MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            *(x,0()) -> 0()
            *(x,s(y)) -> +(x,*(x,y))
            +(0(),y) -> y
            +(s(x),y) -> s(+(x,y))
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            f(s(x)) -> f(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
            twice(0()) -> 0()
            twice(s(x)) -> s(s(twice(x)))
        - Signature:
            {*/2,+/2,-/2,f/1,twice/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*,+,-,f,twice} and constructors {0,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          *#(x,0()) -> c_1()
          *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
          +#(0(),y) -> c_3()
          +#(s(x),y) -> c_4(+#(x,y))
          -#(x,0()) -> c_5()
          -#(s(x),s(y)) -> c_6(-#(x,y))
          f#(s(x)) -> c_7(f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
                         ,-#(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))
                         ,*#(s(s(x)),s(s(x)))
                         ,+#(*(s(x),s(s(x))),s(s(0())))
                         ,*#(s(x),s(s(x))))
          twice#(0()) -> c_8()
          twice#(s(x)) -> c_9(twice#(x))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(x,0()) -> c_1()
            *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
            +#(0(),y) -> c_3()
            +#(s(x),y) -> c_4(+#(x,y))
            -#(x,0()) -> c_5()
            -#(s(x),s(y)) -> c_6(-#(x,y))
            f#(s(x)) -> c_7(f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
                           ,-#(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))
                           ,*#(s(s(x)),s(s(x)))
                           ,+#(*(s(x),s(s(x))),s(s(0())))
                           ,*#(s(x),s(s(x))))
            twice#(0()) -> c_8()
            twice#(s(x)) -> c_9(twice#(x))
        - Weak TRS:
            *(x,0()) -> 0()
            *(x,s(y)) -> +(x,*(x,y))
            +(0(),y) -> y
            +(s(x),y) -> s(+(x,y))
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            f(s(x)) -> f(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
            twice(0()) -> 0()
            twice(s(x)) -> s(s(twice(x)))
        - Signature:
            {*/2,+/2,-/2,f/1,twice/1,*#/2,+#/2,-#/2,f#/1,twice#/1} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/5
            ,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,-#,f#,twice#} and constructors {0,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          *(x,0()) -> 0()
          *(x,s(y)) -> +(x,*(x,y))
          +(0(),y) -> y
          +(s(x),y) -> s(+(x,y))
          -(x,0()) -> x
          -(s(x),s(y)) -> -(x,y)
          *#(x,0()) -> c_1()
          *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
          +#(0(),y) -> c_3()
          +#(s(x),y) -> c_4(+#(x,y))
          -#(x,0()) -> c_5()
          -#(s(x),s(y)) -> c_6(-#(x,y))
          f#(s(x)) -> c_7(f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
                         ,-#(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))
                         ,*#(s(s(x)),s(s(x)))
                         ,+#(*(s(x),s(s(x))),s(s(0())))
                         ,*#(s(x),s(s(x))))
          twice#(0()) -> c_8()
          twice#(s(x)) -> c_9(twice#(x))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(x,0()) -> c_1()
            *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
            +#(0(),y) -> c_3()
            +#(s(x),y) -> c_4(+#(x,y))
            -#(x,0()) -> c_5()
            -#(s(x),s(y)) -> c_6(-#(x,y))
            f#(s(x)) -> c_7(f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
                           ,-#(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))
                           ,*#(s(s(x)),s(s(x)))
                           ,+#(*(s(x),s(s(x))),s(s(0())))
                           ,*#(s(x),s(s(x))))
            twice#(0()) -> c_8()
            twice#(s(x)) -> c_9(twice#(x))
        - Weak TRS:
            *(x,0()) -> 0()
            *(x,s(y)) -> +(x,*(x,y))
            +(0(),y) -> y
            +(s(x),y) -> s(+(x,y))
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
        - Signature:
            {*/2,+/2,-/2,f/1,twice/1,*#/2,+#/2,-#/2,f#/1,twice#/1} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/5
            ,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,-#,f#,twice#} and constructors {0,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,5,8}
        by application of
          Pre({1,3,5,8}) = {2,4,6,7,9}.
        Here rules are labelled as follows:
          1: *#(x,0()) -> c_1()
          2: *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
          3: +#(0(),y) -> c_3()
          4: +#(s(x),y) -> c_4(+#(x,y))
          5: -#(x,0()) -> c_5()
          6: -#(s(x),s(y)) -> c_6(-#(x,y))
          7: f#(s(x)) -> c_7(f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
                            ,-#(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))
                            ,*#(s(s(x)),s(s(x)))
                            ,+#(*(s(x),s(s(x))),s(s(0())))
                            ,*#(s(x),s(s(x))))
          8: twice#(0()) -> c_8()
          9: twice#(s(x)) -> c_9(twice#(x))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
            +#(s(x),y) -> c_4(+#(x,y))
            -#(s(x),s(y)) -> c_6(-#(x,y))
            f#(s(x)) -> c_7(f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
                           ,-#(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))
                           ,*#(s(s(x)),s(s(x)))
                           ,+#(*(s(x),s(s(x))),s(s(0())))
                           ,*#(s(x),s(s(x))))
            twice#(s(x)) -> c_9(twice#(x))
        - Weak DPs:
            *#(x,0()) -> c_1()
            +#(0(),y) -> c_3()
            -#(x,0()) -> c_5()
            twice#(0()) -> c_8()
        - Weak TRS:
            *(x,0()) -> 0()
            *(x,s(y)) -> +(x,*(x,y))
            +(0(),y) -> y
            +(s(x),y) -> s(+(x,y))
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
        - Signature:
            {*/2,+/2,-/2,f/1,twice/1,*#/2,+#/2,-#/2,f#/1,twice#/1} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/5
            ,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,-#,f#,twice#} and constructors {0,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:*#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
             -->_1 +#(s(x),y) -> c_4(+#(x,y)):2
             -->_1 +#(0(),y) -> c_3():7
             -->_2 *#(x,0()) -> c_1():6
             -->_2 *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y)):1
          
