MAYBE

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

Strict Trs:
  { double(x) -> permute(x, x, a())
  , permute(x, y, a()) -> permute(isZero(x), x, b())
  , permute(y, x, c()) -> s(s(permute(x, y, a())))
  , permute(false(), x, b()) -> permute(ack(x, x), p(x), c())
  , permute(true(), x, b()) -> 0()
  , isZero(0()) -> true()
  , isZero(s(x)) -> false()
  , ack(0(), x) -> plus(x, s(0()))
  , ack(s(x), 0()) -> ack(x, s(0()))
  , ack(s(x), s(y)) -> ack(x, ack(s(x), y))
  , p(0()) -> 0()
  , p(s(x)) -> x
  , plus(x, 0()) -> x
  , plus(x, s(0())) -> s(x)
  , plus(x, s(s(y))) -> s(plus(s(x), y))
  , plus(0(), y) -> y
  , plus(s(x), y) -> plus(x, s(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:
     { double^#(x) -> c_1(permute^#(x, x, a()))
     , permute^#(x, y, a()) -> c_2(permute^#(isZero(x), x, b()))
     , permute^#(y, x, c()) -> c_3(permute^#(x, y, a()))
     , permute^#(false(), x, b()) ->
       c_4(permute^#(ack(x, x), p(x), c()))
     , permute^#(true(), x, b()) -> c_5()
     , isZero^#(0()) -> c_6()
     , isZero^#(s(x)) -> c_7()
     , ack^#(0(), x) -> c_8(plus^#(x, s(0())))
     , ack^#(s(x), 0()) -> c_9(ack^#(x, s(0())))
     , ack^#(s(x), s(y)) -> c_10(ack^#(x, ack(s(x), y)))
     , plus^#(x, 0()) -> c_13(x)
     , plus^#(x, s(0())) -> c_14(x)
     , plus^#(x, s(s(y))) -> c_15(plus^#(s(x), y))
     , plus^#(0(), y) -> c_16(y)
     , plus^#(s(x), y) -> c_17(plus^#(x, s(y)))
     , p^#(0()) -> c_11()
     , p^#(s(x)) -> c_12(x) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { double^#(x) -> c_1(permute^#(x, x, a()))
     , permute^#(x, y, a()) -> c_2(permute^#(isZero(x), x, b()))
     , permute^#(y, x, c()) -> c_3(permute^#(x, y, a()))
     , permute^#(false(), x, b()) ->
       c_4(permute^#(ack(x, x), p(x), c()))
     , permute^#(true(), x, b()) -> c_5()
     , isZero^#(0()) -> c_6()
     , isZero^#(s(x)) -> c_7()
     , ack^#(0(), x) -> c_8(plus^#(x, s(0())))
     , ack^#(s(x), 0()) -> c_9(ack^#(x, s(0())))
     , ack^#(s(x), s(y)) -> c_10(ack^#(x, ack(s(x), y)))
     , plus^#(x, 0()) -> c_13(x)
     , plus^#(x, s(0())) -> c_14(x)
     , plus^#(x, s(s(y))) -> c_15(plus^#(s(x), y))
     , plus^#(0(), y) -> c_16(y)
     , plus^#(s(x), y) -> c_17(plus^#(x, s(y)))
     , p^#(0()) -> c_11()
     , p^#(s(x)) -> c_12(x) }
   Strict Trs:
     { double(x) -> permute(x, x, a())
     , permute(x, y, a()) -> permute(isZero(x), x, b())
     , permute(y, x, c()) -> s(s(permute(x, y, a())))
     , permute(false(), x, b()) -> permute(ack(x, x), p(x), c())
     , permute(true(), x, b()) -> 0()
     , isZero(0()) -> true()
     , isZero(s(x)) -> false()
     , ack(0(), x) -> plus(x, s(0()))
     , ack(s(x), 0()) -> ack(x, s(0()))
     , ack(s(x), s(y)) -> ack(x, ack(s(x), y))
     , p(0()) -> 0()
     , p(s(x)) -> x
     , plus(x, 0()) -> x
     , plus(x, s(0())) -> s(x)
     , plus(x, s(s(y))) -> s(plus(s(x), y))
     , plus(0(), y) -> y
     , plus(s(x), y) -> plus(x, s(y)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {5,6,7,16} by applications
   of Pre({5,6,7,16}) = {2,11,12,14,17}. Here rules are labeled as
   follows:
   
