/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 
  app : [o * o] --> o 
  cons : [o * o] --> o 
  false : [] --> o 
  gt : [o * o] --> o 
  id : [o] --> o 
  if : [o * o * o] --> o 
  minus : [o * o] --> o 
  nil : [] --> o 
  not : [o] --> o 
  plus : [o * o] --> o 
  quot : [o * o] --> o 
  s : [o] --> o 
  sum : [o] --> o 
  true : [] --> o 
  zero : [] --> o 

  minus(X, 0) => X 
  minus(s(X), s(Y)) => minus(X, Y) 
  quot(0, s(X)) => 0 
  quot(s(X), s(Y)) => s(quot(minus(X, Y), s(Y))) 
  plus(0, X) => X 
  plus(s(X), Y) => s(plus(X, Y)) 
  minus(minus(X, Y), Z) => minus(X, plus(Y, Z)) 
  app(nil, X) => X 
  app(X, nil) => X 
  app(cons(X, Y), Z) => cons(X, app(Y, Z)) 
  sum(cons(X, nil)) => cons(X, nil) 
  sum(cons(X, cons(Y, Z))) => sum(cons(plus(X, Y), Z)) 
  sum(app(X, cons(Y, cons(Z, U)))) => sum(app(X, sum(cons(Y, cons(Z, U))))) 
  plus(s(X), s(Y)) => s(s(plus(if(gt(X, Y), X, Y), if(not(gt(X, Y)), id(X), id(Y))))) 
  plus(s(X), X) => plus(if(gt(X, X), id(X), id(X)), s(X)) 
  plus(zero, X) => X 
  plus(id(X), s(Y)) => s(plus(X, if(gt(s(Y), Y), Y, s(Y)))) 
  id(X) => X 
  if(true, X, Y) => X 
  if(false, X, Y) => Y 
  not(X) => if(X, false, true) 
  gt(s(X), zero) => true 
  gt(zero, X) => false 
  gt(s(X), s(Y)) => gt(X, Y)