MAYBE

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

Strict Trs:
  { p(0()) -> 0()
  , p(s(x)) -> x
  , plus(x, 0()) -> x
  , plus(x, s(y)) -> s(plus(x, p(s(y))))
  , plus(0(), y) -> y
  , plus(s(x), y) -> s(plus(x, y))
  , plus(s(x), y) -> s(plus(p(s(x)), y))
  , times(0(), y) -> 0()
  , times(s(x), y) -> plus(y, times(x, y))
  , times(s(0()), y) -> y
  , div(x, y) -> quot(x, y, y)
  , div(0(), y) -> 0()
  , div(div(x, y), z) -> div(x, times(y, z))
  , quot(x, 0(), s(z)) -> s(div(x, s(z)))
  , quot(0(), s(y), z) -> 0()
  , quot(s(x), s(y), z) -> quot(x, y, z)
  , eq(0(), 0()) -> true()
  , eq(0(), s(y)) -> false()
  , eq(s(x), 0()) -> false()
  , eq(s(x), s(y)) -> eq(x, y)
  , divides(y, x) -> eq(x, times(div(x, y), y))
  , prime(s(s(x))) -> pr(s(s(x)), s(x))
  , pr(x, s(0())) -> true()
  , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y))
  , if(true(), x, y) -> false()
  , if(false(), x, y) -> pr(x, y) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

Arguments of following rules are not normal-forms:

{ div(div(x, y), z) -> div(x, times(y, z)) }

All above mentioned rules can be savely removed.

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

Strict Trs:
  { p(0()) -> 0()
  , p(s(x)) -> x
  , plus(x, 0()) -> x
  , plus(x, s(y)) -> s(plus(x, p(s(y))))
  , plus(0(), y) -> y
  , plus(s(x), y) -> s(plus(x, y))
  , plus(s(x), y) -> s(plus(p(s(x)), y))
  , times(0(), y) -> 0()
  , times(s(x), y) -> plus(y, times(x, y))
  , times(s(0()), y) -> y
  , div(x, y) -> quot(x, y, y)
  , div(0(), y) -> 0()
  , quot(x, 0(), s(z)) -> s(div(x, s(z)))
  , quot(0(), s(y), z) -> 0()
  , quot(s(x), s(y), z) -> quot(x, y, z)
  , eq(0(), 0()) -> true()
  , eq(0(), s(y)) -> false()
  , eq(s(x), 0()) -> false()
  , eq(s(x), s(y)) -> eq(x, y)
  , divides(y, x) -> eq(x, times(div(x, y), y))
  , prime(s(s(x))) -> pr(s(s(x)), s(x))
  , pr(x, s(0())) -> true()
  , pr(x, s(s(y))) -> if(divides(s(s(y)), x), x, s(y))
  , if(true(), x, y) -> false()
  , if(false(), x, y) -> pr(x, y) }
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 perSymbol-enrichment and initial automaton 'match''
            failed due to the following reason:
            
            match-boundness of the problem could not be verified.
         
         2) 'Bounds with minimal-enrichment and initial automaton 'match''
            failed due to the following reason:
            
            match-boundness of the problem could not be verified.
         
      
   


Arrrr..