     DPs:
       { 1: double^#(x) -> c_1(permute^#(x, x, a()))
       , 2: permute^#(x, y, a()) -> c_2(permute^#(isZero(x), x, b()))
       , 3: permute^#(y, x, c()) -> c_3(permute^#(x, y, a()))
       , 4: permute^#(false(), x, b()) ->
            c_4(permute^#(ack(x, x), p(x), c()))
       , 5: permute^#(true(), x, b()) -> c_5()
       , 6: isZero^#(0()) -> c_6()
       , 7: isZero^#(s(x)) -> c_7()
       , 8: ack^#(0(), x) -> c_8(plus^#(x, s(0())))
       , 9: ack^#(s(x), 0()) -> c_9(ack^#(x, s(0())))
       , 10: ack^#(s(x), s(y)) -> c_10(ack^#(x, ack(s(x), y)))
       , 11: plus^#(x, 0()) -> c_13(x)
       , 12: plus^#(x, s(0())) -> c_14(x)
       , 13: plus^#(x, s(s(y))) -> c_15(plus^#(s(x), y))
       , 14: plus^#(0(), y) -> c_16(y)
       , 15: plus^#(s(x), y) -> c_17(plus^#(x, s(y)))
       , 16: p^#(0()) -> c_11()
       , 17: p^#(s(x)) -> c_12(x) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { double^#(x) -> c_1(permute^#(x, x, a()))
     , permute^#(x, y, a()) -> c_2(permute^#(isZero(x), x, b()))
     , permute^#(y, x, c()) -> c_3(permute^#(x, y, a()))
     , permute^#(false(), x, b()) ->
       c_4(permute^#(ack(x, x), p(x), c()))
     , ack^#(0(), x) -> c_8(plus^#(x, s(0())))
     , ack^#(s(x), 0()) -> c_9(ack^#(x, s(0())))
     , ack^#(s(x), s(y)) -> c_10(ack^#(x, ack(s(x), y)))
     , plus^#(x, 0()) -> c_13(x)
     , plus^#(x, s(0())) -> c_14(x)
     , plus^#(x, s(s(y))) -> c_15(plus^#(s(x), y))
     , plus^#(0(), y) -> c_16(y)
     , plus^#(s(x), y) -> c_17(plus^#(x, s(y)))
     , p^#(s(x)) -> c_12(x) }
   Strict Trs:
     { double(x) -> permute(x, x, a())
     , permute(x, y, a()) -> permute(isZero(x), x, b())
     , permute(y, x, c()) -> s(s(permute(x, y, a())))
     , permute(false(), x, b()) -> permute(ack(x, x), p(x), c())
     , permute(true(), x, b()) -> 0()
     , isZero(0()) -> true()
     , isZero(s(x)) -> false()
     , ack(0(), x) -> plus(x, s(0()))
     , ack(s(x), 0()) -> ack(x, s(0()))
     , ack(s(x), s(y)) -> ack(x, ack(s(x), y))
     , p(0()) -> 0()
     , p(s(x)) -> x
     , plus(x, 0()) -> x
     , plus(x, s(0())) -> s(x)
     , plus(x, s(s(y))) -> s(plus(s(x), y))
     , plus(0(), y) -> y
     , plus(s(x), y) -> plus(x, s(y)) }
   Weak DPs:
     { permute^#(true(), x, b()) -> c_5()
     , isZero^#(0()) -> c_6()
     , isZero^#(s(x)) -> c_7()
     , p^#(0()) -> c_11() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..