MAYBE

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

Strict Trs:
  { U11(tt(), M, N) -> U12(tt(), activate(M), activate(N))
  , U12(tt(), M, N) -> s(plus(activate(N), activate(M)))
  , activate(X) -> X
  , plus(N, s(M)) -> U11(tt(), M, N)
  , plus(N, 0()) -> N
  , U21(tt(), M, N) -> U22(tt(), activate(M), activate(N))
  , U22(tt(), M, N) -> plus(x(activate(N), activate(M)), activate(N))
  , x(N, s(M)) -> U21(tt(), M, N)
  , x(N, 0()) -> 0() }
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) '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
      
      2) '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
      
   
   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:
     { U11^#(tt(), M, N) -> c_1(U12^#(tt(), activate(M), activate(N)))
     , U12^#(tt(), M, N) -> c_2(plus^#(activate(N), activate(M)))
     , plus^#(N, s(M)) -> c_4(U11^#(tt(), M, N))
     , plus^#(N, 0()) -> c_5(N)
     , activate^#(X) -> c_3(X)
     , U21^#(tt(), M, N) -> c_6(U22^#(tt(), activate(M), activate(N)))
     , U22^#(tt(), M, N) ->
       c_7(plus^#(x(activate(N), activate(M)), activate(N)))
     , x^#(N, s(M)) -> c_8(U21^#(tt(), M, N))
     , x^#(N, 0()) -> c_9() }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { U11^#(tt(), M, N) -> c_1(U12^#(tt(), activate(M), activate(N)))
     , U12^#(tt(), M, N) -> c_2(plus^#(activate(N), activate(M)))
     , plus^#(N, s(M)) -> c_4(U11^#(tt(), M, N))
     , plus^#(N, 0()) -> c_5(N)
     , activate^#(X) -> c_3(X)
     , U21^#(tt(), M, N) -> c_6(U22^#(tt(), activate(M), activate(N)))
     , U22^#(tt(), M, N) ->
       c_7(plus^#(x(activate(N), activate(M)), activate(N)))
     , x^#(N, s(M)) -> c_8(U21^#(tt(), M, N))
     , x^#(N, 0()) -> c_9() }
   Strict Trs:
     { U11(tt(), M, N) -> U12(tt(), activate(M), activate(N))
     , U12(tt(), M, N) -> s(plus(activate(N), activate(M)))
     , activate(X) -> X
     , plus(N, s(M)) -> U11(tt(), M, N)
     , plus(N, 0()) -> N
     , U21(tt(), M, N) -> U22(tt(), activate(M), activate(N))
     , U22(tt(), M, N) -> plus(x(activate(N), activate(M)), activate(N))
     , x(N, s(M)) -> U21(tt(), M, N)
     , x(N, 0()) -> 0() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {9} by applications of
   Pre({9}) = {4,5}. Here rules are labeled as follows:
   
     DPs:
       { 1: U11^#(tt(), M, N) ->
            c_1(U12^#(tt(), activate(M), activate(N)))
       , 2: U12^#(tt(), M, N) -> c_2(plus^#(activate(N), activate(M)))
       , 3: plus^#(N, s(M)) -> c_4(U11^#(tt(), M, N))
       , 4: plus^#(N, 0()) -> c_5(N)
       , 5: activate^#(X) -> c_3(X)
       , 6: U21^#(tt(), M, N) ->
            c_6(U22^#(tt(), activate(M), activate(N)))
       , 7: U22^#(tt(), M, N) ->
            c_7(plus^#(x(activate(N), activate(M)), activate(N)))
       , 8: x^#(N, s(M)) -> c_8(U21^#(tt(), M, N))
       , 9: x^#(N, 0()) -> c_9() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { U11^#(tt(), M, N) -> c_1(U12^#(tt(), activate(M), activate(N)))
     , U12^#(tt(), M, N) -> c_2(plus^#(activate(N), activate(M)))
     , plus^#(N, s(M)) -> c_4(U11^#(tt(), M, N))
     , plus^#(N, 0()) -> c_5(N)
     , activate^#(X) -> c_3(X)
     , U21^#(tt(), M, N) -> c_6(U22^#(tt(), activate(M), activate(N)))
     , U22^#(tt(), M, N) ->
       c_7(plus^#(x(activate(N), activate(M)), activate(N)))
     , x^#(N, s(M)) -> c_8(U21^#(tt(), M, N)) }
   Strict Trs:
     { U11(tt(), M, N) -> U12(tt(), activate(M), activate(N))
     , U12(tt(), M, N) -> s(plus(activate(N), activate(M)))
     , activate(X) -> X
     , plus(N, s(M)) -> U11(tt(), M, N)
     , plus(N, 0()) -> N
     , U21(tt(), M, N) -> U22(tt(), activate(M), activate(N))
     , U22(tt(), M, N) -> plus(x(activate(N), activate(M)), activate(N))
     , x(N, s(M)) -> U21(tt(), M, N)
     , x(N, 0()) -> 0() }
   Weak DPs: { x^#(N, 0()) -> c_9() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..