/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!6220!6220diff : [o * o] --> o 
  a!6220!6220if : [o * o * o] --> o 
  a!6220!6220leq : [o * o] --> o 
  a!6220!6220p : [o] --> o 
  diff : [o * o] --> o 
  false : [] --> o 
  if : [o * o * o] --> o 
  leq : [o * o] --> o 
  mark : [o] --> o 
  p : [o] --> o 
  s : [o] --> o 
  true : [] --> o 

  a!6220!6220p(0) => 0 
  a!6220!6220p(s(X)) => mark(X) 
  a!6220!6220leq(0, X) => true 
  a!6220!6220leq(s(X), 0) => false 
  a!6220!6220leq(s(X), s(Y)) => a!6220!6220leq(mark(X), mark(Y)) 
  a!6220!6220if(true, X, Y) => mark(X) 
  a!6220!6220if(false, X, Y) => mark(Y) 
  a!6220!6220diff(X, Y) => a!6220!6220if(a!6220!6220leq(mark(X), mark(Y)), 0, s(diff(p(X), Y))) 
  mark(p(X)) => a!6220!6220p(mark(X)) 
  mark(leq(X, Y)) => a!6220!6220leq(mark(X), mark(Y)) 
  mark(if(X, Y, Z)) => a!6220!6220if(mark(X), Y, Z) 
  mark(diff(X, Y)) => a!6220!6220diff(mark(X), mark(Y)) 
  mark(0) => 0 
  mark(s(X)) => s(mark(X)) 
  mark(true) => true 
  mark(false) => false 
  a!6220!6220p(X) => p(X) 
  a!6220!6220leq(X, Y) => leq(X, Y) 
  a!6220!6220if(X, Y, Z) => if(X, Y, Z) 
  a!6220!6220diff(X, Y) => diff(X, Y)