MAYBE

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

Strict Trs:
  { table() -> gen(s(0()))
  , gen(x) -> if1(le(x, 10()), x)
  , if1(false(), x) -> nil()
  , if1(true(), x) -> if2(x, x)
  , le(s(x), s(y)) -> le(x, y)
  , le(s(x), 0()) -> false()
  , le(0(), y) -> true()
  , 10() -> s(s(s(s(s(s(s(s(s(s(0()))))))))))
  , if2(x, y) -> if3(le(y, 10()), x, y)
  , if3(false(), x, y) -> gen(s(x))
  , if3(true(), x, y) -> cons(entry(x, y, times(x, y)), if2(x, s(y)))
  , times(s(x), y) -> plus(y, times(x, y))
  , times(0(), y) -> 0()
  , plus(s(x), y) -> s(plus(x, y))
  , plus(0(), 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 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) '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:
     { table^#() -> c_1(gen^#(s(0())))
     , gen^#(x) -> c_2(if1^#(le(x, 10()), x))
     , if1^#(false(), x) -> c_3()
     , if1^#(true(), x) -> c_4(if2^#(x, x))
     , if2^#(x, y) -> c_9(if3^#(le(y, 10()), x, y))
     , le^#(s(x), s(y)) -> c_5(le^#(x, y))
     , le^#(s(x), 0()) -> c_6()
     , le^#(0(), y) -> c_7()
     , 10^#() -> c_8()
     , if3^#(false(), x, y) -> c_10(gen^#(s(x)))
     , if3^#(true(), x, y) -> c_11(x, y, times^#(x, y), if2^#(x, s(y)))
     , times^#(s(x), y) -> c_12(plus^#(y, times(x, y)))
     , times^#(0(), y) -> c_13()
     , plus^#(s(x), y) -> c_14(plus^#(x, y))
     , plus^#(0(), y) -> c_15(y) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { table^#() -> c_1(gen^#(s(0())))
     , gen^#(x) -> c_2(if1^#(le(x, 10()), x))
     , if1^#(false(), x) -> c_3()
     , if1^#(true(), x) -> c_4(if2^#(x, x))
     , if2^#(x, y) -> c_9(if3^#(le(y, 10()), x, y))
     , le^#(s(x), s(y)) -> c_5(le^#(x, y))
     , le^#(s(x), 0()) -> c_6()
     , le^#(0(), y) -> c_7()
     , 10^#() -> c_8()
     , if3^#(false(), x, y) -> c_10(gen^#(s(x)))
     , if3^#(true(), x, y) -> c_11(x, y, times^#(x, y), if2^#(x, s(y)))
     , times^#(s(x), y) -> c_12(plus^#(y, times(x, y)))
     , times^#(0(), y) -> c_13()
     , plus^#(s(x), y) -> c_14(plus^#(x, y))
     , plus^#(0(), y) -> c_15(y) }
   Strict Trs:
     { table() -> gen(s(0()))
     , gen(x) -> if1(le(x, 10()), x)
     , if1(false(), x) -> nil()
     , if1(true(), x) -> if2(x, x)
     , le(s(x), s(y)) -> le(x, y)
     , le(s(x), 0()) -> false()
     , le(0(), y) -> true()
     , 10() -> s(s(s(s(s(s(s(s(s(s(0()))))))))))
     , if2(x, y) -> if3(le(y, 10()), x, y)
     , if3(false(), x, y) -> gen(s(x))
     , if3(true(), x, y) -> cons(entry(x, y, times(x, y)), if2(x, s(y)))
     , times(s(x), y) -> plus(y, times(x, y))
     , times(0(), y) -> 0()
     , plus(s(x), y) -> s(plus(x, y))
     , plus(0(), y) -> y }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3,7,8,9,13} by
   applications of Pre({3,7,8,9,13}) = {2,6,11,15}. Here rules are
   labeled as follows:
   
     DPs:
       { 1: table^#() -> c_1(gen^#(s(0())))
       , 2: gen^#(x) -> c_2(if1^#(le(x, 10()), x))
       , 3: if1^#(false(), x) -> c_3()
       , 4: if1^#(true(), x) -> c_4(if2^#(x, x))
       , 5: if2^#(x, y) -> c_9(if3^#(le(y, 10()), x, y))
       , 6: le^#(s(x), s(y)) -> c_5(le^#(x, y))
       , 7: le^#(s(x), 0()) -> c_6()
       , 8: le^#(0(), y) -> c_7()
       , 9: 10^#() -> c_8()
       , 10: if3^#(false(), x, y) -> c_10(gen^#(s(x)))
       , 11: if3^#(true(), x, y) ->
             c_11(x, y, times^#(x, y), if2^#(x, s(y)))
       , 12: times^#(s(x), y) -> c_12(plus^#(y, times(x, y)))
       , 13: times^#(0(), y) -> c_13()
       , 14: plus^#(s(x), y) -> c_14(plus^#(x, y))
       , 15: plus^#(0(), y) -> c_15(y) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { table^#() -> c_1(gen^#(s(0())))
     , gen^#(x) -> c_2(if1^#(le(x, 10()), x))
     , if1^#(true(), x) -> c_4(if2^#(x, x))
     , if2^#(x, y) -> c_9(if3^#(le(y, 10()), x, y))
     , le^#(s(x), s(y)) -> c_5(le^#(x, y))
     , if3^#(false(), x, y) -> c_10(gen^#(s(x)))
     , if3^#(true(), x, y) -> c_11(x, y, times^#(x, y), if2^#(x, s(y)))
     , times^#(s(x), y) -> c_12(plus^#(y, times(x, y)))
     , plus^#(s(x), y) -> c_14(plus^#(x, y))
     , plus^#(0(), y) -> c_15(y) }
   Strict Trs:
     { table() -> gen(s(0()))
     , gen(x) -> if1(le(x, 10()), x)
     , if1(false(), x) -> nil()
     , if1(true(), x) -> if2(x, x)
     , le(s(x), s(y)) -> le(x, y)
     , le(s(x), 0()) -> false()
     , le(0(), y) -> true()
     , 10() -> s(s(s(s(s(s(s(s(s(s(0()))))))))))
     , if2(x, y) -> if3(le(y, 10()), x, y)
     , if3(false(), x, y) -> gen(s(x))
     , if3(true(), x, y) -> cons(entry(x, y, times(x, y)), if2(x, s(y)))
     , times(s(x), y) -> plus(y, times(x, y))
     , times(0(), y) -> 0()
     , plus(s(x), y) -> s(plus(x, y))
     , plus(0(), y) -> y }
   Weak DPs:
     { if1^#(false(), x) -> c_3()
     , le^#(s(x), 0()) -> c_6()
     , le^#(0(), y) -> c_7()
     , 10^#() -> c_8()
     , times^#(0(), y) -> c_13() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..