WORST_CASE(?,O(n^2))
* Step 1: DependencyPairs WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
            U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
            U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            plus(N,0()) -> N
            plus(N,s(M)) -> U11(tt(),M,N)
            x(N,0()) -> 0()
            x(N,s(M)) -> U21(tt(),M,N)
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2} / {0/0,s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11,U12,U21,U22,activate,plus,x} and constructors {0,s
            ,tt}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)),activate#(M),activate#(N))
          U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)),activate#(N),activate#(M))
          U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)),activate#(M),activate#(N))
          U22#(tt(),M,N) -> c_4(plus#(x(activate(N),activate(M)),activate(N))
                               ,x#(activate(N),activate(M))
                               ,activate#(N)
                               ,activate#(M)
                               ,activate#(N))
          activate#(X) -> c_5()
          plus#(N,0()) -> c_6()
          plus#(N,s(M)) -> c_7(U11#(tt(),M,N))
          x#(N,0()) -> c_8()
          x#(N,s(M)) -> c_9(U21#(tt(),M,N))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)),activate#(M),activate#(N))
            U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)),activate#(N),activate#(M))
            U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)),activate#(M),activate#(N))
            U22#(tt(),M,N) -> c_4(plus#(x(activate(N),activate(M)),activate(N))
                                 ,x#(activate(N),activate(M))
                                 ,activate#(N)
                                 ,activate#(M)
                                 ,activate#(N))
            activate#(X) -> c_5()
            plus#(N,0()) -> c_6()
            plus#(N,s(M)) -> c_7(U11#(tt(),M,N))
            x#(N,0()) -> c_8()
            x#(N,s(M)) -> c_9(U21#(tt(),M,N))
        - Weak TRS:
            U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
            U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
            U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            plus(N,0()) -> N
            plus(N,s(M)) -> U11(tt(),M,N)
            x(N,0()) -> 0()
            x(N,s(M)) -> U21(tt(),M,N)
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2,U11#/3,U12#/3,U21#/3,U22#/3,activate#/1,plus#/2,x#/2} / {0/0
            ,s/1,tt/0,c_1/3,c_2/3,c_3/3,c_4/5,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,activate#,plus#
            ,x#} and constructors {0,s,tt}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {5,6,8}
        by application of
          Pre({5,6,8}) = {1,2,3,4}.
        Here rules are labelled as follows:
          1: U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)),activate#(M),activate#(N))
          2: U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)),activate#(N),activate#(M))
          3: U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)),activate#(M),activate#(N))
          4: U22#(tt(),M,N) -> c_4(plus#(x(activate(N),activate(M)),activate(N))
                                  ,x#(activate(N),activate(M))
                                  ,activate#(N)
                                  ,activate#(M)
                                  ,activate#(N))
          5: activate#(X) -> c_5()
          6: plus#(N,0()) -> c_6()
          7: plus#(N,s(M)) -> c_7(U11#(tt(),M,N))
          8: x#(N,0()) -> c_8()
          9: x#(N,s(M)) -> c_9(U21#(tt(),M,N))
* Step 3: RemoveWeakSuffixes WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)),activate#(M),activate#(N))
            U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)),activate#(N),activate#(M))
            U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)),activate#(M),activate#(N))
            U22#(tt(),M,N) -> c_4(plus#(x(activate(N),activate(M)),activate(N))
                                 ,x#(activate(N),activate(M))
                                 ,activate#(N)
                                 ,activate#(M)
                                 ,activate#(N))
            plus#(N,s(M)) -> c_7(U11#(tt(),M,N))
            x#(N,s(M)) -> c_9(U21#(tt(),M,N))
        - Weak DPs:
            activate#(X) -> c_5()
            plus#(N,0()) -> c_6()
            x#(N,0()) -> c_8()
        - Weak TRS:
            U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
            U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
            U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            plus(N,0()) -> N
            plus(N,s(M)) -> U11(tt(),M,N)
            x(N,0()) -> 0()
            x(N,s(M)) -> U21(tt(),M,N)
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2,U11#/3,U12#/3,U21#/3,U22#/3,activate#/1,plus#/2,x#/2} / {0/0
            ,s/1,tt/0,c_1/3,c_2/3,c_3/3,c_4/5,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,activate#,plus#
            ,x#} and constructors {0,s,tt}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)),activate#(M),activate#(N))
             -->_1 U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)),activate#(N),activate#(M)):2
             -->_3 activate#(X) -> c_5():7
             -->_2 activate#(X) -> c_5():7
          
