/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 
  add : [] --> o 
  app : [] --> o 
  app!450 : [o * o] --> o 
  eq : [] --> o 
  false : [] --> o 
  filter : [] --> o 
  filter2 : [] --> o 
  if!6220min : [] --> o 
  if!6220minsort : [] --> o 
  if!6220rm : [] --> o 
  le : [] --> o 
  map : [] --> o 
  min : [] --> o 
  minsort : [] --> o 
  nil : [] --> o 
  rm : [] --> o 
  s : [] --> o 
  true : [] --> o 

  app!450(app!450(eq, 0), 0) => true 
  app!450(app!450(eq, 0), app!450(s, X)) => false 
  app!450(app!450(eq, app!450(s, X)), 0) => false 
  app!450(app!450(eq, app!450(s, X)), app!450(s, Y)) => app!450(app!450(eq, X), Y) 
  app!450(app!450(le, 0), X) => true 
  app!450(app!450(le, app!450(s, X)), 0) => false 
  app!450(app!450(le, app!450(s, X)), app!450(s, Y)) => app!450(app!450(le, X), Y) 
  app!450(app!450(app, nil), X) => X 
  app!450(app!450(app, app!450(app!450(add, X), Y)), Z) => app!450(app!450(add, X), app!450(app!450(app, Y), Z)) 
  app!450(min, app!450(app!450(add, X), nil)) => X 
  app!450(min, app!450(app!450(add, X), app!450(app!450(add, Y), Z))) => app!450(app!450(if!6220min, app!450(app!450(le, X), Y)), app!450(app!450(add, X), app!450(app!450(add, Y), Z))) 
  app!450(app!450(if!6220min, true), app!450(app!450(add, X), app!450(app!450(add, Y), Z))) => app!450(min, app!450(app!450(add, X), Z)) 
  app!450(app!450(if!6220min, false), app!450(app!450(add, X), app!450(app!450(add, Y), Z))) => app!450(min, app!450(app!450(add, Y), Z)) 
  app!450(app!450(rm, X), nil) => nil 
  app!450(app!450(rm, X), app!450(app!450(add, Y), Z)) => app!450(app!450(app!450(if!6220rm, app!450(app!450(eq, X), Y)), X), app!450(app!450(add, Y), Z)) 
  app!450(app!450(app!450(if!6220rm, true), X), app!450(app!450(add, Y), Z)) => app!450(app!450(rm, X), Z) 
  app!450(app!450(app!450(if!6220rm, false), X), app!450(app!450(add, Y), Z)) => app!450(app!450(add, Y), app!450(app!450(rm, X), Z)) 
  app!450(app!450(minsort, nil), nil) => nil 
  app!450(app!450(minsort, app!450(app!450(add, X), Y)), Z) => app!450(app!450(app!450(if!6220minsort, app!450(app!450(eq, X), app!450(min, app!450(app!450(add, X), Y)))), app!450(app!450(add, X), Y)), Z) 
  app!450(app!450(app!450(if!6220minsort, true), app!450(app!450(add, X), Y)), Z) => app!450(app!450(add, X), app!450(app!450(minsort, app!450(app!450(app, app!450(app!450(rm, X), Y)), Z)), nil)) 
  app!450(app!450(app!450(if!6220minsort, false), app!450(app!450(add, X), Y)), Z) => app!450(app!450(minsort, Y), app!450(app!450(add, X), Z)) 
  app!450(app!450(map, X), nil) => nil 
  app!450(app!450(map, X), app!450(app!450(add, Y), Z)) => app!450(app!450(add, app!450(X, Y)), app!450(app!450(map, X), Z)) 
  app!450(app!450(filter, X), nil) => nil 
  app!450(app!450(filter, X), app!450(app!450(add, Y), Z)) => app!450(app!450(app!450(app!450(filter2, app!450(X, Y)), X), Y), Z) 
  app!450(app!450(app!450(app!450(filter2, true), X), Y), Z) => app!450(app!450(add, Y), app!450(app!450(filter, X), Z)) 
  app!450(app!450(app!450(app!450(filter2, false), X), Y), Z) => app!450(app!450(filter, X), Z)