MAYBE

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

Strict Trs:
  { f(x, y, z) -> g(<=(x, y), x, y, z)
  , g(true(), x, y, z) -> z
  , g(false(), x, y, z) ->
    f(f(p(x), y, z), f(p(y), z, x), f(p(z), 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 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.
      
   

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


Arrrr..