)) => Y 
  if2(false, X, Y) => log2(quot(X, s(s(0))), Y)