MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
        - Signature:
            {+/2,add0/2,mult/2,power/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+,add0,mult,power} and constructors {0,S}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          add0#(x,0()) -> c_1()
          add0#(x',S(x)) -> c_2(+#(S(0()),add0(x',x)),add0#(x',x))
          mult#(x,0()) -> c_3()
          mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
          power#(x,0()) -> c_5()
          power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        Weak DPs
          +#(x,S(0())) -> c_7()
          +#(S(0()),y) -> c_8()
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            add0#(x,0()) -> c_1()
            add0#(x',S(x)) -> c_2(+#(S(0()),add0(x',x)),add0#(x',x))
            mult#(x,0()) -> c_3()
            mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
            power#(x,0()) -> c_5()
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak DPs:
            +#(x,S(0())) -> c_7()
            +#(S(0()),y) -> c_8()
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/2,c_3/0,c_4/2,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,5}
        by application of
          Pre({1,3,5}) = {2,4,6}.
        Here rules are labelled as follows:
          1: add0#(x,0()) -> c_1()
          2: add0#(x',S(x)) -> c_2(+#(S(0()),add0(x',x)),add0#(x',x))
          3: mult#(x,0()) -> c_3()
          4: mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
          5: power#(x,0()) -> c_5()
          6: power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
          7: +#(x,S(0())) -> c_7()
          8: +#(S(0()),y) -> c_8()
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            add0#(x',S(x)) -> c_2(+#(S(0()),add0(x',x)),add0#(x',x))
            mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak DPs:
            +#(x,S(0())) -> c_7()
            +#(S(0()),y) -> c_8()
            add0#(x,0()) -> c_1()
            mult#(x,0()) -> c_3()
            power#(x,0()) -> c_5()
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/2,c_3/0,c_4/2,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:add0#(x',S(x)) -> c_2(+#(S(0()),add0(x',x)),add0#(x',x))
             -->_2 add0#(x,0()) -> c_1():6
             -->_1 +#(S(0()),y) -> c_8():5
             -->_1 +#(x,S(0())) -> c_7():4
             -->_2 add0#(x',S(x)) -> c_2(+#(S(0()),add0(x',x)),add0#(x',x)):1
          
          2:S:mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
             -->_2 mult#(x,0()) -> c_3():7
             -->_1 add0#(x,0()) -> c_1():6
             -->_2 mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x)):2
             -->_1 add0#(x',S(x)) -> c_2(+#(S(0()),add0(x',x)),add0#(x',x)):1
          
          3:S:power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
             -->_2 power#(x,0()) -> c_5():8
             -->_1 mult#(x,0()) -> c_3():7
             -->_2 power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x)):3
             -->_1 mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x)):2
          
          4:W:+#(x,S(0())) -> c_7()
             
          
          5:W:+#(S(0()),y) -> c_8()
             
          
          6:W:add0#(x,0()) -> c_1()
             
          
          7:W:mult#(x,0()) -> c_3()
             
          
          8:W:power#(x,0()) -> c_5()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          8: power#(x,0()) -> c_5()
          7: mult#(x,0()) -> c_3()
          4: +#(x,S(0())) -> c_7()
          5: +#(S(0()),y) -> c_8()
          6: add0#(x,0()) -> c_1()
* Step 4: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            add0#(x',S(x)) -> c_2(+#(S(0()),add0(x',x)),add0#(x',x))
            mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/2,c_3/0,c_4/2,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:add0#(x',S(x)) -> c_2(+#(S(0()),add0(x',x)),add0#(x',x))
             -->_2 add0#(x',S(x)) -> c_2(+#(S(0()),add0(x',x)),add0#(x',x)):1
          
          2:S:mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
             -->_2 mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x)):2
             -->_1 add0#(x',S(x)) -> c_2(+#(S(0()),add0(x',x)),add0#(x',x)):1
          
          3:S:power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
             -->_2 power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x)):3
             -->_1 mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x)):2
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          add0#(x',S(x)) -> c_2(add0#(x',x))
* Step 5: Decompose MAYBE
    + Considered Problem:
        - Strict DPs:
            add0#(x',S(x)) -> c_2(add0#(x',x))
            mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        Decompose {onSelection = all cycle independent sub-graph, withBound = RelativeAdd}
    + Details:
        We analyse the complexity of following sub-problems (R) and (S).
        Problem (S) is obtained from the input problem by shifting strict rules from (R) into the weak component.
        