          2:S:+#(s(x),y) -> c_4(+#(x,y))
             -->_1 +#(0(),y) -> c_3():7
             -->_1 +#(s(x),y) -> c_4(+#(x,y)):2
          
          3:S:-#(s(x),s(y)) -> c_6(-#(x,y))
             -->_1 -#(x,0()) -> c_5():8
             -->_1 -#(s(x),s(y)) -> c_6(-#(x,y)):3
          
          4:S:f#(s(x)) -> c_7(f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
                             ,-#(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))
                             ,*#(s(s(x)),s(s(x)))
                             ,+#(*(s(x),s(s(x))),s(s(0())))
                             ,*#(s(x),s(s(x))))
             -->_2 -#(x,0()) -> c_5():8
             -->_4 +#(0(),y) -> c_3():7
             -->_1 f#(s(x)) -> c_7(f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
                                  ,-#(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))
                                  ,*#(s(s(x)),s(s(x)))
                                  ,+#(*(s(x),s(s(x))),s(s(0())))
                                  ,*#(s(x),s(s(x)))):4
             -->_2 -#(s(x),s(y)) -> c_6(-#(x,y)):3
             -->_4 +#(s(x),y) -> c_4(+#(x,y)):2
             -->_5 *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y)):1
             -->_3 *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y)):1
          
          5:S:twice#(s(x)) -> c_9(twice#(x))
             -->_1 twice#(0()) -> c_8():9
             -->_1 twice#(s(x)) -> c_9(twice#(x)):5
          
          6:W:*#(x,0()) -> c_1()
             
          
          7:W:+#(0(),y) -> c_3()
             
          
          8:W:-#(x,0()) -> c_5()
             
          
          9:W:twice#(0()) -> c_8()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          9: twice#(0()) -> c_8()
          8: -#(x,0()) -> c_5()
          6: *#(x,0()) -> c_1()
          7: +#(0(),y) -> c_3()
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          *#(x,s(y)) -> c_2(+#(x,*(x,y)),*#(x,y))
          +#(s(x),y) -> c_4(+#(x,y))
          -#(s(x),s(y)) -> c_6(-#(x,y))
          f#(s(x)) -> c_7(f#(-(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0())))))
                         ,-#(*(s(s(x)),s(s(x))),+(*(s(x),s(s(x))),s(s(0()))))
                         ,*#(s(s(x)),s(s(x)))
                         ,+#(*(s(x),s(s(x))),s(s(0())))
                         ,*#(s(x),s(s(x))))
          twice#(s(x)) -> c_9(twice#(x))
      - Weak TRS:
          *(x,0()) -> 0()
          *(x,s(y)) -> +(x,*(x,y))
          +(0(),y) -> y
          +(s(x),y) -> s(+(x,y))
          -(x,0()) -> x
          -(s(x),s(y)) -> -(x,y)
      - Signature:
          {*/2,+/2,-/2,f/1,twice/1,*#/2,+#/2,-#/2,f#/1,twice#/1} / {0/0,s/1,c_1/0,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/5
          ,c_8/0,c_9/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {*#,+#,-#,f#,twice#} and constructors {0,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE