/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


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 
  p : [o] --> o 
  s : [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)))) 
  mark(p(X)) => active(p(mark(X))) 
  mark(0) => active(0) 
  mark(s(X)) => active(s(mark(X))) 
  mark(leq(X, Y)) => active(leq(mark(X), mark(Y))) 
  mark(true) => active(true) 
  mark(false) => active(false) 
  mark(if(X, Y, Z)) => active(if(mark(X), Y, Z)) 
  mark(diff(X, Y)) => active(diff(mark(X), mark(Y))) 
  p(mark(X)) => p(X) 
  p(active(X)) => p(X) 
  s(mark(X)) => s(X) 
  s(active(X)) => s(X) 
  leq(mark(X), Y) => leq(X, Y) 
  leq(X, mark(Y)) => leq(X, Y) 
  leq(active(X), Y) => leq(X, Y) 
  leq(X, active(Y)) => leq(X, Y) 
  if(mark(X), Y, Z) => if(X, Y, Z) 
  if(X, mark(Y), Z) => if(X, Y, Z) 
  if(X, Y, mark(Z)) => if(X, Y, Z) 
  if(active(X), Y, Z) => if(X, Y, Z) 
  if(X, active(Y), Z) => if(X, Y, Z) 
  if(X, Y, active(Z)) => if(X, Y, Z) 
  diff(mark(X), Y) => diff(X, Y) 
  diff(X, mark(Y)) => diff(X, Y) 
  diff(active(X), Y) => diff(X, Y) 
  diff(X, active(Y)) => diff(X, Y)