MAYBE

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

Strict Trs:
  { le(s(x), s(y)) -> le(x, y)
  , le(s(x), 0()) -> false()
  , le(0(), y) -> true()
  , plus(s(x), y) -> s(plus(x, y))
  , plus(0(), y) -> y
  , times(s(x), y) -> plus(y, times(x, y))
  , times(0(), y) -> 0()
  , log(x, s(0())) -> baseError()
  , log(x, 0()) -> baseError()
  , log(s(x), s(s(b))) -> loop(s(x), s(s(b)), s(0()), 0())
  , log(0(), s(s(b))) -> logZeroError()
  , loop(x, s(s(b)), s(y), z) -> if(le(x, s(y)), x, s(s(b)), s(y), z)
  , if(false(), x, b, y, z) -> loop(x, b, times(b, y), s(z))
  , if(true(), x, b, y, z) -> z }
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 minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with perSymbol-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) '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) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { le^#(s(x), s(y)) -> c_1(le^#(x, y))
     , le^#(s(x), 0()) -> c_2()
     , le^#(0(), y) -> c_3()
     , plus^#(s(x), y) -> c_4(plus^#(x, y))
     , plus^#(0(), y) -> c_5(y)
     , times^#(s(x), y) -> c_6(plus^#(y, times(x, y)))
     , times^#(0(), y) -> c_7()
     , log^#(x, s(0())) -> c_8()
     , log^#(x, 0()) -> c_9()
     , log^#(s(x), s(s(b))) -> c_10(loop^#(s(x), s(s(b)), s(0()), 0()))
     , log^#(0(), s(s(b))) -> c_11()
     , loop^#(x, s(s(b)), s(y), z) ->
       c_12(if^#(le(x, s(y)), x, s(s(b)), s(y), z))
     , if^#(false(), x, b, y, z) ->
       c_13(loop^#(x, b, times(b, y), s(z)))
     , if^#(true(), x, b, y, z) -> c_14(z) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { le^#(s(x), s(y)) -> c_1(le^#(x, y))
     , le^#(s(x), 0()) -> c_2()
     , le^#(0(), y) -> c_3()
     , plus^#(s(x), y) -> c_4(plus^#(x, y))
     , plus^#(0(), y) -> c_5(y)
     , times^#(s(x), y) -> c_6(plus^#(y, times(x, y)))
     , times^#(0(), y) -> c_7()
     , log^#(x, s(0())) -> c_8()
     , log^#(x, 0()) -> c_9()
     , log^#(s(x), s(s(b))) -> c_10(loop^#(s(x), s(s(b)), s(0()), 0()))
     , log^#(0(), s(s(b))) -> c_11()
     , loop^#(x, s(s(b)), s(y), z) ->
       c_12(if^#(le(x, s(y)), x, s(s(b)), s(y), z))
     , if^#(false(), x, b, y, z) ->
       c_13(loop^#(x, b, times(b, y), s(z)))
     , if^#(true(), x, b, y, z) -> c_14(z) }
   Strict Trs:
     { le(s(x), s(y)) -> le(x, y)
     , le(s(x), 0()) -> false()
     , le(0(), y) -> true()
     , plus(s(x), y) -> s(plus(x, y))
     , plus(0(), y) -> y
     , times(s(x), y) -> plus(y, times(x, y))
     , times(0(), y) -> 0()
     , log(x, s(0())) -> baseError()
     , log(x, 0()) -> baseError()
     , log(s(x), s(s(b))) -> loop(s(x), s(s(b)), s(0()), 0())
     , log(0(), s(s(b))) -> logZeroError()
     , loop(x, s(s(b)), s(y), z) -> if(le(x, s(y)), x, s(s(b)), s(y), z)
     , if(false(), x, b, y, z) -> loop(x, b, times(b, y), s(z))
     , if(true(), x, b, y, z) -> z }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {2,3,7,8,9,11} by
   applications of Pre({2,3,7,8,9,11}) = {1,5,14}. Here rules are
   labeled as follows:
   
     DPs:
       { 1: le^#(s(x), s(y)) -> c_1(le^#(x, y))
       , 2: le^#(s(x), 0()) -> c_2()
       , 3: le^#(0(), y) -> c_3()
       , 4: plus^#(s(x), y) -> c_4(plus^#(x, y))
       , 5: plus^#(0(), y) -> c_5(y)
       , 6: times^#(s(x), y) -> c_6(plus^#(y, times(x, y)))
       , 7: times^#(0(), y) -> c_7()
       , 8: log^#(x, s(0())) -> c_8()
       , 9: log^#(x, 0()) -> c_9()
       , 10: log^#(s(x), s(s(b))) ->
             c_10(loop^#(s(x), s(s(b)), s(0()), 0()))
       , 11: log^#(0(), s(s(b))) -> c_11()
       , 12: loop^#(x, s(s(b)), s(y), z) ->
             c_12(if^#(le(x, s(y)), x, s(s(b)), s(y), z))
       , 13: if^#(false(), x, b, y, z) ->
             c_13(loop^#(x, b, times(b, y), s(z)))
       , 14: if^#(true(), x, b, y, z) -> c_14(z) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { le^#(s(x), s(y)) -> c_1(le^#(x, y))
     , plus^#(s(x), y) -> c_4(plus^#(x, y))
     , plus^#(0(), y) -> c_5(y)
     , times^#(s(x), y) -> c_6(plus^#(y, times(x, y)))
     , log^#(s(x), s(s(b))) -> c_10(loop^#(s(x), s(s(b)), s(0()), 0()))
     , loop^#(x, s(s(b)), s(y), z) ->
       c_12(if^#(le(x, s(y)), x, s(s(b)), s(y), z))
     , if^#(false(), x, b, y, z) ->
       c_13(loop^#(x, b, times(b, y), s(z)))
     , if^#(true(), x, b, y, z) -> c_14(z) }
   Strict Trs:
     { le(s(x), s(y)) -> le(x, y)
     , le(s(x), 0()) -> false()
     , le(0(), y) -> true()
     , plus(s(x), y) -> s(plus(x, y))
     , plus(0(), y) -> y
     , times(s(x), y) -> plus(y, times(x, y))
     , times(0(), y) -> 0()
     , log(x, s(0())) -> baseError()
     , log(x, 0()) -> baseError()
     , log(s(x), s(s(b))) -> loop(s(x), s(s(b)), s(0()), 0())
     , log(0(), s(s(b))) -> logZeroError()
     , loop(x, s(s(b)), s(y), z) -> if(le(x, s(y)), x, s(s(b)), s(y), z)
     , if(false(), x, b, y, z) -> loop(x, b, times(b, y), s(z))
     , if(true(), x, b, y, z) -> z }
   Weak DPs:
     { le^#(s(x), 0()) -> c_2()
     , le^#(0(), y) -> c_3()
     , times^#(0(), y) -> c_7()
     , log^#(x, s(0())) -> c_8()
     , log^#(x, 0()) -> c_9()
     , log^#(0(), s(s(b))) -> c_11() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..