          2:S:U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)),activate#(N),activate#(M))
             -->_1 plus#(N,s(M)) -> c_7(U11#(tt(),M,N)):5
             -->_1 plus#(N,0()) -> c_6():8
             -->_3 activate#(X) -> c_5():7
             -->_2 activate#(X) -> c_5():7
          
          3:S:U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)),activate#(M),activate#(N))
             -->_1 U22#(tt(),M,N) -> c_4(plus#(x(activate(N),activate(M)),activate(N))
                                        ,x#(activate(N),activate(M))
                                        ,activate#(N)
                                        ,activate#(M)
                                        ,activate#(N)):4
             -->_3 activate#(X) -> c_5():7
             -->_2 activate#(X) -> c_5():7
          
          4:S:U22#(tt(),M,N) -> c_4(plus#(x(activate(N),activate(M)),activate(N))
                                   ,x#(activate(N),activate(M))
                                   ,activate#(N)
                                   ,activate#(M)
                                   ,activate#(N))
             -->_2 x#(N,s(M)) -> c_9(U21#(tt(),M,N)):6
             -->_1 plus#(N,s(M)) -> c_7(U11#(tt(),M,N)):5
             -->_2 x#(N,0()) -> c_8():9
             -->_1 plus#(N,0()) -> c_6():8
             -->_5 activate#(X) -> c_5():7
             -->_4 activate#(X) -> c_5():7
             -->_3 activate#(X) -> c_5():7
          
          5:S:plus#(N,s(M)) -> c_7(U11#(tt(),M,N))
             -->_1 U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)),activate#(M),activate#(N)):1
          
          6:S:x#(N,s(M)) -> c_9(U21#(tt(),M,N))
             -->_1 U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)),activate#(M),activate#(N)):3
          
          7:W:activate#(X) -> c_5()
             
          
          8:W:plus#(N,0()) -> c_6()
             
          
          9:W:x#(N,0()) -> c_8()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          9: x#(N,0()) -> c_8()
          7: activate#(X) -> c_5()
          8: plus#(N,0()) -> c_6()
* Step 4: SimplifyRHS WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)),activate#(M),activate#(N))
            U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)),activate#(N),activate#(M))
            U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)),activate#(M),activate#(N))
            U22#(tt(),M,N) -> c_4(plus#(x(activate(N),activate(M)),activate(N))
                                 ,x#(activate(N),activate(M))
                                 ,activate#(N)
                                 ,activate#(M)
                                 ,activate#(N))
            plus#(N,s(M)) -> c_7(U11#(tt(),M,N))
            x#(N,s(M)) -> c_9(U21#(tt(),M,N))
        - Weak TRS:
            U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
            U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
            U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            plus(N,0()) -> N
            plus(N,s(M)) -> U11(tt(),M,N)
            x(N,0()) -> 0()
            x(N,s(M)) -> U21(tt(),M,N)
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2,U11#/3,U12#/3,U21#/3,U22#/3,activate#/1,plus#/2,x#/2} / {0/0
            ,s/1,tt/0,c_1/3,c_2/3,c_3/3,c_4/5,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,activate#,plus#
            ,x#} and constructors {0,s,tt}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)),activate#(M),activate#(N))
             -->_1 U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)),activate#(N),activate#(M)):2
          
          2:S:U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)),activate#(N),activate#(M))
             -->_1 plus#(N,s(M)) -> c_7(U11#(tt(),M,N)):5
          
          3:S:U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)),activate#(M),activate#(N))
             -->_1 U22#(tt(),M,N) -> c_4(plus#(x(activate(N),activate(M)),activate(N))
                                        ,x#(activate(N),activate(M))
                                        ,activate#(N)
                                        ,activate#(M)
                                        ,activate#(N)):4
          
          4:S:U22#(tt(),M,N) -> c_4(plus#(x(activate(N),activate(M)),activate(N))
                                   ,x#(activate(N),activate(M))
                                   ,activate#(N)
                                   ,activate#(M)
                                   ,activate#(N))
             -->_2 x#(N,s(M)) -> c_9(U21#(tt(),M,N)):6
             -->_1 plus#(N,s(M)) -> c_7(U11#(tt(),M,N)):5
          
          5:S:plus#(N,s(M)) -> c_7(U11#(tt(),M,N))
             -->_1 U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)),activate#(M),activate#(N)):1
          
