MAYBE

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

Strict Trs:
  { -(x, 0()) -> x
  , -(s(x), s(y)) -> -(x, y)
  , +(0(), y) -> y
  , +(s(x), y) -> s(+(x, y))
  , *(x, 0()) -> 0()
  , *(x, s(y)) -> +(x, *(x, y))
  , f(s(x), y) -> f(-(*(s(x), s(y)), s(*(s(x), y))), *(y, y)) }
Obligation:
  runtime complexity
Answer:
  MAYBE

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) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
         following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
      2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
         to the following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
   
   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.
      
   

3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { -^#(x, 0()) -> c_1(x)
     , -^#(s(x), s(y)) -> c_2(-^#(x, y))
     , +^#(0(), y) -> c_3(y)
     , +^#(s(x), y) -> c_4(+^#(x, y))
     , *^#(x, 0()) -> c_5()
     , *^#(x, s(y)) -> c_6(+^#(x, *(x, y)))
     , f^#(s(x), y) ->
       c_7(f^#(-(*(s(x), s(y)), s(*(s(x), y))), *(y, y))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { -^#(x, 0()) -> c_1(x)
     , -^#(s(x), s(y)) -> c_2(-^#(x, y))
     , +^#(0(), y) -> c_3(y)
     , +^#(s(x), y) -> c_4(+^#(x, y))
     , *^#(x, 0()) -> c_5()
     , *^#(x, s(y)) -> c_6(+^#(x, *(x, y)))
     , f^#(s(x), y) ->
       c_7(f^#(-(*(s(x), s(y)), s(*(s(x), y))), *(y, y))) }
   Strict Trs:
     { -(x, 0()) -> x
     , -(s(x), s(y)) -> -(x, y)
     , +(0(), y) -> y
     , +(s(x), y) -> s(+(x, y))
     , *(x, 0()) -> 0()
     , *(x, s(y)) -> +(x, *(x, y))
     , f(s(x), y) -> f(-(*(s(x), s(y)), s(*(s(x), y))), *(y, y)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {5} by applications of
   Pre({5}) = {1,3}. Here rules are labeled as follows:
   
     DPs:
       { 1: -^#(x, 0()) -> c_1(x)
       , 2: -^#(s(x), s(y)) -> c_2(-^#(x, y))
       , 3: +^#(0(), y) -> c_3(y)
       , 4: +^#(s(x), y) -> c_4(+^#(x, y))
       , 5: *^#(x, 0()) -> c_5()
       , 6: *^#(x, s(y)) -> c_6(+^#(x, *(x, y)))
       , 7: f^#(s(x), y) ->
            c_7(f^#(-(*(s(x), s(y)), s(*(s(x), y))), *(y, y))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { -^#(x, 0()) -> c_1(x)
     , -^#(s(x), s(y)) -> c_2(-^#(x, y))
     , +^#(0(), y) -> c_3(y)
     , +^#(s(x), y) -> c_4(+^#(x, y))
     , *^#(x, s(y)) -> c_6(+^#(x, *(x, y)))
     , f^#(s(x), y) ->
       c_7(f^#(-(*(s(x), s(y)), s(*(s(x), y))), *(y, y))) }
   Strict Trs:
     { -(x, 0()) -> x
     , -(s(x), s(y)) -> -(x, y)
     , +(0(), y) -> y
     , +(s(x), y) -> s(+(x, y))
     , *(x, 0()) -> 0()
     , *(x, s(y)) -> +(x, *(x, y))
     , f(s(x), y) -> f(-(*(s(x), s(y)), s(*(s(x), y))), *(y, y)) }
   Weak DPs: { *^#(x, 0()) -> c_5() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..