/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 
  a : [] --> o 
  b : [] --> o 
  c : [] --> o 
  cons : [o * o] --> o 
  double : [o] --> o 
  droplast : [o] --> o 
  error : [] --> o 
  false : [] --> o 
  if : [o * o * o * o] --> o 
  ifmap : [o * o * o] --> o 
  isempty : [o] --> o 
  last : [o] --> o 
  le : [o * o] --> o 
  log : [o] --> o 
  logError : [] --> o 
  loop : [o * o * o] --> o 
  mapIter : [o * o] --> o 
  maplog : [o] --> o 
  nil : [] --> o 
  s : [o] --> o 
  true : [] --> o 

  le(s(X), 0) => false 
  le(0, X) => true 
  le(s(X), s(Y)) => le(X, Y) 
  double(0) => 0 
  double(s(X)) => s(s(double(X))) 
  log(0) => logError 
  log(s(X)) => loop(s(X), s(0), 0) 
  loop(X, s(Y), Z) => if(le(X, s(Y)), X, s(Y), Z) 
  if(true, X, Y, Z) => Z 
  if(false, X, Y, Z) => loop(X, double(Y), s(Z)) 
  maplog(X) => mapIter(X, nil) 
  mapIter(X, Y) => ifmap(isempty(X), X, Y) 
  ifmap(true, X, Y) => Y 
  ifmap(false, X, Y) => mapIter(droplast(X), cons(log(last(X)), Y)) 
  isempty(nil) => true 
  isempty(cons(X, Y)) => false 
  last(nil) => error 
  last(cons(X, nil)) => X 
  last(cons(X, cons(Y, Z))) => last(cons(Y, Z)) 
  droplast(nil) => nil 
  droplast(cons(X, nil)) => nil 
  droplast(cons(X, cons(Y, Z))) => cons(X, droplast(cons(Y, Z))) 
  a => b 
  a => c