        Problem (R)
          - Strict DPs:
              add0#(x',S(x)) -> c_2(add0#(x',x))
          - Weak DPs:
              mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
              power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
          - Weak TRS:
              +(x,S(0())) -> S(x)
              +(S(0()),y) -> S(y)
              add0(x,0()) -> x
              add0(x',S(x)) -> +(S(0()),add0(x',x))
              mult(x,0()) -> 0()
              mult(x',S(x)) -> add0(x',mult(x',x))
              power(x,0()) -> S(0())
              power(x',S(x)) -> mult(x',power(x',x))
          - Signature:
              {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/2
              ,c_7/0,c_8/0}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
        
        Problem (S)
          - Strict DPs:
              mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
              power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
          - Weak DPs:
              add0#(x',S(x)) -> c_2(add0#(x',x))
          - Weak TRS:
              +(x,S(0())) -> S(x)
              +(S(0()),y) -> S(y)
              add0(x,0()) -> x
              add0(x',S(x)) -> +(S(0()),add0(x',x))
              mult(x,0()) -> 0()
              mult(x',S(x)) -> add0(x',mult(x',x))
              power(x,0()) -> S(0())
              power(x',S(x)) -> mult(x',power(x',x))
          - Signature:
              {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/2
              ,c_7/0,c_8/0}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
** Step 5.a:1: DecomposeDG MAYBE
    + Considered Problem:
        - Strict DPs:
            add0#(x',S(x)) -> c_2(add0#(x',x))
        - Weak DPs:
            mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        DecomposeDG {onSelection = all below first cut in WDG, onUpper = Just someStrategy, onLower = Nothing}
    + Details:
        We decompose the input problem according to the dependency graph into the upper component
          power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        and a lower component
          add0#(x',S(x)) -> c_2(add0#(x',x))
          mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
        Further, following extension rules are added to the lower component.
          power#(x',S(x)) -> mult#(x',power(x',x))
          power#(x',S(x)) -> power#(x',x)
*** Step 5.a:1.a:1: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
          
        The strictly oriented rules are moved into the weak component.
**** Step 5.a:1.a:1.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_6) = {1,2}
        
        Following symbols are considered usable:
          {+#,add0#,mult#,power#}
        TcT has computed the following interpretation:
               p(+) = [1] x1 + [3] x2 + [1] 
               p(0) = [2]                   
               p(S) = [1] x1 + [4]          
            p(add0) = [2]                   
            p(mult) = [4] x2 + [8]          
           p(power) = [0]                   
              p(+#) = [1] x1 + [0]          
           p(add0#) = [4] x1 + [1] x2 + [1] 
           p(mult#) = [1]                   
          p(power#) = [4] x1 + [4] x2 + [8] 
             p(c_1) = [2]                   
             p(c_2) = [2] x1 + [1]          
             p(c_3) = [8]                   
             p(c_4) = [1] x1 + [4]          
             p(c_5) = [8]                   
             p(c_6) = [1] x1 + [1] x2 + [11]
             p(c_7) = [1]                   
             p(c_8) = [1]                   
        
        Following rules are strictly oriented:
        power#(x',S(x)) = [4] x + [4] x' + [24]                  
                        > [4] x + [4] x' + [20]                  
                        = c_6(mult#(x',power(x',x)),power#(x',x))
        
        
        Following rules are (at-least) weakly oriented:
        
**** Step 5.a:1.a:1.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

**** Step 5.a:1.a:1.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
             -->_2 power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
**** Step 5.a:1.a:1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

*** Step 5.a:1.b:1: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          add0#(x',S(x)) -> c_2(add0#(x',x))
      - Weak DPs:
          mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
          power#(x',S(x)) -> mult#(x',power(x',x))
          power#(x',S(x)) -> power#(x',x)
      - Weak TRS:
          +(x,S(0())) -> S(x)
          +(S(0()),y) -> S(y)
          add0(x,0()) -> x
          add0(x',S(x)) -> +(S(0()),add0(x',x))
          mult(x,0()) -> 0()
          mult(x',S(x)) -> add0(x',mult(x',x))
          power(x,0()) -> S(0())
          power(x',S(x)) -> mult(x',power(x',x))
      - Signature:
          {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/2
          ,c_7/0,c_8/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
** Step 5.b:1: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak DPs:
            add0#(x',S(x)) -> c_2(add0#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
             -->_1 add0#(x',S(x)) -> c_2(add0#(x',x)):3
             -->_2 mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x)):1
          
          2:S:power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
             -->_2 power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x)):2
             -->_1 mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x)):1
          
