MAYBE

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

Strict Trs:
  { p(0()) -> 0()
  , p(s(X)) -> X
  , 0() -> n__0()
  , s(X) -> n__s(X)
  , leq(0(), Y) -> true()
  , leq(s(X), 0()) -> false()
  , leq(s(X), s(Y)) -> leq(X, Y)
  , if(true(), X, Y) -> activate(X)
  , if(false(), X, Y) -> activate(Y)
  , activate(X) -> X
  , activate(n__0()) -> 0()
  , activate(n__s(X)) -> s(X)
  , diff(X, Y) -> if(leq(X, Y), n__0(), n__s(diff(p(X), 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:
     { p^#(0()) -> c_1(0^#())
     , p^#(s(X)) -> c_2(X)
     , 0^#() -> c_3()
     , s^#(X) -> c_4(X)
     , leq^#(0(), Y) -> c_5()
     , leq^#(s(X), 0()) -> c_6()
     , leq^#(s(X), s(Y)) -> c_7(leq^#(X, Y))
     , if^#(true(), X, Y) -> c_8(activate^#(X))
     , if^#(false(), X, Y) -> c_9(activate^#(Y))
     , activate^#(X) -> c_10(X)
     , activate^#(n__0()) -> c_11(0^#())
     , activate^#(n__s(X)) -> c_12(s^#(X))
     , diff^#(X, Y) ->
       c_13(if^#(leq(X, Y), n__0(), n__s(diff(p(X), Y)))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { p^#(0()) -> c_1(0^#())
     , p^#(s(X)) -> c_2(X)
     , 0^#() -> c_3()
     , s^#(X) -> c_4(X)
     , leq^#(0(), Y) -> c_5()
     , leq^#(s(X), 0()) -> c_6()
     , leq^#(s(X), s(Y)) -> c_7(leq^#(X, Y))
     , if^#(true(), X, Y) -> c_8(activate^#(X))
     , if^#(false(), X, Y) -> c_9(activate^#(Y))
     , activate^#(X) -> c_10(X)
     , activate^#(n__0()) -> c_11(0^#())
     , activate^#(n__s(X)) -> c_12(s^#(X))
     , diff^#(X, Y) ->
       c_13(if^#(leq(X, Y), n__0(), n__s(diff(p(X), Y)))) }
   Strict Trs:
     { p(0()) -> 0()
     , p(s(X)) -> X
     , 0() -> n__0()
     , s(X) -> n__s(X)
     , leq(0(), Y) -> true()
     , leq(s(X), 0()) -> false()
     , leq(s(X), s(Y)) -> leq(X, Y)
     , if(true(), X, Y) -> activate(X)
     , if(false(), X, Y) -> activate(Y)
     , activate(X) -> X
     , activate(n__0()) -> 0()
     , activate(n__s(X)) -> s(X)
     , diff(X, Y) -> if(leq(X, Y), n__0(), n__s(diff(p(X), Y))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3,5,6} by applications of
   Pre({3,5,6}) = {1,2,4,7,10,11}. Here rules are labeled as follows:
   
