/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 
  app : [o * o] --> o 
  cons : [] --> o 
  del : [] --> o 
  eq : [] --> o 
  false : [] --> o 
  filter : [] --> o 
  filter2 : [] --> o 
  if : [] --> o 
  le : [] --> o 
  map : [] --> o 
  min : [] --> o 
  minsort : [] --> o 
  nil : [] --> o 
  s : [] --> o 
  true : [] --> o 

  app(app(le, 0), X) => true 
  app(app(le, app(s, X)), 0) => false 
  app(app(le, app(s, X)), app(s, Y)) => app(app(le, X), Y) 
  app(app(eq, 0), 0) => true 
  app(app(eq, 0), app(s, X)) => false 
  app(app(eq, app(s, X)), 0) => false 
  app(app(eq, app(s, X)), app(s, Y)) => app(app(eq, X), Y) 
  app(app(app(if, true), X), Y) => X 
  app(app(app(if, false), X), Y) => Y 
  app(minsort, nil) => nil 
  app(minsort, app(app(cons, X), Y)) => app(app(cons, app(app(min, X), Y)), app(minsort, app(app(del, app(app(min, X), Y)), app(app(cons, X), Y)))) 
  app(app(min, X), nil) => X 
  app(app(min, X), app(app(cons, Y), Z)) => app(app(app(if, app(app(le, X), Y)), app(app(min, X), Z)), app(app(min, Y), Z)) 
  app(app(del, X), nil) => nil 
  app(app(del, X), app(app(cons, Y), Z)) => app(app(app(if, app(app(eq, X), Y)), Z), app(app(cons, Y), app(app(del, X), Z))) 
  app(app(map, X), nil) => nil 
  app(app(map, X), app(app(cons, Y), Z)) => app(app(cons, app(X, Y)), app(app(map, X), Z)) 
  app(app(filter, X), nil) => nil 
  app(app(filter, X), app(app(cons, Y), Z)) => app(app(app(app(filter2, app(X, Y)), X), Y), Z) 
  app(app(app(app(filter2, true), X), Y), Z) => app(app(cons, Y), app(app(filter, X), Z)) 
  app(app(app(app(filter2, false), X), Y), Z) => app(app(filter, X), Z)