MAYBE

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

Strict Trs:
  { sort(l) -> st(0(), l)
  , st(n, l) -> cond1(member(n, l), n, l)
  , cond1(true(), n, l) -> cons(n, st(s(n), l))
  , cond1(false(), n, l) -> cond2(gt(n, max(l)), n, l)
  , member(n, cons(m, l)) -> or(equal(n, m), member(n, l))
  , member(n, nil()) -> false()
  , cond2(true(), n, l) -> nil()
  , cond2(false(), n, l) -> st(s(n), l)
  , gt(0(), v) -> false()
  , gt(s(u), 0()) -> true()
  , gt(s(u), s(v)) -> gt(u, v)
  , max(cons(u, l)) -> if(gt(u, max(l)), u, max(l))
  , max(nil()) -> 0()
  , or(x, true()) -> true()
  , or(x, false()) -> x
  , equal(0(), 0()) -> true()
  , equal(0(), s(y)) -> false()
  , equal(s(x), 0()) -> false()
  , equal(s(x), s(y)) -> equal(x, y)
  , if(true(), u, v) -> u
  , if(false(), u, v) -> v }
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 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) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { sort^#(l) -> c_1(st^#(0(), l))
     , st^#(n, l) -> c_2(cond1^#(member(n, l), n, l))
     , cond1^#(true(), n, l) -> c_3(n, st^#(s(n), l))
     , cond1^#(false(), n, l) -> c_4(cond2^#(gt(n, max(l)), n, l))
     , cond2^#(true(), n, l) -> c_7()
     , cond2^#(false(), n, l) -> c_8(st^#(s(n), l))
     , member^#(n, cons(m, l)) -> c_5(or^#(equal(n, m), member(n, l)))
     , member^#(n, nil()) -> c_6()
     , or^#(x, true()) -> c_14()
     , or^#(x, false()) -> c_15(x)
     , gt^#(0(), v) -> c_9()
     , gt^#(s(u), 0()) -> c_10()
     , gt^#(s(u), s(v)) -> c_11(gt^#(u, v))
     , max^#(cons(u, l)) -> c_12(if^#(gt(u, max(l)), u, max(l)))
     , max^#(nil()) -> c_13()
     , if^#(true(), u, v) -> c_20(u)
     , if^#(false(), u, v) -> c_21(v)
     , equal^#(0(), 0()) -> c_16()
     , equal^#(0(), s(y)) -> c_17()
     , equal^#(s(x), 0()) -> c_18()
     , equal^#(s(x), s(y)) -> c_19(equal^#(x, y)) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { sort^#(l) -> c_1(st^#(0(), l))
     , st^#(n, l) -> c_2(cond1^#(member(n, l), n, l))
     , cond1^#(true(), n, l) -> c_3(n, st^#(s(n), l))
     , cond1^#(false(), n, l) -> c_4(cond2^#(gt(n, max(l)), n, l))
     , cond2^#(true(), n, l) -> c_7()
     , cond2^#(false(), n, l) -> c_8(st^#(s(n), l))
     , member^#(n, cons(m, l)) -> c_5(or^#(equal(n, m), member(n, l)))
     , member^#(n, nil()) -> c_6()
     , or^#(x, true()) -> c_14()
     , or^#(x, false()) -> c_15(x)
     , gt^#(0(), v) -> c_9()
     , gt^#(s(u), 0()) -> c_10()
     , gt^#(s(u), s(v)) -> c_11(gt^#(u, v))
     , max^#(cons(u, l)) -> c_12(if^#(gt(u, max(l)), u, max(l)))
     , max^#(nil()) -> c_13()
     , if^#(true(), u, v) -> c_20(u)
     , if^#(false(), u, v) -> c_21(v)
     , equal^#(0(), 0()) -> c_16()
     , equal^#(0(), s(y)) -> c_17()
     , equal^#(s(x), 0()) -> c_18()
     , equal^#(s(x), s(y)) -> c_19(equal^#(x, y)) }
   Strict Trs:
     { sort(l) -> st(0(), l)
     , st(n, l) -> cond1(member(n, l), n, l)
     , cond1(true(), n, l) -> cons(n, st(s(n), l))
     , cond1(false(), n, l) -> cond2(gt(n, max(l)), n, l)
     , member(n, cons(m, l)) -> or(equal(n, m), member(n, l))
     , member(n, nil()) -> false()
     , cond2(true(), n, l) -> nil()
     , cond2(false(), n, l) -> st(s(n), l)
     , gt(0(), v) -> false()
     , gt(s(u), 0()) -> true()
     , gt(s(u), s(v)) -> gt(u, v)
     , max(cons(u, l)) -> if(gt(u, max(l)), u, max(l))
     , max(nil()) -> 0()
     , or(x, true()) -> true()
     , or(x, false()) -> x
     , equal(0(), 0()) -> true()
     , equal(0(), s(y)) -> false()
     , equal(s(x), 0()) -> false()
     , equal(s(x), s(y)) -> equal(x, y)
     , if(true(), u, v) -> u
     , if(false(), u, v) -> v }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {5,8,9,11,12,15,18,19,20}
   by applications of Pre({5,8,9,11,12,15,18,19,20}) =
   {3,4,7,10,13,16,17,21}. Here rules are labeled as follows:
   
     DPs:
       { 1: sort^#(l) -> c_1(st^#(0(), l))
       , 2: st^#(n, l) -> c_2(cond1^#(member(n, l), n, l))
       , 3: cond1^#(true(), n, l) -> c_3(n, st^#(s(n), l))
       , 4: cond1^#(false(), n, l) -> c_4(cond2^#(gt(n, max(l)), n, l))
       , 5: cond2^#(true(), n, l) -> c_7()
       , 6: cond2^#(false(), n, l) -> c_8(st^#(s(n), l))
       , 7: member^#(n, cons(m, l)) ->
            c_5(or^#(equal(n, m), member(n, l)))
       , 8: member^#(n, nil()) -> c_6()
       , 9: or^#(x, true()) -> c_14()
       , 10: or^#(x, false()) -> c_15(x)
       , 11: gt^#(0(), v) -> c_9()
       , 12: gt^#(s(u), 0()) -> c_10()
       , 13: gt^#(s(u), s(v)) -> c_11(gt^#(u, v))
       , 14: max^#(cons(u, l)) -> c_12(if^#(gt(u, max(l)), u, max(l)))
       , 15: max^#(nil()) -> c_13()
       , 16: if^#(true(), u, v) -> c_20(u)
       , 17: if^#(false(), u, v) -> c_21(v)
       , 18: equal^#(0(), 0()) -> c_16()
       , 19: equal^#(0(), s(y)) -> c_17()
       , 20: equal^#(s(x), 0()) -> c_18()
       , 21: equal^#(s(x), s(y)) -> c_19(equal^#(x, y)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { sort^#(l) -> c_1(st^#(0(), l))
     , st^#(n, l) -> c_2(cond1^#(member(n, l), n, l))
     , cond1^#(true(), n, l) -> c_3(n, st^#(s(n), l))
     , cond1^#(false(), n, l) -> c_4(cond2^#(gt(n, max(l)), n, l))
     , cond2^#(false(), n, l) -> c_8(st^#(s(n), l))
     , member^#(n, cons(m, l)) -> c_5(or^#(equal(n, m), member(n, l)))
     , or^#(x, false()) -> c_15(x)
     , gt^#(s(u), s(v)) -> c_11(gt^#(u, v))
     , max^#(cons(u, l)) -> c_12(if^#(gt(u, max(l)), u, max(l)))
     , if^#(true(), u, v) -> c_20(u)
     , if^#(false(), u, v) -> c_21(v)
     , equal^#(s(x), s(y)) -> c_19(equal^#(x, y)) }
   Strict Trs:
     { sort(l) -> st(0(), l)
     , st(n, l) -> cond1(member(n, l), n, l)
     , cond1(true(), n, l) -> cons(n, st(s(n), l))
     , cond1(false(), n, l) -> cond2(gt(n, max(l)), n, l)
     , member(n, cons(m, l)) -> or(equal(n, m), member(n, l))
     , member(n, nil()) -> false()
     , cond2(true(), n, l) -> nil()
     , cond2(false(), n, l) -> st(s(n), l)
     , gt(0(), v) -> false()
     , gt(s(u), 0()) -> true()
     , gt(s(u), s(v)) -> gt(u, v)
     , max(cons(u, l)) -> if(gt(u, max(l)), u, max(l))
     , max(nil()) -> 0()
     , or(x, true()) -> true()
     , or(x, false()) -> x
     , equal(0(), 0()) -> true()
     , equal(0(), s(y)) -> false()
     , equal(s(x), 0()) -> false()
     , equal(s(x), s(y)) -> equal(x, y)
     , if(true(), u, v) -> u
     , if(false(), u, v) -> v }
   Weak DPs:
     { cond2^#(true(), n, l) -> c_7()
     , member^#(n, nil()) -> c_6()
     , or^#(x, true()) -> c_14()
     , gt^#(0(), v) -> c_9()
     , gt^#(s(u), 0()) -> c_10()
     , max^#(nil()) -> c_13()
     , equal^#(0(), 0()) -> c_16()
     , equal^#(0(), s(y)) -> c_17()
     , equal^#(s(x), 0()) -> c_18() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..