MAYBE

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

Strict Trs:
  { g(s(x), s(y)) ->
    if(and(f(s(x)), f(s(y))),
       t(g(k(minus(m(x, y), n(x, y)), s(s(0()))),
           k(n(s(x), s(y)), s(s(0()))))),
       g(minus(m(x, y), n(x, y)), n(s(x), s(y))))
  , if(true(), x, y) -> x
  , if(false(), x, y) -> y
  , and(x, false()) -> false()
  , and(true(), true()) -> true()
  , f(s(x)) -> h(x)
  , f(0()) -> true()
  , t(x) -> p(x, x)
  , k(s(x), s(y)) -> s(k(minus(x, y), s(y)))
  , k(0(), s(y)) -> 0()
  , minus(x, 0()) -> x
  , minus(s(x), s(y)) -> minus(x, y)
  , m(x, 0()) -> x
  , m(s(x), s(y)) -> s(m(x, y))
  , m(0(), y) -> y
  , n(x, 0()) -> 0()
  , n(s(x), s(y)) -> s(n(x, y))
  , n(0(), y) -> 0()
  , p(s(x), x) -> p(if(gt(x, x), id(x), id(x)), s(x))
  , p(s(x), s(y)) ->
    s(s(p(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
  , p(0(), y) -> y
  , p(id(x), s(y)) -> s(p(x, if(gt(s(y), y), y, s(y))))
  , gt(s(x), s(y)) -> gt(x, y)
  , gt(s(x), 0()) -> true()
  , gt(0(), y) -> false()
  , not(x) -> if(x, false(), true())
  , id(x) -> x
  , h(s(x)) -> f(x)
  , h(0()) -> false() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Arguments of following rules are not normal-forms:

{ p(id(x), s(y)) -> s(p(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:
  { g(s(x), s(y)) ->
    if(and(f(s(x)), f(s(y))),
       t(g(k(minus(m(x, y), n(x, y)), s(s(0()))),
           k(n(s(x), s(y)), s(s(0()))))),
       g(minus(m(x, y), n(x, y)), n(s(x), s(y))))
  , if(true(), x, y) -> x
  , if(false(), x, y) -> y
  , and(x, false()) -> false()
  , and(true(), true()) -> true()
  , f(s(x)) -> h(x)
  , f(0()) -> true()
  , t(x) -> p(x, x)
  , k(s(x), s(y)) -> s(k(minus(x, y), s(y)))
  , k(0(), s(y)) -> 0()
  , minus(x, 0()) -> x
  , minus(s(x), s(y)) -> minus(x, y)
  , m(x, 0()) -> x
  , m(s(x), s(y)) -> s(m(x, y))
  , m(0(), y) -> y
  , n(x, 0()) -> 0()
  , n(s(x), s(y)) -> s(n(x, y))
  , n(0(), y) -> 0()
  , p(s(x), x) -> p(if(gt(x, x), id(x), id(x)), s(x))
  , p(s(x), s(y)) ->
    s(s(p(if(gt(x, y), x, y), if(not(gt(x, y)), id(x), id(y)))))
  , p(0(), y) -> y
  , gt(s(x), s(y)) -> gt(x, y)
  , gt(s(x), 0()) -> true()
  , gt(0(), y) -> false()
  , not(x) -> if(x, false(), true())
  , id(x) -> x
  , h(s(x)) -> f(x)
  , h(0()) -> false() }
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..