MAYBE

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

Strict Trs:
  { p(0()) -> 0()
  , p(s(x)) -> x
  , le(0(), y) -> true()
  , le(s(x), 0()) -> false()
  , le(s(x), s(y)) -> le(x, y)
  , minus(x, 0()) -> x
  , minus(x, s(y)) -> if(le(x, s(y)), 0(), p(minus(x, p(s(y)))))
  , if(true(), x, y) -> x
  , if(false(), x, y) -> 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) '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) 'Best' failed due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) '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) '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
      
   

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()
     , p^#(s(x)) -> c_2(x)
     , le^#(0(), y) -> c_3()
     , le^#(s(x), 0()) -> c_4()
     , le^#(s(x), s(y)) -> c_5(le^#(x, y))
     , minus^#(x, 0()) -> c_6(x)
     , minus^#(x, s(y)) ->
       c_7(if^#(le(x, s(y)), 0(), p(minus(x, p(s(y))))))
     , if^#(true(), x, y) -> c_8(x)
     , if^#(false(), x, y) -> c_9(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()
     , p^#(s(x)) -> c_2(x)
     , le^#(0(), y) -> c_3()
     , le^#(s(x), 0()) -> c_4()
     , le^#(s(x), s(y)) -> c_5(le^#(x, y))
     , minus^#(x, 0()) -> c_6(x)
     , minus^#(x, s(y)) ->
       c_7(if^#(le(x, s(y)), 0(), p(minus(x, p(s(y))))))
     , if^#(true(), x, y) -> c_8(x)
     , if^#(false(), x, y) -> c_9(y) }
   Strict Trs:
     { p(0()) -> 0()
     , p(s(x)) -> x
     , le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , minus(x, 0()) -> x
     , minus(x, s(y)) -> if(le(x, s(y)), 0(), p(minus(x, p(s(y)))))
     , if(true(), x, y) -> x
     , if(false(), x, y) -> y }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,3,4} by applications of
   Pre({1,3,4}) = {2,5,6,8,9}. Here rules are labeled as follows:
   
     DPs:
       { 1: p^#(0()) -> c_1()
       , 2: p^#(s(x)) -> c_2(x)
       , 3: le^#(0(), y) -> c_3()
       , 4: le^#(s(x), 0()) -> c_4()
       , 5: le^#(s(x), s(y)) -> c_5(le^#(x, y))
       , 6: minus^#(x, 0()) -> c_6(x)
       , 7: minus^#(x, s(y)) ->
            c_7(if^#(le(x, s(y)), 0(), p(minus(x, p(s(y))))))
       , 8: if^#(true(), x, y) -> c_8(x)
       , 9: if^#(false(), x, y) -> c_9(y) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { p^#(s(x)) -> c_2(x)
     , le^#(s(x), s(y)) -> c_5(le^#(x, y))
     , minus^#(x, 0()) -> c_6(x)
     , minus^#(x, s(y)) ->
       c_7(if^#(le(x, s(y)), 0(), p(minus(x, p(s(y))))))
     , if^#(true(), x, y) -> c_8(x)
     , if^#(false(), x, y) -> c_9(y) }
   Strict Trs:
     { p(0()) -> 0()
     , p(s(x)) -> x
     , le(0(), y) -> true()
     , le(s(x), 0()) -> false()
     , le(s(x), s(y)) -> le(x, y)
     , minus(x, 0()) -> x
     , minus(x, s(y)) -> if(le(x, s(y)), 0(), p(minus(x, p(s(y)))))
     , if(true(), x, y) -> x
     , if(false(), x, y) -> y }
   Weak DPs:
     { p^#(0()) -> c_1()
     , le^#(0(), y) -> c_3()
     , le^#(s(x), 0()) -> c_4() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..