          6:S:x#(N,s(M)) -> c_9(U21#(tt(),M,N))
             -->_1 U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)),activate#(M),activate#(N)):3
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)))
          U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)))
          U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)))
          U22#(tt(),M,N) -> c_4(plus#(x(activate(N),activate(M)),activate(N)),x#(activate(N),activate(M)))
* Step 5: DecomposeDG WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict DPs:
            U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)))
            U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)))
            U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)))
            U22#(tt(),M,N) -> c_4(plus#(x(activate(N),activate(M)),activate(N)),x#(activate(N),activate(M)))
            plus#(N,s(M)) -> c_7(U11#(tt(),M,N))
            x#(N,s(M)) -> c_9(U21#(tt(),M,N))
        - Weak TRS:
            U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
            U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
            U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            plus(N,0()) -> N
            plus(N,s(M)) -> U11(tt(),M,N)
            x(N,0()) -> 0()
            x(N,s(M)) -> U21(tt(),M,N)
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2,U11#/3,U12#/3,U21#/3,U22#/3,activate#/1,plus#/2,x#/2} / {0/0
            ,s/1,tt/0,c_1/1,c_2/1,c_3/1,c_4/2,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,activate#,plus#
            ,x#} and constructors {0,s,tt}
    + Applied Processor:
        DecomposeDG {onSelection = all below first cut in WDG, onUpper = Nothing, onLower = Nothing}
    + Details:
        We decompose the input problem according to the dependency graph into the upper component
          U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)))
          U22#(tt(),M,N) -> c_4(plus#(x(activate(N),activate(M)),activate(N)),x#(activate(N),activate(M)))
          x#(N,s(M)) -> c_9(U21#(tt(),M,N))
        and a lower component
          U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)))
          U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)))
          plus#(N,s(M)) -> c_7(U11#(tt(),M,N))
        Further, following extension rules are added to the lower component.
          U21#(tt(),M,N) -> U22#(tt(),activate(M),activate(N))
          U22#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N))
          U22#(tt(),M,N) -> x#(activate(N),activate(M))
          x#(N,s(M)) -> U21#(tt(),M,N)
** Step 5.a:1: SimplifyRHS WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)))
            U22#(tt(),M,N) -> c_4(plus#(x(activate(N),activate(M)),activate(N)),x#(activate(N),activate(M)))
            x#(N,s(M)) -> c_9(U21#(tt(),M,N))
        - Weak TRS:
            U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
            U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
            U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            plus(N,0()) -> N
            plus(N,s(M)) -> U11(tt(),M,N)
            x(N,0()) -> 0()
            x(N,s(M)) -> U21(tt(),M,N)
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2,U11#/3,U12#/3,U21#/3,U22#/3,activate#/1,plus#/2,x#/2} / {0/0
            ,s/1,tt/0,c_1/1,c_2/1,c_3/1,c_4/2,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,activate#,plus#
            ,x#} and constructors {0,s,tt}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)))
             -->_1 U22#(tt(),M,N) -> c_4(plus#(x(activate(N),activate(M)),activate(N)),x#(activate(N),activate(M))):2
          
          2:S:U22#(tt(),M,N) -> c_4(plus#(x(activate(N),activate(M)),activate(N)),x#(activate(N),activate(M)))
             -->_2 x#(N,s(M)) -> c_9(U21#(tt(),M,N)):3
          
