MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            *(x,0()) -> 0()
            *(x,s(y)) -> +(*(x,y),x)
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            fact(x) -> iffact(x,ge(x,s(s(0()))))
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            iffact(x,false()) -> s(0())
            iffact(x,true()) -> *(x,fact(-(x,s(0()))))
        - Signature:
            {*/2,+/2,-/2,fact/1,ge/2,iffact/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*,+,-,fact,ge,iffact} and constructors {0,false,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          *#(x,0()) -> c_1()
          *#(x,s(y)) -> c_2(+#(*(x,y),x),*#(x,y))
          +#(x,0()) -> c_3()
          +#(x,s(y)) -> c_4(+#(x,y))
          -#(x,0()) -> c_5()
          -#(s(x),s(y)) -> c_6(-#(x,y))
          fact#(x) -> c_7(iffact#(x,ge(x,s(s(0())))),ge#(x,s(s(0()))))
          ge#(x,0()) -> c_8()
          ge#(0(),s(y)) -> c_9()
          ge#(s(x),s(y)) -> c_10(ge#(x,y))
          iffact#(x,false()) -> c_11()
          iffact#(x,true()) -> c_12(*#(x,fact(-(x,s(0())))),fact#(-(x,s(0()))),-#(x,s(0())))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(x,0()) -> c_1()
            *#(x,s(y)) -> c_2(+#(*(x,y),x),*#(x,y))
            +#(x,0()) -> c_3()
            +#(x,s(y)) -> c_4(+#(x,y))
            -#(x,0()) -> c_5()
            -#(s(x),s(y)) -> c_6(-#(x,y))
            fact#(x) -> c_7(iffact#(x,ge(x,s(s(0())))),ge#(x,s(s(0()))))
            ge#(x,0()) -> c_8()
            ge#(0(),s(y)) -> c_9()
            ge#(s(x),s(y)) -> c_10(ge#(x,y))
            iffact#(x,false()) -> c_11()
            iffact#(x,true()) -> c_12(*#(x,fact(-(x,s(0())))),fact#(-(x,s(0()))),-#(x,s(0())))
        - Weak TRS:
            *(x,0()) -> 0()
            *(x,s(y)) -> +(*(x,y),x)
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            fact(x) -> iffact(x,ge(x,s(s(0()))))
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            iffact(x,false()) -> s(0())
            iffact(x,true()) -> *(x,fact(-(x,s(0()))))
        - Signature:
            {*/2,+/2,-/2,fact/1,ge/2,iffact/2,*#/2,+#/2,-#/2,fact#/1,ge#/2,iffact#/2} / {0/0,false/0,s/1,true/0,c_1/0
            ,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/2,c_8/0,c_9/0,c_10/1,c_11/0,c_12/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,-#,fact#,ge#,iffact#} and constructors {0,false,s
            ,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,5,8,9,11}
        by application of
          Pre({1,3,5,8,9,11}) = {2,4,6,7,10,12}.
        Here rules are labelled as follows:
          1: *#(x,0()) -> c_1()
          2: *#(x,s(y)) -> c_2(+#(*(x,y),x),*#(x,y))
          3: +#(x,0()) -> c_3()
          4: +#(x,s(y)) -> c_4(+#(x,y))
          5: -#(x,0()) -> c_5()
          6: -#(s(x),s(y)) -> c_6(-#(x,y))
          7: fact#(x) -> c_7(iffact#(x,ge(x,s(s(0())))),ge#(x,s(s(0()))))
          8: ge#(x,0()) -> c_8()
          9: ge#(0(),s(y)) -> c_9()
          10: ge#(s(x),s(y)) -> c_10(ge#(x,y))
          11: iffact#(x,false()) -> c_11()
          12: iffact#(x,true()) -> c_12(*#(x,fact(-(x,s(0())))),fact#(-(x,s(0()))),-#(x,s(0())))
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            *#(x,s(y)) -> c_2(+#(*(x,y),x),*#(x,y))
            +#(x,s(y)) -> c_4(+#(x,y))
            -#(s(x),s(y)) -> c_6(-#(x,y))
            fact#(x) -> c_7(iffact#(x,ge(x,s(s(0())))),ge#(x,s(s(0()))))
            ge#(s(x),s(y)) -> c_10(ge#(x,y))
            iffact#(x,true()) -> c_12(*#(x,fact(-(x,s(0())))),fact#(-(x,s(0()))),-#(x,s(0())))
        - Weak DPs:
            *#(x,0()) -> c_1()
            +#(x,0()) -> c_3()
            -#(x,0()) -> c_5()
            ge#(x,0()) -> c_8()
            ge#(0(),s(y)) -> c_9()
            iffact#(x,false()) -> c_11()
        - Weak TRS:
            *(x,0()) -> 0()
            *(x,s(y)) -> +(*(x,y),x)
            +(x,0()) -> x
            +(x,s(y)) -> s(+(x,y))
            -(x,0()) -> x
            -(s(x),s(y)) -> -(x,y)
            fact(x) -> iffact(x,ge(x,s(s(0()))))
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            iffact(x,false()) -> s(0())
            iffact(x,true()) -> *(x,fact(-(x,s(0()))))
        - Signature:
            {*/2,+/2,-/2,fact/1,ge/2,iffact/2,*#/2,+#/2,-#/2,fact#/1,ge#/2,iffact#/2} / {0/0,false/0,s/1,true/0,c_1/0
            ,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/2,c_8/0,c_9/0,c_10/1,c_11/0,c_12/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*#,+#,-#,fact#,ge#,iffact#} and constructors {0,false,s
            ,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:*#(x,s(y)) -> c_2(+#(*(x,y),x),*#(x,y))
             -->_1 +#(x,s(y)) -> c_4(+#(x,y)):2
             -->_1 +#(x,0()) -> c_3():8
             -->_2 *#(x,0()) -> c_1():7
             -->_2 *#(x,s(y)) -> c_2(+#(*(x,y),x),*#(x,y)):1
          