     DPs:
       { 1: p^#(0()) -> c_1(0^#())
       , 2: p^#(s(X)) -> c_2(X)
       , 3: 0^#() -> c_3()
       , 4: s^#(X) -> c_4(X)
       , 5: leq^#(0(), Y) -> c_5()
       , 6: leq^#(s(X), 0()) -> c_6()
       , 7: leq^#(s(X), s(Y)) -> c_7(leq^#(X, Y))
       , 8: if^#(true(), X, Y) -> c_8(activate^#(X))
       , 9: if^#(false(), X, Y) -> c_9(activate^#(Y))
       , 10: activate^#(X) -> c_10(X)
       , 11: activate^#(n__0()) -> c_11(0^#())
       , 12: activate^#(n__s(X)) -> c_12(s^#(X))
       , 13: diff^#(X, Y) ->
             c_13(if^#(leq(X, Y), n__0(), n__s(diff(p(X), Y)))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { p^#(0()) -> c_1(0^#())
     , p^#(s(X)) -> c_2(X)
     , s^#(X) -> c_4(X)
     , leq^#(s(X), s(Y)) -> c_7(leq^#(X, Y))
     , if^#(true(), X, Y) -> c_8(activate^#(X))
     , if^#(false(), X, Y) -> c_9(activate^#(Y))
     , activate^#(X) -> c_10(X)
     , activate^#(n__0()) -> c_11(0^#())
     , activate^#(n__s(X)) -> c_12(s^#(X))
     , diff^#(X, Y) ->
       c_13(if^#(leq(X, Y), n__0(), n__s(diff(p(X), Y)))) }
   Strict Trs:
     { p(0()) -> 0()
     , p(s(X)) -> X
     , 0() -> n__0()
     , s(X) -> n__s(X)
     , leq(0(), Y) -> true()
     , leq(s(X), 0()) -> false()
     , leq(s(X), s(Y)) -> leq(X, Y)
     , if(true(), X, Y) -> activate(X)
     , if(false(), X, Y) -> activate(Y)
     , activate(X) -> X
     , activate(n__0()) -> 0()
     , activate(n__s(X)) -> s(X)
     , diff(X, Y) -> if(leq(X, Y), n__0(), n__s(diff(p(X), Y))) }
   Weak DPs:
     { 0^#() -> c_3()
     , leq^#(0(), Y) -> c_5()
     , leq^#(s(X), 0()) -> c_6() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,8} by applications of
   Pre({1,8}) = {2,3,5,6,7}. Here rules are labeled as follows:
   
     DPs:
       { 1: p^#(0()) -> c_1(0^#())
       , 2: p^#(s(X)) -> c_2(X)
       , 3: s^#(X) -> c_4(X)
       , 4: leq^#(s(X), s(Y)) -> c_7(leq^#(X, Y))
       , 5: if^#(true(), X, Y) -> c_8(activate^#(X))
       , 6: if^#(false(), X, Y) -> c_9(activate^#(Y))
       , 7: activate^#(X) -> c_10(X)
       , 8: activate^#(n__0()) -> c_11(0^#())
       , 9: activate^#(n__s(X)) -> c_12(s^#(X))
       , 10: diff^#(X, Y) ->
             c_13(if^#(leq(X, Y), n__0(), n__s(diff(p(X), Y))))
       , 11: 0^#() -> c_3()
       , 12: leq^#(0(), Y) -> c_5()
       , 13: leq^#(s(X), 0()) -> c_6() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { p^#(s(X)) -> c_2(X)
     , s^#(X) -> c_4(X)
     , leq^#(s(X), s(Y)) -> c_7(leq^#(X, Y))
     , if^#(true(), X, Y) -> c_8(activate^#(X))
     , if^#(false(), X, Y) -> c_9(activate^#(Y))
     , activate^#(X) -> c_10(X)
     , activate^#(n__s(X)) -> c_12(s^#(X))
     , diff^#(X, Y) ->
       c_13(if^#(leq(X, Y), n__0(), n__s(diff(p(X), Y)))) }
   Strict Trs:
     { p(0()) -> 0()
     , p(s(X)) -> X
     , 0() -> n__0()
     , s(X) -> n__s(X)
     , leq(0(), Y) -> true()
     , leq(s(X), 0()) -> false()
     , leq(s(X), s(Y)) -> leq(X, Y)
     , if(true(), X, Y) -> activate(X)
     , if(false(), X, Y) -> activate(Y)
     , activate(X) -> X
     , activate(n__0()) -> 0()
     , activate(n__s(X)) -> s(X)
     , diff(X, Y) -> if(leq(X, Y), n__0(), n__s(diff(p(X), Y))) }
   Weak DPs:
     { p^#(0()) -> c_1(0^#())
     , 0^#() -> c_3()
     , leq^#(0(), Y) -> c_5()
     , leq^#(s(X), 0()) -> c_6()
     , activate^#(n__0()) -> c_11(0^#()) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..