          3:S:x#(N,s(M)) -> c_9(U21#(tt(),M,N))
             -->_1 U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N))):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          U22#(tt(),M,N) -> c_4(x#(activate(N),activate(M)))
** Step 5.a:2: UsableRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)))
            U22#(tt(),M,N) -> c_4(x#(activate(N),activate(M)))
            x#(N,s(M)) -> c_9(U21#(tt(),M,N))
        - Weak TRS:
            U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
            U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
            U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            plus(N,0()) -> N
            plus(N,s(M)) -> U11(tt(),M,N)
            x(N,0()) -> 0()
            x(N,s(M)) -> U21(tt(),M,N)
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2,U11#/3,U12#/3,U21#/3,U22#/3,activate#/1,plus#/2,x#/2} / {0/0
            ,s/1,tt/0,c_1/1,c_2/1,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,activate#,plus#
            ,x#} and constructors {0,s,tt}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate(X) -> X
          U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)))
          U22#(tt(),M,N) -> c_4(x#(activate(N),activate(M)))
          x#(N,s(M)) -> c_9(U21#(tt(),M,N))
** Step 5.a:3: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)))
            U22#(tt(),M,N) -> c_4(x#(activate(N),activate(M)))
            x#(N,s(M)) -> c_9(U21#(tt(),M,N))
        - Weak TRS:
            activate(X) -> X
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2,U11#/3,U12#/3,U21#/3,U22#/3,activate#/1,plus#/2,x#/2} / {0/0
            ,s/1,tt/0,c_1/1,c_2/1,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,activate#,plus#
            ,x#} and constructors {0,s,tt}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation:
          The following argument positions are considered usable:
            uargs(U22#) = {2,3},
            uargs(x#) = {1,2},
            uargs(c_3) = {1},
            uargs(c_4) = {1},
            uargs(c_9) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                    p(0) = [0]                            
                  p(U11) = [0]                            
                  p(U12) = [2] x2 + [1]                   
                  p(U21) = [0]                            
                  p(U22) = [0]                            
             p(activate) = [1] x1 + [9]                   
                 p(plus) = [0]                            
                    p(s) = [1] x1 + [15]                  
                   p(tt) = [1]                            
                    p(x) = [2] x1 + [0]                   
                 p(U11#) = [0]                            
                 p(U12#) = [0]                            
                 p(U21#) = [10] x1 + [1] x2 + [1] x3 + [0]
                 p(U22#) = [4] x1 + [1] x2 + [1] x3 + [7] 
            p(activate#) = [0]                            
                p(plus#) = [2] x1 + [0]                   
                   p(x#) = [1] x1 + [1] x2 + [0]          
                  p(c_1) = [0]                            
                  p(c_2) = [0]                            
                  p(c_3) = [1] x1 + [0]                   
                  p(c_4) = [1] x1 + [0]                   
                  p(c_5) = [0]                            
                  p(c_6) = [0]                            
                  p(c_7) = [0]                            
                  p(c_8) = [0]                            
                  p(c_9) = [1] x1 + [0]                   
          
          Following rules are strictly oriented:
          x#(N,s(M)) = [1] M + [1] N + [15]
                     > [1] M + [1] N + [10]
                     = c_9(U21#(tt(),M,N)) 
          
          
          Following rules are (at-least) weakly oriented:
          U21#(tt(),M,N) =  [1] M + [1] N + [10]                   
                         >= [1] M + [1] N + [29]                   
                         =  c_3(U22#(tt(),activate(M),activate(N)))
          
          U22#(tt(),M,N) =  [1] M + [1] N + [11]                   
                         >= [1] M + [1] N + [18]                   
                         =  c_4(x#(activate(N),activate(M)))       
          
             activate(X) =  [1] X + [9]                            
                         >= [1] X + [0]                            
                         =  X                                      
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
** Step 5.a:4: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)))
            U22#(tt(),M,N) -> c_4(x#(activate(N),activate(M)))
        - Weak DPs:
            x#(N,s(M)) -> c_9(U21#(tt(),M,N))
        - Weak TRS:
            activate(X) -> X
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2,U11#/3,U12#/3,U21#/3,U22#/3,activate#/1,plus#/2,x#/2} / {0/0
            ,s/1,tt/0,c_1/1,c_2/1,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,activate#,plus#
            ,x#} and constructors {0,s,tt}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation:
          The following argument positions are considered usable:
            uargs(U22#) = {2,3},
            uargs(x#) = {1,2},
            uargs(c_3) = {1},
            uargs(c_4) = {1},
            uargs(c_9) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                    p(0) = [0]                            
                  p(U11) = [0]                            
                  p(U12) = [1]                            
                  p(U21) = [1]                            
                  p(U22) = [0]                            
             p(activate) = [1] x1 + [4]                   
                 p(plus) = [8] x1 + [0]                   
                    p(s) = [1] x1 + [9]                   
                   p(tt) = [1]                            
                    p(x) = [0]                            
                 p(U11#) = [0]                            
                 p(U12#) = [4] x2 + [1] x3 + [0]          
                 p(U21#) = [2] x1 + [1] x2 + [1] x3 + [2] 
                 p(U22#) = [4] x1 + [1] x2 + [1] x3 + [11]
            p(activate#) = [2]                            
                p(plus#) = [4] x1 + [1] x2 + [0]          
                   p(x#) = [1] x1 + [1] x2 + [0]          
                  p(c_1) = [0]                            
                  p(c_2) = [0]                            
                  p(c_3) = [1] x1 + [0]                   
                  p(c_4) = [1] x1 + [0]                   
                  p(c_5) = [0]                            
                  p(c_6) = [0]                            
                  p(c_7) = [0]                            
                  p(c_8) = [0]                            
                  p(c_9) = [1] x1 + [5]                   
          
          Following rules are strictly oriented:
          U22#(tt(),M,N) = [1] M + [1] N + [15]            
                         > [1] M + [1] N + [8]             
                         = c_4(x#(activate(N),activate(M)))
          
          
          Following rules are (at-least) weakly oriented:
          U21#(tt(),M,N) =  [1] M + [1] N + [4]                    
                         >= [1] M + [1] N + [23]                   
                         =  c_3(U22#(tt(),activate(M),activate(N)))
          
              x#(N,s(M)) =  [1] M + [1] N + [9]                    
                         >= [1] M + [1] N + [9]                    
                         =  c_9(U21#(tt(),M,N))                    
          
             activate(X) =  [1] X + [4]                            
                         >= [1] X + [0]                            
                         =  X                                      
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
** Step 5.a:5: WeightGap WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)))
        - Weak DPs:
            U22#(tt(),M,N) -> c_4(x#(activate(N),activate(M)))
            x#(N,s(M)) -> c_9(U21#(tt(),M,N))
        - Weak TRS:
            activate(X) -> X
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2,U11#/3,U12#/3,U21#/3,U22#/3,activate#/1,plus#/2,x#/2} / {0/0
            ,s/1,tt/0,c_1/1,c_2/1,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,activate#,plus#
            ,x#} and constructors {0,s,tt}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation:
          The following argument positions are considered usable:
            uargs(U22#) = {2,3},
            uargs(x#) = {1,2},
            uargs(c_3) = {1},
            uargs(c_4) = {1},
            uargs(c_9) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                    p(0) = [8]                           
                  p(U11) = [1]                           
                  p(U12) = [0]                           
                  p(U21) = [0]                           
                  p(U22) = [0]                           
             p(activate) = [1] x1 + [3]                  
                 p(plus) = [0]                           
                    p(s) = [1] x1 + [13]                 
                   p(tt) = [6]                           
                    p(x) = [0]                           
                 p(U11#) = [0]                           
                 p(U12#) = [0]                           
                 p(U21#) = [1] x2 + [1] x3 + [13]        
                 p(U22#) = [1] x1 + [1] x2 + [1] x3 + [0]
            p(activate#) = [1] x1 + [1]                  
                p(plus#) = [2] x1 + [0]                  
                   p(x#) = [1] x1 + [1] x2 + [0]         
                  p(c_1) = [0]                           
                  p(c_2) = [0]                           
                  p(c_3) = [1] x1 + [0]                  
                  p(c_4) = [1] x1 + [0]                  
                  p(c_5) = [0]                           
                  p(c_6) = [0]                           
                  p(c_7) = [0]                           
                  p(c_8) = [0]                           
                  p(c_9) = [1] x1 + [0]                  
          
          Following rules are strictly oriented:
          U21#(tt(),M,N) = [1] M + [1] N + [13]                   
                         > [1] M + [1] N + [12]                   
                         = c_3(U22#(tt(),activate(M),activate(N)))
          
          
          Following rules are (at-least) weakly oriented:
          U22#(tt(),M,N) =  [1] M + [1] N + [6]             
                         >= [1] M + [1] N + [6]             
                         =  c_4(x#(activate(N),activate(M)))
          
              x#(N,s(M)) =  [1] M + [1] N + [13]            
                         >= [1] M + [1] N + [13]            
                         =  c_9(U21#(tt(),M,N))             
          
             activate(X) =  [1] X + [3]                     
                         >= [1] X + [0]                     
                         =  X                               
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
** Step 5.a:6: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            U21#(tt(),M,N) -> c_3(U22#(tt(),activate(M),activate(N)))
            U22#(tt(),M,N) -> c_4(x#(activate(N),activate(M)))
            x#(N,s(M)) -> c_9(U21#(tt(),M,N))
        - Weak TRS:
            activate(X) -> X
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2,U11#/3,U12#/3,U21#/3,U22#/3,activate#/1,plus#/2,x#/2} / {0/0
            ,s/1,tt/0,c_1/1,c_2/1,c_3/1,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,activate#,plus#
            ,x#} and constructors {0,s,tt}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

** Step 5.b:1: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)))
            U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)))
            plus#(N,s(M)) -> c_7(U11#(tt(),M,N))
        - Weak DPs:
            U21#(tt(),M,N) -> U22#(tt(),activate(M),activate(N))
            U22#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N))
            U22#(tt(),M,N) -> x#(activate(N),activate(M))
            x#(N,s(M)) -> U21#(tt(),M,N)
        - Weak TRS:
            U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
            U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
            U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            plus(N,0()) -> N
            plus(N,s(M)) -> U11(tt(),M,N)
            x(N,0()) -> 0()
            x(N,s(M)) -> U21(tt(),M,N)
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2,U11#/3,U12#/3,U21#/3,U22#/3,activate#/1,plus#/2,x#/2} / {0/0
            ,s/1,tt/0,c_1/1,c_2/1,c_3/1,c_4/2,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,activate#,plus#
            ,x#} and constructors {0,s,tt}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_1) = {1},
          uargs(c_2) = {1},
          uargs(c_7) = {1}
        
        Following symbols are considered usable:
          {activate,U11#,U12#,U21#,U22#,activate#,plus#,x#}
        TcT has computed the following interpretation:
                  p(0) = [1]                  
                p(U11) = [2] x1 + [1] x2 + [0]
                p(U12) = [2] x1 + [1]         
                p(U21) = [4] x2 + [0]         
                p(U22) = [9] x2 + [1] x3 + [0]
           p(activate) = [1] x1 + [0]         
               p(plus) = [4]                  
                  p(s) = [1] x1 + [4]         
                 p(tt) = [2]                  
                  p(x) = [2]                  
               p(U11#) = [9] x1 + [4] x2 + [0]
               p(U12#) = [7] x1 + [4] x2 + [2]
               p(U21#) = [4] x3 + [4]         
               p(U22#) = [2] x1 + [4] x3 + [0]
          p(activate#) = [2] x1 + [1]         
              p(plus#) = [4] x2 + [2]         
                 p(x#) = [4] x1 + [4]         
                p(c_1) = [1] x1 + [2]         
                p(c_2) = [1] x1 + [12]        
                p(c_3) = [1] x1 + [1]         
                p(c_4) = [4] x2 + [4]         
                p(c_5) = [1]                  
                p(c_6) = [8]                  
                p(c_7) = [1] x1 + [0]         
                p(c_8) = [0]                  
                p(c_9) = [1] x1 + [1]         
        
        Following rules are strictly oriented:
        U12#(tt(),M,N) = [4] M + [16]                       
                       > [4] M + [14]                       
                       = c_2(plus#(activate(N),activate(M)))
        
        
        Following rules are (at-least) weakly oriented:
        U11#(tt(),M,N) =  [4] M + [18]                                 
                       >= [4] M + [18]                                 
                       =  c_1(U12#(tt(),activate(M),activate(N)))      
        
        U21#(tt(),M,N) =  [4] N + [4]                                  
                       >= [4] N + [4]                                  
                       =  U22#(tt(),activate(M),activate(N))           
        
        U22#(tt(),M,N) =  [4] N + [4]                                  
                       >= [4] N + [2]                                  
                       =  plus#(x(activate(N),activate(M)),activate(N))
        
        U22#(tt(),M,N) =  [4] N + [4]                                  
                       >= [4] N + [4]                                  
                       =  x#(activate(N),activate(M))                  
        
         plus#(N,s(M)) =  [4] M + [18]                                 
                       >= [4] M + [18]                                 
                       =  c_7(U11#(tt(),M,N))                          
        
            x#(N,s(M)) =  [4] N + [4]                                  
                       >= [4] N + [4]                                  
                       =  U21#(tt(),M,N)                               
        
           activate(X) =  [1] X + [0]                                  
                       >= [1] X + [0]                                  
                       =  X                                            
        
** Step 5.b:2: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)))
            plus#(N,s(M)) -> c_7(U11#(tt(),M,N))
        - Weak DPs:
            U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)))
            U21#(tt(),M,N) -> U22#(tt(),activate(M),activate(N))
            U22#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N))
            U22#(tt(),M,N) -> x#(activate(N),activate(M))
            x#(N,s(M)) -> U21#(tt(),M,N)
        - Weak TRS:
            U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
            U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
            U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            plus(N,0()) -> N
            plus(N,s(M)) -> U11(tt(),M,N)
            x(N,0()) -> 0()
            x(N,s(M)) -> U21(tt(),M,N)
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2,U11#/3,U12#/3,U21#/3,U22#/3,activate#/1,plus#/2,x#/2} / {0/0
            ,s/1,tt/0,c_1/1,c_2/1,c_3/1,c_4/2,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,activate#,plus#
            ,x#} and constructors {0,s,tt}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_1) = {1},
          uargs(c_2) = {1},
          uargs(c_7) = {1}
        