          3:W:add0#(x',S(x)) -> c_2(add0#(x',x))
             -->_1 add0#(x',S(x)) -> c_2(add0#(x',x)):3
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          3: add0#(x',S(x)) -> c_2(add0#(x',x))
** Step 5.b:2: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x))
             -->_2 mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x)):1
          
          2:S:power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
             -->_2 power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x)):2
             -->_1 mult#(x',S(x)) -> c_4(add0#(x',mult(x',x)),mult#(x',x)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          mult#(x',S(x)) -> c_4(mult#(x',x))
** Step 5.b:3: Decompose MAYBE
    + Considered Problem:
        - Strict DPs:
            mult#(x',S(x)) -> c_4(mult#(x',x))
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        Decompose {onSelection = all cycle independent sub-graph, withBound = RelativeAdd}
    + Details:
        We analyse the complexity of following sub-problems (R) and (S).
        Problem (S) is obtained from the input problem by shifting strict rules from (R) into the weak component.
        
        Problem (R)
          - Strict DPs:
              mult#(x',S(x)) -> c_4(mult#(x',x))
          - Weak DPs:
              power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
          - Weak TRS:
              +(x,S(0())) -> S(x)
              +(S(0()),y) -> S(y)
              add0(x,0()) -> x
              add0(x',S(x)) -> +(S(0()),add0(x',x))
              mult(x,0()) -> 0()
              mult(x',S(x)) -> add0(x',mult(x',x))
              power(x,0()) -> S(0())
              power(x',S(x)) -> mult(x',power(x',x))
          - Signature:
              {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/2
              ,c_7/0,c_8/0}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
        
        Problem (S)
          - Strict DPs:
              power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
          - Weak DPs:
              mult#(x',S(x)) -> c_4(mult#(x',x))
          - Weak TRS:
              +(x,S(0())) -> S(x)
              +(S(0()),y) -> S(y)
              add0(x,0()) -> x
              add0(x',S(x)) -> +(S(0()),add0(x',x))
              mult(x,0()) -> 0()
              mult(x',S(x)) -> add0(x',mult(x',x))
              power(x,0()) -> S(0())
              power(x',S(x)) -> mult(x',power(x',x))
          - Signature:
              {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/2
              ,c_7/0,c_8/0}
          - Obligation:
              innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
*** Step 5.b:3.a:1: DecomposeDG MAYBE
    + Considered Problem:
        - Strict DPs:
            mult#(x',S(x)) -> c_4(mult#(x',x))
        - Weak DPs:
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        DecomposeDG {onSelection = all below first cut in WDG, onUpper = Just someStrategy, onLower = Nothing}
    + Details:
        We decompose the input problem according to the dependency graph into the upper component
          power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        and a lower component
          mult#(x',S(x)) -> c_4(mult#(x',x))
        Further, following extension rules are added to the lower component.
          power#(x',S(x)) -> mult#(x',power(x',x))
          power#(x',S(x)) -> power#(x',x)
**** Step 5.b:3.a:1.a:1: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
          
        The strictly oriented rules are moved into the weak component.
***** Step 5.b:3.a:1.a:1.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_6) = {1,2}
        
        Following symbols are considered usable:
          {+#,add0#,mult#,power#}
        TcT has computed the following interpretation:
               p(+) = [2] x2 + [0]         
               p(0) = [0]                  
               p(S) = [1] x1 + [9]         
            p(add0) = [1] x2 + [0]         
            p(mult) = [0]                  
           p(power) = [0]                  
              p(+#) = [0]                  
           p(add0#) = [0]                  
           p(mult#) = [2]                  
          p(power#) = [2] x2 + [5]         
             p(c_1) = [0]                  
             p(c_2) = [0]                  
             p(c_3) = [0]                  
             p(c_4) = [0]                  
             p(c_5) = [2]                  
             p(c_6) = [4] x1 + [1] x2 + [1]
             p(c_7) = [0]                  
             p(c_8) = [0]                  
        
        Following rules are strictly oriented:
        power#(x',S(x)) = [2] x + [23]                           
                        > [2] x + [14]                           
                        = c_6(mult#(x',power(x',x)),power#(x',x))
        
        
        Following rules are (at-least) weakly oriented:
        
***** Step 5.b:3.a:1.a:1.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

***** Step 5.b:3.a:1.a:1.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
             -->_2 power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
***** Step 5.b:3.a:1.a:1.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

