MAYBE

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

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


Arrrr..