          2:S:+#(x,s(y)) -> c_4(+#(x,y))
             -->_1 +#(x,0()) -> c_3():8
             -->_1 +#(x,s(y)) -> c_4(+#(x,y)):2
          
          3:S:-#(s(x),s(y)) -> c_6(-#(x,y))
             -->_1 -#(x,0()) -> c_5():9
             -->_1 -#(s(x),s(y)) -> c_6(-#(x,y)):3
          
          4:S:fact#(x) -> c_7(iffact#(x,ge(x,s(s(0())))),ge#(x,s(s(0()))))
             -->_1 iffact#(x,true()) -> c_12(*#(x,fact(-(x,s(0())))),fact#(-(x,s(0()))),-#(x,s(0()))):6
             -->_2 ge#(s(x),s(y)) -> c_10(ge#(x,y)):5
             -->_1 iffact#(x,false()) -> c_11():12
             -->_2 ge#(0(),s(y)) -> c_9():11
          
          5:S:ge#(s(x),s(y)) -> c_10(ge#(x,y))
             -->_1 ge#(0(),s(y)) -> c_9():11
             -->_1 ge#(x,0()) -> c_8():10
             -->_1 ge#(s(x),s(y)) -> c_10(ge#(x,y)):5
          
          6:S:iffact#(x,true()) -> c_12(*#(x,fact(-(x,s(0())))),fact#(-(x,s(0()))),-#(x,s(0())))
             -->_1 *#(x,0()) -> c_1():7
             -->_2 fact#(x) -> c_7(iffact#(x,ge(x,s(s(0())))),ge#(x,s(s(0())))):4
             -->_3 -#(s(x),s(y)) -> c_6(-#(x,y)):3
             -->_1 *#(x,s(y)) -> c_2(+#(*(x,y),x),*#(x,y)):1
          
          7:W:*#(x,0()) -> c_1()
             
          
          8:W:+#(x,0()) -> c_3()
             
          
          9:W:-#(x,0()) -> c_5()
             
          
          10:W:ge#(x,0()) -> c_8()
             
          
          11:W:ge#(0(),s(y)) -> c_9()
             
          
          12:W:iffact#(x,false()) -> c_11()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          12: iffact#(x,false()) -> c_11()
          10: ge#(x,0()) -> c_8()
          11: ge#(0(),s(y)) -> c_9()
          9: -#(x,0()) -> c_5()
          7: *#(x,0()) -> c_1()
          8: +#(x,0()) -> c_3()
* Step 4: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          *#(x,s(y)) -> c_2(+#(*(x,y),x),*#(x,y))
          +#(x,s(y)) -> c_4(+#(x,y))
          -#(s(x),s(y)) -> c_6(-#(x,y))
          fact#(x) -> c_7(iffact#(x,ge(x,s(s(0())))),ge#(x,s(s(0()))))
          ge#(s(x),s(y)) -> c_10(ge#(x,y))
          iffact#(x,true()) -> c_12(*#(x,fact(-(x,s(0())))),fact#(-(x,s(0()))),-#(x,s(0())))
      - Weak TRS:
          *(x,0()) -> 0()
          *(x,s(y)) -> +(*(x,y),x)
          +(x,0()) -> x
          +(x,s(y)) -> s(+(x,y))
          -(x,0()) -> x
          -(s(x),s(y)) -> -(x,y)
          fact(x) -> iffact(x,ge(x,s(s(0()))))
          ge(x,0()) -> true()
          ge(0(),s(y)) -> false()
          ge(s(x),s(y)) -> ge(x,y)
          iffact(x,false()) -> s(0())
          iffact(x,true()) -> *(x,fact(-(x,s(0()))))
      - Signature:
          {*/2,+/2,-/2,fact/1,ge/2,iffact/2,*#/2,+#/2,-#/2,fact#/1,ge#/2,iffact#/2} / {0/0,false/0,s/1,true/0,c_1/0
          ,c_2/2,c_3/0,c_4/1,c_5/0,c_6/1,c_7/2,c_8/0,c_9/0,c_10/1,c_11/0,c_12/3}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {*#,+#,-#,fact#,ge#,iffact#} and constructors {0,false,s
          ,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE