MAYBE
* Step 1: InnermostRuleRemoval MAYBE
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__app(X1,X2)) -> app(X1,X2)
            activate(n__from(X)) -> from(X)
            activate(n__nil()) -> nil()
            activate(n__zWadr(X1,X2)) -> zWadr(X1,X2)
            app(X1,X2) -> n__app(X1,X2)
            app(cons(X,XS),YS) -> cons(X,n__app(activate(XS),YS))
            app(nil(),YS) -> YS
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            nil() -> n__nil()
            prefix(L) -> cons(nil(),n__zWadr(L,prefix(L)))
            zWadr(X1,X2) -> n__zWadr(X1,X2)
            zWadr(XS,nil()) -> nil()
            zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,n__nil())),n__zWadr(activate(XS),activate(YS)))
            zWadr(nil(),YS) -> nil()
        - Signature:
            {activate/1,app/2,from/1,nil/0,prefix/1,zWadr/2} / {cons/2,n__app/2,n__from/1,n__nil/0,n__zWadr/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,app,from,nil,prefix
            ,zWadr} and constructors {cons,n__app,n__from,n__nil,n__zWadr,s}
    + Applied Processor:
        InnermostRuleRemoval
    + Details:
        Arguments of following rules are not normal-forms.
          app(nil(),YS) -> YS
          zWadr(XS,nil()) -> nil()
          zWadr(nil(),YS) -> nil()
        All above mentioned rules can be savely removed.
* Step 2: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__app(X1,X2)) -> app(X1,X2)
            activate(n__from(X)) -> from(X)
            activate(n__nil()) -> nil()
            activate(n__zWadr(X1,X2)) -> zWadr(X1,X2)
            app(X1,X2) -> n__app(X1,X2)
            app(cons(X,XS),YS) -> cons(X,n__app(activate(XS),YS))
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            nil() -> n__nil()
            prefix(L) -> cons(nil(),n__zWadr(L,prefix(L)))
            zWadr(X1,X2) -> n__zWadr(X1,X2)
            zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,n__nil())),n__zWadr(activate(XS),activate(YS)))
        - Signature:
            {activate/1,app/2,from/1,nil/0,prefix/1,zWadr/2} / {cons/2,n__app/2,n__from/1,n__nil/0,n__zWadr/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,app,from,nil,prefix
            ,zWadr} and constructors {cons,n__app,n__from,n__nil,n__zWadr,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          activate#(X) -> c_1()
          activate#(n__app(X1,X2)) -> c_2(app#(X1,X2))
          activate#(n__from(X)) -> c_3(from#(X))
          activate#(n__nil()) -> c_4(nil#())
          activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2))
          app#(X1,X2) -> c_6()
          app#(cons(X,XS),YS) -> c_7(activate#(XS))
          from#(X) -> c_8()
          from#(X) -> c_9()
          nil#() -> c_10()
          prefix#(L) -> c_11(nil#(),prefix#(L))
          zWadr#(X1,X2) -> c_12()
          zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__app(X1,X2)) -> c_2(app#(X1,X2))
            activate#(n__from(X)) -> c_3(from#(X))
            activate#(n__nil()) -> c_4(nil#())
            activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2))
            app#(X1,X2) -> c_6()
            app#(cons(X,XS),YS) -> c_7(activate#(XS))
            from#(X) -> c_8()
            from#(X) -> c_9()
            nil#() -> c_10()
            prefix#(L) -> c_11(nil#(),prefix#(L))
            zWadr#(X1,X2) -> c_12()
            zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
        - Weak TRS:
            activate(X) -> X
            activate(n__app(X1,X2)) -> app(X1,X2)
            activate(n__from(X)) -> from(X)
            activate(n__nil()) -> nil()
            activate(n__zWadr(X1,X2)) -> zWadr(X1,X2)
            app(X1,X2) -> n__app(X1,X2)
            app(cons(X,XS),YS) -> cons(X,n__app(activate(XS),YS))
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            nil() -> n__nil()
            prefix(L) -> cons(nil(),n__zWadr(L,prefix(L)))
            zWadr(X1,X2) -> n__zWadr(X1,X2)
            zWadr(cons(X,XS),cons(Y,YS)) -> cons(app(Y,cons(X,n__nil())),n__zWadr(activate(XS),activate(YS)))
        - Signature:
            {activate/1,app/2,from/1,nil/0,prefix/1,zWadr/2,activate#/1,app#/2,from#/1,nil#/0,prefix#/1
            ,zWadr#/2} / {cons/2,n__app/2,n__from/1,n__nil/0,n__zWadr/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1
            ,c_8/0,c_9/0,c_10/0,c_11/2,c_12/0,c_13/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,app#,from#,nil#,prefix#
            ,zWadr#} and constructors {cons,n__app,n__from,n__nil,n__zWadr,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate#(X) -> c_1()
          activate#(n__app(X1,X2)) -> c_2(app#(X1,X2))
          activate#(n__from(X)) -> c_3(from#(X))
          activate#(n__nil()) -> c_4(nil#())
          activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2))
          app#(X1,X2) -> c_6()
          app#(cons(X,XS),YS) -> c_7(activate#(XS))
          from#(X) -> c_8()
          from#(X) -> c_9()
          nil#() -> c_10()
          prefix#(L) -> c_11(nil#(),prefix#(L))
          zWadr#(X1,X2) -> c_12()
          zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__app(X1,X2)) -> c_2(app#(X1,X2))
            activate#(n__from(X)) -> c_3(from#(X))
            activate#(n__nil()) -> c_4(nil#())
            activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2))
            app#(X1,X2) -> c_6()
            app#(cons(X,XS),YS) -> c_7(activate#(XS))
            from#(X) -> c_8()
            from#(X) -> c_9()
            nil#() -> c_10()
            prefix#(L) -> c_11(nil#(),prefix#(L))
            zWadr#(X1,X2) -> c_12()
            zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
        - Signature:
            {activate/1,app/2,from/1,nil/0,prefix/1,zWadr/2,activate#/1,app#/2,from#/1,nil#/0,prefix#/1
            ,zWadr#/2} / {cons/2,n__app/2,n__from/1,n__nil/0,n__zWadr/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1
            ,c_8/0,c_9/0,c_10/0,c_11/2,c_12/0,c_13/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,app#,from#,nil#,prefix#
            ,zWadr#} and constructors {cons,n__app,n__from,n__nil,n__zWadr,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,6,8,9,10,12}
        by application of
          Pre({1,6,8,9,10,12}) = {2,3,4,5,7,11,13}.
        Here rules are labelled as follows:
          1: activate#(X) -> c_1()
          2: activate#(n__app(X1,X2)) -> c_2(app#(X1,X2))
          3: activate#(n__from(X)) -> c_3(from#(X))
          4: activate#(n__nil()) -> c_4(nil#())
          5: activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2))
          6: app#(X1,X2) -> c_6()
          7: app#(cons(X,XS),YS) -> c_7(activate#(XS))
          8: from#(X) -> c_8()
          9: from#(X) -> c_9()
          10: nil#() -> c_10()
          11: prefix#(L) -> c_11(nil#(),prefix#(L))
          12: zWadr#(X1,X2) -> c_12()
          13: zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
* Step 5: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__app(X1,X2)) -> c_2(app#(X1,X2))
            activate#(n__from(X)) -> c_3(from#(X))
            activate#(n__nil()) -> c_4(nil#())
            activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2))
            app#(cons(X,XS),YS) -> c_7(activate#(XS))
            prefix#(L) -> c_11(nil#(),prefix#(L))
            zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
        - Weak DPs:
            activate#(X) -> c_1()
            app#(X1,X2) -> c_6()
            from#(X) -> c_8()
            from#(X) -> c_9()
            nil#() -> c_10()
            zWadr#(X1,X2) -> c_12()
        - Signature:
            {activate/1,app/2,from/1,nil/0,prefix/1,zWadr/2,activate#/1,app#/2,from#/1,nil#/0,prefix#/1
            ,zWadr#/2} / {cons/2,n__app/2,n__from/1,n__nil/0,n__zWadr/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1
            ,c_8/0,c_9/0,c_10/0,c_11/2,c_12/0,c_13/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,app#,from#,nil#,prefix#
            ,zWadr#} and constructors {cons,n__app,n__from,n__nil,n__zWadr,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,3}
        by application of
          Pre({2,3}) = {5,7}.
        Here rules are labelled as follows:
          1: activate#(n__app(X1,X2)) -> c_2(app#(X1,X2))
          2: activate#(n__from(X)) -> c_3(from#(X))
          3: activate#(n__nil()) -> c_4(nil#())
          4: activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2))
          5: app#(cons(X,XS),YS) -> c_7(activate#(XS))
          6: prefix#(L) -> c_11(nil#(),prefix#(L))
          7: zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
          8: activate#(X) -> c_1()
          9: app#(X1,X2) -> c_6()
          10: from#(X) -> c_8()
          11: from#(X) -> c_9()
          12: nil#() -> c_10()
          13: zWadr#(X1,X2) -> c_12()
* Step 6: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__app(X1,X2)) -> c_2(app#(X1,X2))
            activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2))
            app#(cons(X,XS),YS) -> c_7(activate#(XS))
            prefix#(L) -> c_11(nil#(),prefix#(L))
            zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
        - Weak DPs:
            activate#(X) -> c_1()
            activate#(n__from(X)) -> c_3(from#(X))
            activate#(n__nil()) -> c_4(nil#())
            app#(X1,X2) -> c_6()
            from#(X) -> c_8()
            from#(X) -> c_9()
            nil#() -> c_10()
            zWadr#(X1,X2) -> c_12()
        - Signature:
            {activate/1,app/2,from/1,nil/0,prefix/1,zWadr/2,activate#/1,app#/2,from#/1,nil#/0,prefix#/1
            ,zWadr#/2} / {cons/2,n__app/2,n__from/1,n__nil/0,n__zWadr/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1
            ,c_8/0,c_9/0,c_10/0,c_11/2,c_12/0,c_13/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,app#,from#,nil#,prefix#
            ,zWadr#} and constructors {cons,n__app,n__from,n__nil,n__zWadr,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:activate#(n__app(X1,X2)) -> c_2(app#(X1,X2))
             -->_1 app#(cons(X,XS),YS) -> c_7(activate#(XS)):3
             -->_1 app#(X1,X2) -> c_6():9
          
          2:S:activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2))
             -->_1 zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS)):5
             -->_1 zWadr#(X1,X2) -> c_12():13
          
          3:S:app#(cons(X,XS),YS) -> c_7(activate#(XS))
             -->_1 activate#(n__nil()) -> c_4(nil#()):8
             -->_1 activate#(n__from(X)) -> c_3(from#(X)):7
             -->_1 activate#(X) -> c_1():6
             -->_1 activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2)):2
             -->_1 activate#(n__app(X1,X2)) -> c_2(app#(X1,X2)):1
          
          4:S:prefix#(L) -> c_11(nil#(),prefix#(L))
             -->_1 nil#() -> c_10():12
             -->_2 prefix#(L) -> c_11(nil#(),prefix#(L)):4
          
          5:S:zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
             -->_3 activate#(n__nil()) -> c_4(nil#()):8
             -->_2 activate#(n__nil()) -> c_4(nil#()):8
             -->_3 activate#(n__from(X)) -> c_3(from#(X)):7
             -->_2 activate#(n__from(X)) -> c_3(from#(X)):7
             -->_1 app#(X1,X2) -> c_6():9
             -->_3 activate#(X) -> c_1():6
             -->_2 activate#(X) -> c_1():6
             -->_1 app#(cons(X,XS),YS) -> c_7(activate#(XS)):3
             -->_3 activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2)):2
             -->_2 activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2)):2
             -->_3 activate#(n__app(X1,X2)) -> c_2(app#(X1,X2)):1
             -->_2 activate#(n__app(X1,X2)) -> c_2(app#(X1,X2)):1
          
          6:W:activate#(X) -> c_1()
             
          
          7:W:activate#(n__from(X)) -> c_3(from#(X))
             -->_1 from#(X) -> c_9():11
             -->_1 from#(X) -> c_8():10
          
          8:W:activate#(n__nil()) -> c_4(nil#())
             -->_1 nil#() -> c_10():12
          
          9:W:app#(X1,X2) -> c_6()
             
          
          10:W:from#(X) -> c_8()
             
          
          11:W:from#(X) -> c_9()
             
          
          12:W:nil#() -> c_10()
             
          
          13:W:zWadr#(X1,X2) -> c_12()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          13: zWadr#(X1,X2) -> c_12()
          9: app#(X1,X2) -> c_6()
          6: activate#(X) -> c_1()
          7: activate#(n__from(X)) -> c_3(from#(X))
          10: from#(X) -> c_8()
          11: from#(X) -> c_9()
          8: activate#(n__nil()) -> c_4(nil#())
          12: nil#() -> c_10()
* Step 7: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__app(X1,X2)) -> c_2(app#(X1,X2))
            activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2))
            app#(cons(X,XS),YS) -> c_7(activate#(XS))
            prefix#(L) -> c_11(nil#(),prefix#(L))
            zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
        - Signature:
            {activate/1,app/2,from/1,nil/0,prefix/1,zWadr/2,activate#/1,app#/2,from#/1,nil#/0,prefix#/1
            ,zWadr#/2} / {cons/2,n__app/2,n__from/1,n__nil/0,n__zWadr/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1
            ,c_8/0,c_9/0,c_10/0,c_11/2,c_12/0,c_13/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,app#,from#,nil#,prefix#
            ,zWadr#} and constructors {cons,n__app,n__from,n__nil,n__zWadr,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:activate#(n__app(X1,X2)) -> c_2(app#(X1,X2))
             -->_1 app#(cons(X,XS),YS) -> c_7(activate#(XS)):3
          
          2:S:activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2))
             -->_1 zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS)):5
          
          3:S:app#(cons(X,XS),YS) -> c_7(activate#(XS))
             -->_1 activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2)):2
             -->_1 activate#(n__app(X1,X2)) -> c_2(app#(X1,X2)):1
          
          4:S:prefix#(L) -> c_11(nil#(),prefix#(L))
             -->_2 prefix#(L) -> c_11(nil#(),prefix#(L)):4
          
          5:S:zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
             -->_1 app#(cons(X,XS),YS) -> c_7(activate#(XS)):3
             -->_3 activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2)):2
             -->_2 activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2)):2
             -->_3 activate#(n__app(X1,X2)) -> c_2(app#(X1,X2)):1
             -->_2 activate#(n__app(X1,X2)) -> c_2(app#(X1,X2)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          prefix#(L) -> c_11(prefix#(L))
* Step 8: WeightGap MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__app(X1,X2)) -> c_2(app#(X1,X2))
            activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2))
            app#(cons(X,XS),YS) -> c_7(activate#(XS))
            prefix#(L) -> c_11(prefix#(L))
            zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
        - Signature:
            {activate/1,app/2,from/1,nil/0,prefix/1,zWadr/2,activate#/1,app#/2,from#/1,nil#/0,prefix#/1
            ,zWadr#/2} / {cons/2,n__app/2,n__from/1,n__nil/0,n__zWadr/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1
            ,c_8/0,c_9/0,c_10/0,c_11/1,c_12/0,c_13/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,app#,from#,nil#,prefix#
            ,zWadr#} and constructors {cons,n__app,n__from,n__nil,n__zWadr,s}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 0, 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 (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
          The following argument positions are considered usable:
            uargs(c_2) = {1},
            uargs(c_5) = {1},
            uargs(c_7) = {1},
            uargs(c_11) = {1},
            uargs(c_13) = {1,2,3}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
             p(activate) = [0]                           
                  p(app) = [1] x1 + [0]                  
                 p(cons) = [0]                           
                 p(from) = [0]                           
               p(n__app) = [0]                           
              p(n__from) = [0]                           
               p(n__nil) = [0]                           
             p(n__zWadr) = [0]                           
                  p(nil) = [0]                           
               p(prefix) = [1]                           
                    p(s) = [0]                           
                p(zWadr) = [0]                           
            p(activate#) = [0]                           
                 p(app#) = [0]                           
                p(from#) = [0]                           
                 p(nil#) = [0]                           
              p(prefix#) = [1] x1 + [0]                  
               p(zWadr#) = [7]                           
                  p(c_1) = [0]                           
                  p(c_2) = [1] x1 + [0]                  
                  p(c_3) = [0]                           
                  p(c_4) = [0]                           
                  p(c_5) = [1] x1 + [0]                  
                  p(c_6) = [0]                           
                  p(c_7) = [1] x1 + [0]                  
                  p(c_8) = [0]                           
                  p(c_9) = [0]                           
                 p(c_10) = [0]                           
                 p(c_11) = [1] x1 + [0]                  
                 p(c_12) = [0]                           
                 p(c_13) = [1] x1 + [1] x2 + [1] x3 + [0]
          
          Following rules are strictly oriented:
          zWadr#(cons(X,XS),cons(Y,YS)) = [7]                                                       
                                        > [0]                                                       
                                        = c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
          
          
          Following rules are (at-least) weakly oriented:
            activate#(n__app(X1,X2)) =  [0]               
                                     >= [0]               
                                     =  c_2(app#(X1,X2))  
          
          activate#(n__zWadr(X1,X2)) =  [0]               
                                     >= [7]               
                                     =  c_5(zWadr#(X1,X2))
          
                 app#(cons(X,XS),YS) =  [0]               
                                     >= [0]               
                                     =  c_7(activate#(XS))
          
                          prefix#(L) =  [1] L + [0]       
                                     >= [1] L + [0]       
                                     =  c_11(prefix#(L))  
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 9: WeightGap MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__app(X1,X2)) -> c_2(app#(X1,X2))
            activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2))
            app#(cons(X,XS),YS) -> c_7(activate#(XS))
            prefix#(L) -> c_11(prefix#(L))
        - Weak DPs:
            zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
        - Signature:
            {activate/1,app/2,from/1,nil/0,prefix/1,zWadr/2,activate#/1,app#/2,from#/1,nil#/0,prefix#/1
            ,zWadr#/2} / {cons/2,n__app/2,n__from/1,n__nil/0,n__zWadr/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1
            ,c_8/0,c_9/0,c_10/0,c_11/1,c_12/0,c_13/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,app#,from#,nil#,prefix#
            ,zWadr#} and constructors {cons,n__app,n__from,n__nil,n__zWadr,s}
    + Applied Processor:
        WeightGap {wgDimension = 1, wgDegree = 0, 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 (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima):
          The following argument positions are considered usable:
            uargs(c_2) = {1},
            uargs(c_5) = {1},
            uargs(c_7) = {1},
            uargs(c_11) = {1},
            uargs(c_13) = {1,2,3}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
             p(activate) = [2]                           
                  p(app) = [2] x1 + [2]                  
                 p(cons) = [0]                           
                 p(from) = [2]                           
               p(n__app) = [0]                           
              p(n__from) = [0]                           
               p(n__nil) = [0]                           
             p(n__zWadr) = [0]                           
                  p(nil) = [0]                           
               p(prefix) = [0]                           
                    p(s) = [2]                           
                p(zWadr) = [0]                           
            p(activate#) = [4]                           
                 p(app#) = [0]                           
                p(from#) = [0]                           
                 p(nil#) = [0]                           
              p(prefix#) = [8] x1 + [11]                 
               p(zWadr#) = [12]                          
                  p(c_1) = [0]                           
                  p(c_2) = [1] x1 + [0]                  
                  p(c_3) = [0]                           
                  p(c_4) = [0]                           
                  p(c_5) = [1] x1 + [0]                  
                  p(c_6) = [0]                           
                  p(c_7) = [1] x1 + [11]                 
                  p(c_8) = [0]                           
                  p(c_9) = [0]                           
                 p(c_10) = [0]                           
                 p(c_11) = [1] x1 + [4]                  
                 p(c_12) = [0]                           
                 p(c_13) = [1] x1 + [1] x2 + [1] x3 + [4]
          
          Following rules are strictly oriented:
          activate#(n__app(X1,X2)) = [4]             
                                   > [0]             
                                   = c_2(app#(X1,X2))
          
          
          Following rules are (at-least) weakly oriented:
             activate#(n__zWadr(X1,X2)) =  [4]                                                       
                                        >= [12]                                                      
                                        =  c_5(zWadr#(X1,X2))                                        
          
                    app#(cons(X,XS),YS) =  [0]                                                       
                                        >= [15]                                                      
                                        =  c_7(activate#(XS))                                        
          
                             prefix#(L) =  [8] L + [11]                                              
                                        >= [8] L + [15]                                              
                                        =  c_11(prefix#(L))                                          
          
          zWadr#(cons(X,XS),cons(Y,YS)) =  [12]                                                      
                                        >= [12]                                                      
                                        =  c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 10: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          activate#(n__zWadr(X1,X2)) -> c_5(zWadr#(X1,X2))
          app#(cons(X,XS),YS) -> c_7(activate#(XS))
          prefix#(L) -> c_11(prefix#(L))
      - Weak DPs:
          activate#(n__app(X1,X2)) -> c_2(app#(X1,X2))
          zWadr#(cons(X,XS),cons(Y,YS)) -> c_13(app#(Y,cons(X,n__nil())),activate#(XS),activate#(YS))
      - Signature:
          {activate/1,app/2,from/1,nil/0,prefix/1,zWadr/2,activate#/1,app#/2,from#/1,nil#/0,prefix#/1
          ,zWadr#/2} / {cons/2,n__app/2,n__from/1,n__nil/0,n__zWadr/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/0,c_7/1
          ,c_8/0,c_9/0,c_10/0,c_11/1,c_12/0,c_13/3}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {activate#,app#,from#,nil#,prefix#
          ,zWadr#} and constructors {cons,n__app,n__from,n__nil,n__zWadr,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE