MAYBE

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

Strict Trs:
  { minus(n__0(), Y) -> 0()
  , minus(n__s(X), n__s(Y)) -> minus(activate(X), activate(Y))
  , 0() -> n__0()
  , activate(X) -> X
  , activate(n__0()) -> 0()
  , activate(n__s(X)) -> s(X)
  , geq(X, n__0()) -> true()
  , geq(n__0(), n__s(Y)) -> false()
  , geq(n__s(X), n__s(Y)) -> geq(activate(X), activate(Y))
  , div(0(), n__s(Y)) -> 0()
  , div(s(X), n__s(Y)) ->
    if(geq(X, activate(Y)),
       n__s(div(minus(X, activate(Y)), n__s(activate(Y)))),
       n__0())
  , s(X) -> n__s(X)
  , if(true(), X, Y) -> activate(X)
  , if(false(), X, Y) -> activate(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:
     { minus^#(n__0(), Y) -> c_1(0^#())
     , minus^#(n__s(X), n__s(Y)) ->
       c_2(minus^#(activate(X), activate(Y)))
     , 0^#() -> c_3()
     , activate^#(X) -> c_4(X)
     , activate^#(n__0()) -> c_5(0^#())
     , activate^#(n__s(X)) -> c_6(s^#(X))
     , s^#(X) -> c_12(X)
     , geq^#(X, n__0()) -> c_7()
     , geq^#(n__0(), n__s(Y)) -> c_8()
     , geq^#(n__s(X), n__s(Y)) -> c_9(geq^#(activate(X), activate(Y)))
     , div^#(0(), n__s(Y)) -> c_10(0^#())
     , div^#(s(X), n__s(Y)) ->
       c_11(if^#(geq(X, activate(Y)),
                 n__s(div(minus(X, activate(Y)), n__s(activate(Y)))),
                 n__0()))
     , if^#(true(), X, Y) -> c_13(activate^#(X))
     , if^#(false(), X, Y) -> c_14(activate^#(Y)) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { minus^#(n__0(), Y) -> c_1(0^#())
     , minus^#(n__s(X), n__s(Y)) ->
       c_2(minus^#(activate(X), activate(Y)))
     , 0^#() -> c_3()
     , activate^#(X) -> c_4(X)
     , activate^#(n__0()) -> c_5(0^#())
     , activate^#(n__s(X)) -> c_6(s^#(X))
     , s^#(X) -> c_12(X)
     , geq^#(X, n__0()) -> c_7()
     , geq^#(n__0(), n__s(Y)) -> c_8()
     , geq^#(n__s(X), n__s(Y)) -> c_9(geq^#(activate(X), activate(Y)))
     , div^#(0(), n__s(Y)) -> c_10(0^#())
     , div^#(s(X), n__s(Y)) ->
       c_11(if^#(geq(X, activate(Y)),
                 n__s(div(minus(X, activate(Y)), n__s(activate(Y)))),
                 n__0()))
     , if^#(true(), X, Y) -> c_13(activate^#(X))
     , if^#(false(), X, Y) -> c_14(activate^#(Y)) }
   Strict Trs:
     { minus(n__0(), Y) -> 0()
     , minus(n__s(X), n__s(Y)) -> minus(activate(X), activate(Y))
     , 0() -> n__0()
     , activate(X) -> X
     , activate(n__0()) -> 0()
     , activate(n__s(X)) -> s(X)
     , geq(X, n__0()) -> true()
     , geq(n__0(), n__s(Y)) -> false()
     , geq(n__s(X), n__s(Y)) -> geq(activate(X), activate(Y))
     , div(0(), n__s(Y)) -> 0()
     , div(s(X), n__s(Y)) ->
       if(geq(X, activate(Y)),
          n__s(div(minus(X, activate(Y)), n__s(activate(Y)))),
          n__0())
     , s(X) -> n__s(X)
     , if(true(), X, Y) -> activate(X)
     , if(false(), X, Y) -> activate(Y) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3,8,9} by applications of
   Pre({3,8,9}) = {1,4,5,7,10,11}. Here rules are labeled as follows:
   
     DPs:
       { 1: minus^#(n__0(), Y) -> c_1(0^#())
       , 2: minus^#(n__s(X), n__s(Y)) ->
            c_2(minus^#(activate(X), activate(Y)))
       , 3: 0^#() -> c_3()
       , 4: activate^#(X) -> c_4(X)
       , 5: activate^#(n__0()) -> c_5(0^#())
       , 6: activate^#(n__s(X)) -> c_6(s^#(X))
       , 7: s^#(X) -> c_12(X)
       , 8: geq^#(X, n__0()) -> c_7()
       , 9: geq^#(n__0(), n__s(Y)) -> c_8()
       , 10: geq^#(n__s(X), n__s(Y)) ->
             c_9(geq^#(activate(X), activate(Y)))
       , 11: div^#(0(), n__s(Y)) -> c_10(0^#())
       , 12: div^#(s(X), n__s(Y)) ->
             c_11(if^#(geq(X, activate(Y)),
                       n__s(div(minus(X, activate(Y)), n__s(activate(Y)))),
                       n__0()))
       , 13: if^#(true(), X, Y) -> c_13(activate^#(X))
       , 14: if^#(false(), X, Y) -> c_14(activate^#(Y)) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { minus^#(n__0(), Y) -> c_1(0^#())
     , minus^#(n__s(X), n__s(Y)) ->
       c_2(minus^#(activate(X), activate(Y)))
     , activate^#(X) -> c_4(X)
     , activate^#(n__0()) -> c_5(0^#())
     , activate^#(n__s(X)) -> c_6(s^#(X))
     , s^#(X) -> c_12(X)
     , geq^#(n__s(X), n__s(Y)) -> c_9(geq^#(activate(X), activate(Y)))
     , div^#(0(), n__s(Y)) -> c_10(0^#())
     , div^#(s(X), n__s(Y)) ->
       c_11(if^#(geq(X, activate(Y)),
                 n__s(div(minus(X, activate(Y)), n__s(activate(Y)))),
                 n__0()))
     , if^#(true(), X, Y) -> c_13(activate^#(X))
     , if^#(false(), X, Y) -> c_14(activate^#(Y)) }
   Strict Trs:
     { minus(n__0(), Y) -> 0()
     , minus(n__s(X), n__s(Y)) -> minus(activate(X), activate(Y))
     , 0() -> n__0()
     , activate(X) -> X
     , activate(n__0()) -> 0()
     , activate(n__s(X)) -> s(X)
     , geq(X, n__0()) -> true()
     , geq(n__0(), n__s(Y)) -> false()
     , geq(n__s(X), n__s(Y)) -> geq(activate(X), activate(Y))
     , div(0(), n__s(Y)) -> 0()
     , div(s(X), n__s(Y)) ->
       if(geq(X, activate(Y)),
          n__s(div(minus(X, activate(Y)), n__s(activate(Y)))),
          n__0())
     , s(X) -> n__s(X)
     , if(true(), X, Y) -> activate(X)
     , if(false(), X, Y) -> activate(Y) }
   Weak DPs:
     { 0^#() -> c_3()
     , geq^#(X, n__0()) -> c_7()
     , geq^#(n__0(), n__s(Y)) -> c_8() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,4,8} by applications of
   Pre({1,4,8}) = {2,3,6,10,11}. Here rules are labeled as follows:
   
     DPs:
       { 1: minus^#(n__0(), Y) -> c_1(0^#())
       , 2: minus^#(n__s(X), n__s(Y)) ->
            c_2(minus^#(activate(X), activate(Y)))
       , 3: activate^#(X) -> c_4(X)
       , 4: activate^#(n__0()) -> c_5(0^#())
       , 5: activate^#(n__s(X)) -> c_6(s^#(X))
       , 6: s^#(X) -> c_12(X)
       , 7: geq^#(n__s(X), n__s(Y)) ->
            c_9(geq^#(activate(X), activate(Y)))
       , 8: div^#(0(), n__s(Y)) -> c_10(0^#())
       , 9: div^#(s(X), n__s(Y)) ->
            c_11(if^#(geq(X, activate(Y)),
                      n__s(div(minus(X, activate(Y)), n__s(activate(Y)))),
                      n__0()))
       , 10: if^#(true(), X, Y) -> c_13(activate^#(X))
       , 11: if^#(false(), X, Y) -> c_14(activate^#(Y))
       , 12: 0^#() -> c_3()
       , 13: geq^#(X, n__0()) -> c_7()
       , 14: geq^#(n__0(), n__s(Y)) -> c_8() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { minus^#(n__s(X), n__s(Y)) ->
       c_2(minus^#(activate(X), activate(Y)))
     , activate^#(X) -> c_4(X)
     , activate^#(n__s(X)) -> c_6(s^#(X))
     , s^#(X) -> c_12(X)
     , geq^#(n__s(X), n__s(Y)) -> c_9(geq^#(activate(X), activate(Y)))
     , div^#(s(X), n__s(Y)) ->
       c_11(if^#(geq(X, activate(Y)),
                 n__s(div(minus(X, activate(Y)), n__s(activate(Y)))),
                 n__0()))
     , if^#(true(), X, Y) -> c_13(activate^#(X))
     , if^#(false(), X, Y) -> c_14(activate^#(Y)) }
   Strict Trs:
     { minus(n__0(), Y) -> 0()
     , minus(n__s(X), n__s(Y)) -> minus(activate(X), activate(Y))
     , 0() -> n__0()
     , activate(X) -> X
     , activate(n__0()) -> 0()
     , activate(n__s(X)) -> s(X)
     , geq(X, n__0()) -> true()
     , geq(n__0(), n__s(Y)) -> false()
     , geq(n__s(X), n__s(Y)) -> geq(activate(X), activate(Y))
     , div(0(), n__s(Y)) -> 0()
     , div(s(X), n__s(Y)) ->
       if(geq(X, activate(Y)),
          n__s(div(minus(X, activate(Y)), n__s(activate(Y)))),
          n__0())
     , s(X) -> n__s(X)
     , if(true(), X, Y) -> activate(X)
     , if(false(), X, Y) -> activate(Y) }
   Weak DPs:
     { minus^#(n__0(), Y) -> c_1(0^#())
     , 0^#() -> c_3()
     , activate^#(n__0()) -> c_5(0^#())
     , geq^#(X, n__0()) -> c_7()
     , geq^#(n__0(), n__s(Y)) -> c_8()
     , div^#(0(), n__s(Y)) -> c_10(0^#()) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..