MAYBE

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

Strict Trs:
  { cond(true(), x) -> cond(and(even(x), gr(x, 0())), p(x))
  , and(x, false()) -> false()
  , and(true(), true()) -> true()
  , and(false(), x) -> false()
  , even(0()) -> true()
  , even(s(0())) -> false()
  , even(s(s(x))) -> even(x)
  , gr(0(), x) -> false()
  , gr(s(x), 0()) -> true()
  , gr(s(x), s(y())) -> gr(x, y())
  , p(0()) -> 0()
  , p(s(x)) -> x }
Obligation:
  runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) '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 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.
      
   

2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { cond^#(true(), x) -> c_1(cond^#(and(even(x), gr(x, 0())), p(x)))
     , and^#(x, false()) -> c_2()
     , and^#(true(), true()) -> c_3()
     , and^#(false(), x) -> c_4()
     , even^#(0()) -> c_5()
     , even^#(s(0())) -> c_6()
     , even^#(s(s(x))) -> c_7(even^#(x))
     , gr^#(0(), x) -> c_8()
     , gr^#(s(x), 0()) -> c_9()
     , gr^#(s(x), s(y())) -> c_10(gr^#(x, y()))
     , p^#(0()) -> c_11()
     , p^#(s(x)) -> c_12(x) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { cond^#(true(), x) -> c_1(cond^#(and(even(x), gr(x, 0())), p(x)))
     , and^#(x, false()) -> c_2()
     , and^#(true(), true()) -> c_3()
     , and^#(false(), x) -> c_4()
     , even^#(0()) -> c_5()
     , even^#(s(0())) -> c_6()
     , even^#(s(s(x))) -> c_7(even^#(x))
     , gr^#(0(), x) -> c_8()
     , gr^#(s(x), 0()) -> c_9()
     , gr^#(s(x), s(y())) -> c_10(gr^#(x, y()))
     , p^#(0()) -> c_11()
     , p^#(s(x)) -> c_12(x) }
   Strict Trs:
     { cond(true(), x) -> cond(and(even(x), gr(x, 0())), p(x))
     , and(x, false()) -> false()
     , and(true(), true()) -> true()
     , and(false(), x) -> false()
     , even(0()) -> true()
     , even(s(0())) -> false()
     , even(s(s(x))) -> even(x)
     , gr(0(), x) -> false()
     , gr(s(x), 0()) -> true()
     , gr(s(x), s(y())) -> gr(x, y())
     , p(0()) -> 0()
     , p(s(x)) -> x }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {2,3,4,5,6,8,9,11} by
   applications of Pre({2,3,4,5,6,8,9,11}) = {7,10,12}. Here rules are
   labeled as follows:
   
     DPs:
       { 1: cond^#(true(), x) ->
            c_1(cond^#(and(even(x), gr(x, 0())), p(x)))
       , 2: and^#(x, false()) -> c_2()
       , 3: and^#(true(), true()) -> c_3()
       , 4: and^#(false(), x) -> c_4()
       , 5: even^#(0()) -> c_5()
       , 6: even^#(s(0())) -> c_6()
       , 7: even^#(s(s(x))) -> c_7(even^#(x))
       , 8: gr^#(0(), x) -> c_8()
       , 9: gr^#(s(x), 0()) -> c_9()
       , 10: gr^#(s(x), s(y())) -> c_10(gr^#(x, y()))
       , 11: p^#(0()) -> c_11()
       , 12: p^#(s(x)) -> c_12(x) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { cond^#(true(), x) -> c_1(cond^#(and(even(x), gr(x, 0())), p(x)))
     , even^#(s(s(x))) -> c_7(even^#(x))
     , gr^#(s(x), s(y())) -> c_10(gr^#(x, y()))
     , p^#(s(x)) -> c_12(x) }
   Strict Trs:
     { cond(true(), x) -> cond(and(even(x), gr(x, 0())), p(x))
     , and(x, false()) -> false()
     , and(true(), true()) -> true()
     , and(false(), x) -> false()
     , even(0()) -> true()
     , even(s(0())) -> false()
     , even(s(s(x))) -> even(x)
     , gr(0(), x) -> false()
     , gr(s(x), 0()) -> true()
     , gr(s(x), s(y())) -> gr(x, y())
     , p(0()) -> 0()
     , p(s(x)) -> x }
   Weak DPs:
     { and^#(x, false()) -> c_2()
     , and^#(true(), true()) -> c_3()
     , and^#(false(), x) -> c_4()
     , even^#(0()) -> c_5()
     , even^#(s(0())) -> c_6()
     , gr^#(0(), x) -> c_8()
     , gr^#(s(x), 0()) -> c_9()
     , p^#(0()) -> c_11() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3} by applications of
   Pre({3}) = {4}. Here rules are labeled as follows:
   
     DPs:
       { 1: cond^#(true(), x) ->
            c_1(cond^#(and(even(x), gr(x, 0())), p(x)))
       , 2: even^#(s(s(x))) -> c_7(even^#(x))
       , 3: gr^#(s(x), s(y())) -> c_10(gr^#(x, y()))
       , 4: p^#(s(x)) -> c_12(x)
       , 5: and^#(x, false()) -> c_2()
       , 6: and^#(true(), true()) -> c_3()
       , 7: and^#(false(), x) -> c_4()
       , 8: even^#(0()) -> c_5()
       , 9: even^#(s(0())) -> c_6()
       , 10: gr^#(0(), x) -> c_8()
       , 11: gr^#(s(x), 0()) -> c_9()
       , 12: p^#(0()) -> c_11() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { cond^#(true(), x) -> c_1(cond^#(and(even(x), gr(x, 0())), p(x)))
     , even^#(s(s(x))) -> c_7(even^#(x))
     , p^#(s(x)) -> c_12(x) }
   Strict Trs:
     { cond(true(), x) -> cond(and(even(x), gr(x, 0())), p(x))
     , and(x, false()) -> false()
     , and(true(), true()) -> true()
     , and(false(), x) -> false()
     , even(0()) -> true()
     , even(s(0())) -> false()
     , even(s(s(x))) -> even(x)
     , gr(0(), x) -> false()
     , gr(s(x), 0()) -> true()
     , gr(s(x), s(y())) -> gr(x, y())
     , p(0()) -> 0()
     , p(s(x)) -> x }
   Weak DPs:
     { and^#(x, false()) -> c_2()
     , and^#(true(), true()) -> c_3()
     , and^#(false(), x) -> c_4()
     , even^#(0()) -> c_5()
     , even^#(s(0())) -> c_6()
     , gr^#(0(), x) -> c_8()
     , gr^#(s(x), 0()) -> c_9()
     , gr^#(s(x), s(y())) -> c_10(gr^#(x, y()))
     , p^#(0()) -> c_11() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..