MAYBE

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

Strict Trs:
  { f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z))
  , f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z)
  , gt(s(u), s(v)) -> gt(u, v)
  , gt(s(u), 0()) -> true()
  , gt(0(), v) -> false()
  , plus(n, s(m)) -> s(plus(n, m))
  , plus(n, 0()) -> n }
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^#(true(), x, y, z) -> c_1(f^#(gt(x, plus(y, z)), x, y, s(z)))
     , f^#(true(), x, y, z) -> c_2(f^#(gt(x, plus(y, z)), x, s(y), z))
     , gt^#(s(u), s(v)) -> c_3(gt^#(u, v))
     , gt^#(s(u), 0()) -> c_4()
     , gt^#(0(), v) -> c_5()
     , plus^#(n, s(m)) -> c_6(plus^#(n, m))
     , plus^#(n, 0()) -> c_7(n) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { f^#(true(), x, y, z) -> c_1(f^#(gt(x, plus(y, z)), x, y, s(z)))
     , f^#(true(), x, y, z) -> c_2(f^#(gt(x, plus(y, z)), x, s(y), z))
     , gt^#(s(u), s(v)) -> c_3(gt^#(u, v))
     , gt^#(s(u), 0()) -> c_4()
     , gt^#(0(), v) -> c_5()
     , plus^#(n, s(m)) -> c_6(plus^#(n, m))
     , plus^#(n, 0()) -> c_7(n) }
   Strict Trs:
     { f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z))
     , f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z)
     , gt(s(u), s(v)) -> gt(u, v)
     , gt(s(u), 0()) -> true()
     , gt(0(), v) -> false()
     , plus(n, s(m)) -> s(plus(n, m))
     , plus(n, 0()) -> n }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {4,5} by applications of
   Pre({4,5}) = {3,7}. Here rules are labeled as follows:
   
     DPs:
       { 1: f^#(true(), x, y, z) ->
            c_1(f^#(gt(x, plus(y, z)), x, y, s(z)))
       , 2: f^#(true(), x, y, z) ->
            c_2(f^#(gt(x, plus(y, z)), x, s(y), z))
       , 3: gt^#(s(u), s(v)) -> c_3(gt^#(u, v))
       , 4: gt^#(s(u), 0()) -> c_4()
       , 5: gt^#(0(), v) -> c_5()
       , 6: plus^#(n, s(m)) -> c_6(plus^#(n, m))
       , 7: plus^#(n, 0()) -> c_7(n) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { f^#(true(), x, y, z) -> c_1(f^#(gt(x, plus(y, z)), x, y, s(z)))
     , f^#(true(), x, y, z) -> c_2(f^#(gt(x, plus(y, z)), x, s(y), z))
     , gt^#(s(u), s(v)) -> c_3(gt^#(u, v))
     , plus^#(n, s(m)) -> c_6(plus^#(n, m))
     , plus^#(n, 0()) -> c_7(n) }
   Strict Trs:
     { f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z))
     , f(true(), x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z)
     , gt(s(u), s(v)) -> gt(u, v)
     , gt(s(u), 0()) -> true()
     , gt(0(), v) -> false()
     , plus(n, s(m)) -> s(plus(n, m))
     , plus(n, 0()) -> n }
   Weak DPs:
     { gt^#(s(u), 0()) -> c_4()
     , gt^#(0(), v) -> c_5() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..