        Following symbols are considered usable:
          {activate,U11#,U12#,U21#,U22#,activate#,plus#,x#}
        TcT has computed the following interpretation:
                  p(0) = [0]                             
                p(U11) = [1] x1 + [8]                    
                p(U12) = [4] x2 + [0]                    
                p(U21) = [2] x3 + [0]                    
                p(U22) = [1] x1 + [8] x2 + [7]           
           p(activate) = [1] x1 + [0]                    
               p(plus) = [5] x1 + [8] x2 + [0]           
                  p(s) = [1] x1 + [2]                    
                 p(tt) = [2]                             
                  p(x) = [4] x1 + [2] x2 + [0]           
               p(U11#) = [8] x1 + [8] x2 + [0]           
               p(U12#) = [6] x1 + [8] x2 + [0]           
               p(U21#) = [4] x1 + [10] x2 + [8] x3 + [14]
               p(U22#) = [2] x1 + [10] x2 + [8] x3 + [0] 
          p(activate#) = [8] x1 + [0]                    
              p(plus#) = [8] x2 + [4]                    
                 p(x#) = [8] x1 + [10] x2 + [2]          
                p(c_1) = [1] x1 + [0]                    
                p(c_2) = [1] x1 + [8]                    
                p(c_3) = [0]                             
                p(c_4) = [1] x1 + [1]                    
                p(c_5) = [1]                             
                p(c_6) = [0]                             
                p(c_7) = [1] x1 + [4]                    
                p(c_8) = [1]                             
                p(c_9) = [1] x1 + [2]                    
        
        Following rules are strictly oriented:
        U11#(tt(),M,N) = [8] M + [16]                           
                       > [8] M + [12]                           
                       = c_1(U12#(tt(),activate(M),activate(N)))
        
        
        Following rules are (at-least) weakly oriented:
        U12#(tt(),M,N) =  [8] M + [12]                                 
                       >= [8] M + [12]                                 
                       =  c_2(plus#(activate(N),activate(M)))          
        
        U21#(tt(),M,N) =  [10] M + [8] N + [22]                        
                       >= [10] M + [8] N + [4]                         
                       =  U22#(tt(),activate(M),activate(N))           
        
        U22#(tt(),M,N) =  [10] M + [8] N + [4]                         
                       >= [8] N + [4]                                  
                       =  plus#(x(activate(N),activate(M)),activate(N))
        
        U22#(tt(),M,N) =  [10] M + [8] N + [4]                         
                       >= [10] M + [8] N + [2]                         
                       =  x#(activate(N),activate(M))                  
        
         plus#(N,s(M)) =  [8] M + [20]                                 
                       >= [8] M + [20]                                 
                       =  c_7(U11#(tt(),M,N))                          
        
            x#(N,s(M)) =  [10] M + [8] N + [22]                        
                       >= [10] M + [8] N + [22]                        
                       =  U21#(tt(),M,N)                               
        
           activate(X) =  [1] X + [0]                                  
                       >= [1] X + [0]                                  
                       =  X                                            
        
** Step 5.b:3: NaturalMI WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict DPs:
            plus#(N,s(M)) -> c_7(U11#(tt(),M,N))
        - Weak DPs:
            U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)))
            U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)))
            U21#(tt(),M,N) -> U22#(tt(),activate(M),activate(N))
            U22#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N))
            U22#(tt(),M,N) -> x#(activate(N),activate(M))
            x#(N,s(M)) -> U21#(tt(),M,N)
        - Weak TRS:
            U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
            U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
            U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            plus(N,0()) -> N
            plus(N,s(M)) -> U11(tt(),M,N)
            x(N,0()) -> 0()
            x(N,s(M)) -> U21(tt(),M,N)
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2,U11#/3,U12#/3,U21#/3,U22#/3,activate#/1,plus#/2,x#/2} / {0/0
            ,s/1,tt/0,c_1/1,c_2/1,c_3/1,c_4/2,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,activate#,plus#
            ,x#} and constructors {0,s,tt}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        We apply a matrix interpretation of kind constructor based matrix interpretation:
        The following argument positions are considered usable:
          uargs(c_1) = {1},
          uargs(c_2) = {1},
          uargs(c_7) = {1}
        
