/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 
  a : [] --> o 
  app : [o * o] --> o 
  append : [o * o] --> o 
  averIter : [o * o * o] --> o 
  average : [o * o] --> o 
  b : [] --> o 
  c : [] --> o 
  cons : [o * o] --> o 
  error : [] --> o 
  false : [] --> o 
  ge : [o * o] --> o 
  head : [o] --> o 
  high : [o * o] --> o 
  if : [o * o * o] --> o 
  if!6220high : [o * o * o] --> o 
  if!6220low : [o * o * o] --> o 
  ifIter : [o * o * o * o] --> o 
  ifquick : [o * o] --> o 
  isempty : [o] --> o 
  low : [o * o] --> o 
  nil : [] --> o 
  plus : [o * o] --> o 
  quicksort : [o] --> o 
  s : [o] --> o 
  tail : [o] --> o 
  true : [] --> o 

  average(X, Y) => if(ge(X, Y), X, Y) 
  if(true, X, Y) => averIter(Y, X, Y) 
  if(false, X, Y) => averIter(X, Y, X) 
  averIter(X, Y, Z) => ifIter(ge(X, Y), X, Y, Z) 
  ifIter(true, X, Y, Z) => Z 
  ifIter(false, X, Y, Z) => averIter(plus(X, s(s(s(0)))), plus(Y, s(0)), plus(Z, s(0))) 
  append(nil, X) => X 
  append(cons(X, Y), Z) => cons(X, app(Y, Z)) 
  low(X, nil) => nil 
  low(X, cons(Y, Z)) => if!6220low(ge(Y, X), X, cons(Y, Z)) 
  if!6220low(false, X, cons(Y, Z)) => cons(Y, low(X, Z)) 
  if!6220low(true, X, cons(Y, Z)) => low(X, Z) 
  high(X, nil) => nil 
  high(X, cons(Y, Z)) => if!6220high(ge(Y, X), X, cons(Y, Z)) 
  if!6220high(false, X, cons(Y, Z)) => high(X, Z) 
  if!6220high(true, X, cons(Y, Z)) => cons(average(Y, Y), high(X, Z)) 
  quicksort(X) => ifquick(isempty(X), X) 
  ifquick(true, X) => nil 
  ifquick(false, X) => append(quicksort(low(head(X), tail(X))), cons(tail(X), quicksort(high(head(X), tail(X))))) 
  plus(0, X) => X 
  plus(s(X), Y) => s(plus(X, Y)) 
  isempty(nil) => true 
  isempty(cons(X, Y)) => false 
  head(nil) => error 
  head(cons(X, Y)) => X 
  tail(nil) => nil 
  tail(cons(X, Y)) => Y 
  ge(X, 0) => true 
  ge(0, s(X)) => false 
  ge(s(X), s(Y)) => ge(X, Y) 
  a => b 
  a => c