MAYBE

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

Strict Trs:
  { cond1(true(), x, y, z) -> cond2(gr(x, 0()), x, y, z)
  , cond2(true(), x, y, z) ->
    cond1(or(gr(x, z), gr(y, z)), p(x), y, z)
  , cond2(false(), x, y, z) -> cond3(gr(y, 0()), x, y, z)
  , gr(0(), x) -> false()
  , gr(s(x), 0()) -> true()
  , gr(s(x), s(y)) -> gr(x, y)
  , or(x, true()) -> true()
  , or(true(), x) -> true()
  , or(false(), false()) -> false()
  , p(0()) -> 0()
  , p(s(x)) -> x
  , cond3(true(), x, y, z) ->
    cond1(or(gr(x, z), gr(y, z)), x, p(y), z)
  , cond3(false(), x, y, z) ->
    cond1(or(gr(x, z), gr(y, z)), x, y, z) }
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) '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.
      
   
   3) '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
      
   

2) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { cond1^#(true(), x, y, z) -> c_1(cond2^#(gr(x, 0()), x, y, z))
     , cond2^#(true(), x, y, z) ->
       c_2(cond1^#(or(gr(x, z), gr(y, z)), p(x), y, z))
     , cond2^#(false(), x, y, z) -> c_3(cond3^#(gr(y, 0()), x, y, z))
     , cond3^#(true(), x, y, z) ->
       c_12(cond1^#(or(gr(x, z), gr(y, z)), x, p(y), z))
     , cond3^#(false(), x, y, z) ->
       c_13(cond1^#(or(gr(x, z), gr(y, z)), x, y, z))
     , gr^#(0(), x) -> c_4()
     , gr^#(s(x), 0()) -> c_5()
     , gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
     , or^#(x, true()) -> c_7()
     , or^#(true(), x) -> c_8()
     , or^#(false(), false()) -> c_9()
     , p^#(0()) -> c_10()
     , p^#(s(x)) -> c_11(x) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { cond1^#(true(), x, y, z) -> c_1(cond2^#(gr(x, 0()), x, y, z))
     , cond2^#(true(), x, y, z) ->
       c_2(cond1^#(or(gr(x, z), gr(y, z)), p(x), y, z))
     , cond2^#(false(), x, y, z) -> c_3(cond3^#(gr(y, 0()), x, y, z))
     , cond3^#(true(), x, y, z) ->
       c_12(cond1^#(or(gr(x, z), gr(y, z)), x, p(y), z))
     , cond3^#(false(), x, y, z) ->
       c_13(cond1^#(or(gr(x, z), gr(y, z)), x, y, z))
     , gr^#(0(), x) -> c_4()
     , gr^#(s(x), 0()) -> c_5()
     , gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
     , or^#(x, true()) -> c_7()
     , or^#(true(), x) -> c_8()
     , or^#(false(), false()) -> c_9()
     , p^#(0()) -> c_10()
     , p^#(s(x)) -> c_11(x) }
   Strict Trs:
     { cond1(true(), x, y, z) -> cond2(gr(x, 0()), x, y, z)
     , cond2(true(), x, y, z) ->
       cond1(or(gr(x, z), gr(y, z)), p(x), y, z)
     , cond2(false(), x, y, z) -> cond3(gr(y, 0()), x, y, z)
     , gr(0(), x) -> false()
     , gr(s(x), 0()) -> true()
     , gr(s(x), s(y)) -> gr(x, y)
     , or(x, true()) -> true()
     , or(true(), x) -> true()
     , or(false(), false()) -> false()
     , p(0()) -> 0()
     , p(s(x)) -> x
     , cond3(true(), x, y, z) ->
       cond1(or(gr(x, z), gr(y, z)), x, p(y), z)
     , cond3(false(), x, y, z) ->
       cond1(or(gr(x, z), gr(y, z)), x, y, z) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {6,7,9,10,11,12} by
   applications of Pre({6,7,9,10,11,12}) = {8,13}. Here rules are
   labeled as follows:
   
     DPs:
       { 1: cond1^#(true(), x, y, z) -> c_1(cond2^#(gr(x, 0()), x, y, z))
       , 2: cond2^#(true(), x, y, z) ->
            c_2(cond1^#(or(gr(x, z), gr(y, z)), p(x), y, z))
       , 3: cond2^#(false(), x, y, z) -> c_3(cond3^#(gr(y, 0()), x, y, z))
       , 4: cond3^#(true(), x, y, z) ->
            c_12(cond1^#(or(gr(x, z), gr(y, z)), x, p(y), z))
       , 5: cond3^#(false(), x, y, z) ->
            c_13(cond1^#(or(gr(x, z), gr(y, z)), x, y, z))
       , 6: gr^#(0(), x) -> c_4()
       , 7: gr^#(s(x), 0()) -> c_5()
       , 8: gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
       , 9: or^#(x, true()) -> c_7()
       , 10: or^#(true(), x) -> c_8()
       , 11: or^#(false(), false()) -> c_9()
       , 12: p^#(0()) -> c_10()
       , 13: p^#(s(x)) -> c_11(x) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { cond1^#(true(), x, y, z) -> c_1(cond2^#(gr(x, 0()), x, y, z))
     , cond2^#(true(), x, y, z) ->
       c_2(cond1^#(or(gr(x, z), gr(y, z)), p(x), y, z))
     , cond2^#(false(), x, y, z) -> c_3(cond3^#(gr(y, 0()), x, y, z))
     , cond3^#(true(), x, y, z) ->
       c_12(cond1^#(or(gr(x, z), gr(y, z)), x, p(y), z))
     , cond3^#(false(), x, y, z) ->
       c_13(cond1^#(or(gr(x, z), gr(y, z)), x, y, z))
     , gr^#(s(x), s(y)) -> c_6(gr^#(x, y))
     , p^#(s(x)) -> c_11(x) }
   Strict Trs:
     { cond1(true(), x, y, z) -> cond2(gr(x, 0()), x, y, z)
     , cond2(true(), x, y, z) ->
       cond1(or(gr(x, z), gr(y, z)), p(x), y, z)
     , cond2(false(), x, y, z) -> cond3(gr(y, 0()), x, y, z)
     , gr(0(), x) -> false()
     , gr(s(x), 0()) -> true()
     , gr(s(x), s(y)) -> gr(x, y)
     , or(x, true()) -> true()
     , or(true(), x) -> true()
     , or(false(), false()) -> false()
     , p(0()) -> 0()
     , p(s(x)) -> x
     , cond3(true(), x, y, z) ->
       cond1(or(gr(x, z), gr(y, z)), x, p(y), z)
     , cond3(false(), x, y, z) ->
       cond1(or(gr(x, z), gr(y, z)), x, y, z) }
   Weak DPs:
     { gr^#(0(), x) -> c_4()
     , gr^#(s(x), 0()) -> c_5()
     , or^#(x, true()) -> c_7()
     , or^#(true(), x) -> c_8()
     , or^#(false(), false()) -> c_9()
     , p^#(0()) -> c_10() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..