MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { app(l, nil()) -> l
  , app(nil(), k) -> k
  , app(cons(x, l), k) -> cons(x, app(l, k))
  , sum(app(l, cons(x, cons(y, k)))) ->
    sum(app(l, sum(cons(x, cons(y, k)))))
  , sum(cons(x, nil())) -> cons(x, nil())
  , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l))
  , sum(plus(cons(0(), x), cons(y, l))) ->
    pred(sum(cons(s(x), cons(y, l))))
  , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x))
  , plus(s(x), s(y)) ->
    s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
  , plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y))))
  , plus(zero(), y) -> y
  , pred(cons(s(x), nil())) -> cons(x, nil())
  , if(true(), x, y) -> x
  , if(false(), x, y) -> y
  , gt(s(x), s(y)) -> gt(x, y)
  , gt(s(x), zero()) -> true()
  , gt(zero(), y) -> false()
  , not(x) -> if(x, false(), true())
  , id(x) -> x }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Arguments of following rules are not normal-forms:

{ plus(id(x), s(y)) -> s(plus(x, if(gt(s(y), y), y, s(y)))) }

All above mentioned rules can be savely removed.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { app(l, nil()) -> l
  , app(nil(), k) -> k
  , app(cons(x, l), k) -> cons(x, app(l, k))
  , sum(app(l, cons(x, cons(y, k)))) ->
    sum(app(l, sum(cons(x, cons(y, k)))))
  , sum(cons(x, nil())) -> cons(x, nil())
  , sum(cons(x, cons(y, l))) -> sum(cons(plus(x, y), l))
  , sum(plus(cons(0(), x), cons(y, l))) ->
    pred(sum(cons(s(x), cons(y, l))))
  , plus(s(x), x) -> plus(if(gt(x, x), id(x), id(x)), s(x))
  , plus(s(x), s(y)) ->
    s(s(plus(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
  , plus(zero(), y) -> y
  , pred(cons(s(x), nil())) -> cons(x, nil())
  , if(true(), x, y) -> x
  , if(false(), x, y) -> y
  , gt(s(x), s(y)) -> gt(x, y)
  , gt(s(x), zero()) -> true()
  , gt(zero(), y) -> false()
  , not(x) -> if(x, false(), true())
  , id(x) -> x }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'empty' failed due to the following reason:
   
   Empty strict component of the problem is NOT empty.

2) 'Best' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'WithProblem (timeout of 60 seconds)' failed due to the
      following reason:
      
      Computation stopped due to timeout after 60.0 seconds.
   
   2) 'Best' failed due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
         failed due to the following reason:
         
         Computation stopped due to timeout after 30.0 seconds.
      
      2) 'Best' failed due to the following reason:
         
         None of the processors succeeded.
         
         Details of failed attempt(s):
         -----------------------------
         1) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
            to the following reason:
            
            The input cannot be shown compatible
         
         2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
            following reason:
            
            The input cannot be shown compatible
         
      
      3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
         due to the following reason:
         
         None of the processors succeeded.
         
         Details of failed attempt(s):
         -----------------------------
         1) 'Bounds with minimal-enrichment and initial automaton 'match''
            failed due to the following reason:
            
            match-boundness of the problem could not be verified.
         
         2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
            failed due to the following reason:
            
            match-boundness of the problem could not be verified.
         
      
   


Arrrr..