        Following symbols are considered usable:
          {activate,U11#,U12#,U21#,U22#,activate#,plus#,x#}
        TcT has computed the following interpretation:
                  p(0) = [6]                   
                p(U11) = [1] x3 + [0]          
                p(U12) = [2] x2 + [4] x3 + [0] 
                p(U21) = [2] x2 + [13]         
                p(U22) = [4] x2 + [0]          
           p(activate) = [1] x1 + [0]          
               p(plus) = [2] x2 + [0]          
                  p(s) = [1] x1 + [2]          
                 p(tt) = [4]                   
                  p(x) = [1] x2 + [1]          
               p(U11#) = [2] x1 + [14] x2 + [5]
               p(U12#) = [2] x1 + [14] x2 + [0]
               p(U21#) = [1] x1 + [14] x3 + [4]
               p(U22#) = [14] x3 + [8]         
          p(activate#) = [0]                   
              p(plus#) = [14] x2 + [0]         
                 p(x#) = [14] x1 + [8]         
                p(c_1) = [1] x1 + [4]          
                p(c_2) = [1] x1 + [8]          
                p(c_3) = [2] x1 + [2]          
                p(c_4) = [0]                   
                p(c_5) = [0]                   
                p(c_6) = [1]                   
                p(c_7) = [1] x1 + [1]          
                p(c_8) = [1]                   
                p(c_9) = [1] x1 + [0]          
        
        Following rules are strictly oriented:
        plus#(N,s(M)) = [14] M + [28]      
                      > [14] M + [14]      
                      = c_7(U11#(tt(),M,N))
        
        
        Following rules are (at-least) weakly oriented:
        U11#(tt(),M,N) =  [14] M + [13]                                
                       >= [14] M + [12]                                
                       =  c_1(U12#(tt(),activate(M),activate(N)))      
        
        U12#(tt(),M,N) =  [14] M + [8]                                 
                       >= [14] M + [8]                                 
                       =  c_2(plus#(activate(N),activate(M)))          
        
        U21#(tt(),M,N) =  [14] N + [8]                                 
                       >= [14] N + [8]                                 
                       =  U22#(tt(),activate(M),activate(N))           
        
        U22#(tt(),M,N) =  [14] N + [8]                                 
                       >= [14] N + [0]                                 
                       =  plus#(x(activate(N),activate(M)),activate(N))
        
        U22#(tt(),M,N) =  [14] N + [8]                                 
                       >= [14] N + [8]                                 
                       =  x#(activate(N),activate(M))                  
        
            x#(N,s(M)) =  [14] N + [8]                                 
                       >= [14] N + [8]                                 
                       =  U21#(tt(),M,N)                               
        
           activate(X) =  [1] X + [0]                                  
                       >= [1] X + [0]                                  
                       =  X                                            
        
** Step 5.b:4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            U11#(tt(),M,N) -> c_1(U12#(tt(),activate(M),activate(N)))
            U12#(tt(),M,N) -> c_2(plus#(activate(N),activate(M)))
            U21#(tt(),M,N) -> U22#(tt(),activate(M),activate(N))
            U22#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N))
            U22#(tt(),M,N) -> x#(activate(N),activate(M))
            plus#(N,s(M)) -> c_7(U11#(tt(),M,N))
            x#(N,s(M)) -> U21#(tt(),M,N)
        - Weak TRS:
            U11(tt(),M,N) -> U12(tt(),activate(M),activate(N))
            U12(tt(),M,N) -> s(plus(activate(N),activate(M)))
            U21(tt(),M,N) -> U22(tt(),activate(M),activate(N))
            U22(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N))
            activate(X) -> X
            plus(N,0()) -> N
            plus(N,s(M)) -> U11(tt(),M,N)
            x(N,0()) -> 0()
            x(N,s(M)) -> U21(tt(),M,N)
        - Signature:
            {U11/3,U12/3,U21/3,U22/3,activate/1,plus/2,x/2,U11#/3,U12#/3,U21#/3,U22#/3,activate#/1,plus#/2,x#/2} / {0/0
            ,s/1,tt/0,c_1/1,c_2/1,c_3/1,c_4/2,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,U21#,U22#,activate#,plus#
            ,x#} and constructors {0,s,tt}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^2))