/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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 
  active : [o] --> o 
  diff : [o * o] --> o 
  false : [] --> o 
  if : [o * o * o] --> o 
  leq : [o * o] --> o 
  mark : [o] --> o 
  ok : [o] --> o 
  p : [o] --> o 
  proper : [o] --> o 
  s : [o] --> o 
  top : [o] --> o 
  true : [] --> o 

  active(p(0)) => mark(0) 
  active(p(s(X))) => mark(X) 
  active(leq(0, X)) => mark(true) 
  active(leq(s(X), 0)) => mark(false) 
  active(leq(s(X), s(Y))) => mark(leq(X, Y)) 
  active(if(true, X, Y)) => mark(X) 
  active(if(false, X, Y)) => mark(Y) 
  active(diff(X, Y)) => mark(if(leq(X, Y), 0, s(diff(p(X), Y)))) 
  active(p(X)) => p(active(X)) 
  active(s(X)) => s(active(X)) 
  active(leq(X, Y)) => leq(active(X), Y) 
  active(leq(X, Y)) => leq(X, active(Y)) 
  active(if(X, Y, Z)) => if(active(X), Y, Z) 
  active(diff(X, Y)) => diff(active(X), Y) 
  active(diff(X, Y)) => diff(X, active(Y)) 
  p(mark(X)) => mark(p(X)) 
  s(mark(X)) => mark(s(X)) 
  leq(mark(X), Y) => mark(leq(X, Y)) 
  leq(X, mark(Y)) => mark(leq(X, Y)) 
  if(mark(X), Y, Z) => mark(if(X, Y, Z)) 
  diff(mark(X), Y) => mark(diff(X, Y)) 
  diff(X, mark(Y)) => mark(diff(X, Y)) 
  proper(p(X)) => p(proper(X)) 
  proper(0) => ok(0) 
  proper(s(X)) => s(proper(X)) 
  proper(leq(X, Y)) => leq(proper(X), proper(Y)) 
  proper(true) => ok(true) 
  proper(false) => ok(false) 
  proper(if(X, Y, Z)) => if(proper(X), proper(Y), proper(Z)) 
  proper(diff(X, Y)) => diff(proper(X), proper(Y)) 
  p(ok(X)) => ok(p(X)) 
  s(ok(X)) => ok(s(X)) 
  leq(ok(X), ok(Y)) => ok(leq(X, Y)) 
  if(ok(X), ok(Y), ok(Z)) => ok(if(X, Y, Z)) 
  diff(ok(X), ok(Y)) => ok(diff(X, Y)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(X))