**** Step 5.b:3.a:1.b:1: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          mult#(x',S(x)) -> c_4(mult#(x',x))
      - Weak DPs:
          power#(x',S(x)) -> mult#(x',power(x',x))
          power#(x',S(x)) -> power#(x',x)
      - Weak TRS:
          +(x,S(0())) -> S(x)
          +(S(0()),y) -> S(y)
          add0(x,0()) -> x
          add0(x',S(x)) -> +(S(0()),add0(x',x))
          mult(x,0()) -> 0()
          mult(x',S(x)) -> add0(x',mult(x',x))
          power(x,0()) -> S(0())
          power(x',S(x)) -> mult(x',power(x',x))
      - Signature:
          {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/2
          ,c_7/0,c_8/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
*** Step 5.b:3.b:1: RemoveWeakSuffixes WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak DPs:
            mult#(x',S(x)) -> c_4(mult#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
             -->_1 mult#(x',S(x)) -> c_4(mult#(x',x)):2
             -->_2 power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x)):1
          
          2:W:mult#(x',S(x)) -> c_4(mult#(x',x))
             -->_1 mult#(x',S(x)) -> c_4(mult#(x',x)):2
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          2: mult#(x',S(x)) -> c_4(mult#(x',x))
*** Step 5.b:3.b:2: SimplifyRHS WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/2
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x))
             -->_2 power#(x',S(x)) -> c_6(mult#(x',power(x',x)),power#(x',x)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          power#(x',S(x)) -> c_6(power#(x',x))
*** Step 5.b:3.b:3: UsableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',S(x)) -> c_6(power#(x',x))
        - Weak TRS:
            +(x,S(0())) -> S(x)
            +(S(0()),y) -> S(y)
            add0(x,0()) -> x
            add0(x',S(x)) -> +(S(0()),add0(x',x))
            mult(x,0()) -> 0()
            mult(x',S(x)) -> add0(x',mult(x',x))
            power(x,0()) -> S(0())
            power(x',S(x)) -> mult(x',power(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/1
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          power#(x',S(x)) -> c_6(power#(x',x))
*** Step 5.b:3.b:4: PredecessorEstimationCP WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',S(x)) -> c_6(power#(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/1
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}}
    + Details:
        We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly:
          1: power#(x',S(x)) -> c_6(power#(x',x))
          
        The strictly oriented rules are moved into the weak component.
**** Step 5.b:3.b:4.a:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            power#(x',S(x)) -> c_6(power#(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/1
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_6) = {1}
        
        Following symbols are considered usable:
          {+#,add0#,mult#,power#}
        TcT has computed the following interpretation:
               p(+) = [1] x2 + [2]         
               p(0) = [0]                  
               p(S) = [1] x1 + [4]         
            p(add0) = [1] x1 + [1] x2 + [2]
            p(mult) = [1] x2 + [1]         
           p(power) = [8] x2 + [0]         
              p(+#) = [1] x1 + [1]         
           p(add0#) = [2] x1 + [1]         
           p(mult#) = [8] x2 + [1]         
          p(power#) = [4] x1 + [4] x2 + [0]
             p(c_1) = [0]                  
             p(c_2) = [2] x1 + [1]         
             p(c_3) = [1]                  
             p(c_4) = [1]                  
             p(c_5) = [1]                  
             p(c_6) = [1] x1 + [14]        
             p(c_7) = [0]                  
             p(c_8) = [0]                  
        
        Following rules are strictly oriented:
        power#(x',S(x)) = [4] x + [4] x' + [16]
                        > [4] x + [4] x' + [14]
                        = c_6(power#(x',x))    
        
        
        Following rules are (at-least) weakly oriented:
        
**** Step 5.b:3.b:4.a:2: Assumption WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            power#(x',S(x)) -> c_6(power#(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/1
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        Assumption {assumed = Certificate {spaceUB = Unknown, spaceLB = Unknown, timeUB = Poly (Just 0), timeLB = Unknown}}
    + Details:
        ()

**** Step 5.b:3.b:4.b:1: RemoveWeakSuffixes WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            power#(x',S(x)) -> c_6(power#(x',x))
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/1
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:power#(x',S(x)) -> c_6(power#(x',x))
             -->_1 power#(x',S(x)) -> c_6(power#(x',x)):1
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          1: power#(x',S(x)) -> c_6(power#(x',x))
**** Step 5.b:3.b:4.b:2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {+/2,add0/2,mult/2,power/2,+#/2,add0#/2,mult#/2,power#/2} / {0/0,S/1,c_1/0,c_2/1,c_3/0,c_4/1,c_5/0,c_6/1
            ,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {+#,add0#,mult#,power#} and constructors {0,S}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

MAYBE