MAYBE
* Step 1: InnermostRuleRemoval MAYBE
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__incr(X)) -> incr(X)
            activate(n__repItems(X)) -> repItems(X)
            activate(n__take(X1,X2)) -> take(X1,X2)
            activate(n__zip(X1,X2)) -> zip(X1,X2)
            cons(X1,X2) -> n__cons(X1,X2)
            incr(X) -> n__incr(X)
            incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS)))
            oddNs() -> incr(pairNs())
            pairNs() -> cons(0(),n__incr(oddNs()))
            repItems(X) -> n__repItems(X)
            repItems(cons(X,XS)) -> cons(X,n__cons(X,n__repItems(activate(XS))))
            repItems(nil()) -> nil()
            tail(cons(X,XS)) -> activate(XS)
            take(X1,X2) -> n__take(X1,X2)
            take(0(),XS) -> nil()
            take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
            zip(X,nil()) -> nil()
            zip(X1,X2) -> n__zip(X1,X2)
            zip(cons(X,XS),cons(Y,YS)) -> cons(pair(X,Y),n__zip(activate(XS),activate(YS)))
            zip(nil(),XS) -> nil()
        - Signature:
            {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2} / {0/0,n__cons/2,n__incr/1
            ,n__repItems/1,n__take/2,n__zip/2,nil/0,pair/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,cons,incr,oddNs,pairNs,repItems,tail,take
            ,zip} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s}
    + Applied Processor:
        InnermostRuleRemoval
    + Details:
        Arguments of following rules are not normal-forms.
          incr(cons(X,XS)) -> cons(s(X),n__incr(activate(XS)))
          repItems(cons(X,XS)) -> cons(X,n__cons(X,n__repItems(activate(XS))))
          tail(cons(X,XS)) -> activate(XS)
          take(s(N),cons(X,XS)) -> cons(X,n__take(N,activate(XS)))
          zip(cons(X,XS),cons(Y,YS)) -> cons(pair(X,Y),n__zip(activate(XS),activate(YS)))
        All above mentioned rules can be savely removed.
* Step 2: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__incr(X)) -> incr(X)
            activate(n__repItems(X)) -> repItems(X)
            activate(n__take(X1,X2)) -> take(X1,X2)
            activate(n__zip(X1,X2)) -> zip(X1,X2)
            cons(X1,X2) -> n__cons(X1,X2)
            incr(X) -> n__incr(X)
            oddNs() -> incr(pairNs())
            pairNs() -> cons(0(),n__incr(oddNs()))
            repItems(X) -> n__repItems(X)
            repItems(nil()) -> nil()
            take(X1,X2) -> n__take(X1,X2)
            take(0(),XS) -> nil()
            zip(X,nil()) -> nil()
            zip(X1,X2) -> n__zip(X1,X2)
            zip(nil(),XS) -> nil()
        - Signature:
            {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2} / {0/0,n__cons/2,n__incr/1
            ,n__repItems/1,n__take/2,n__zip/2,nil/0,pair/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,cons,incr,oddNs,pairNs,repItems,tail,take
            ,zip} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          activate#(X) -> c_1()
          activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
          activate#(n__incr(X)) -> c_3(incr#(X))
          activate#(n__repItems(X)) -> c_4(repItems#(X))
          activate#(n__take(X1,X2)) -> c_5(take#(X1,X2))
          activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2))
          cons#(X1,X2) -> c_7()
          incr#(X) -> c_8()
          oddNs#() -> c_9(incr#(pairNs()),pairNs#())
          pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#())
          repItems#(X) -> c_11()
          repItems#(nil()) -> c_12()
          take#(X1,X2) -> c_13()
          take#(0(),XS) -> c_14()
          zip#(X,nil()) -> c_15()
          zip#(X1,X2) -> c_16()
          zip#(nil(),XS) -> c_17()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
            activate#(n__incr(X)) -> c_3(incr#(X))
            activate#(n__repItems(X)) -> c_4(repItems#(X))
            activate#(n__take(X1,X2)) -> c_5(take#(X1,X2))
            activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2))
            cons#(X1,X2) -> c_7()
            incr#(X) -> c_8()
            oddNs#() -> c_9(incr#(pairNs()),pairNs#())
            pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#())
            repItems#(X) -> c_11()
            repItems#(nil()) -> c_12()
            take#(X1,X2) -> c_13()
            take#(0(),XS) -> c_14()
            zip#(X,nil()) -> c_15()
            zip#(X1,X2) -> c_16()
            zip#(nil(),XS) -> c_17()
        - Weak TRS:
            activate(X) -> X
            activate(n__cons(X1,X2)) -> cons(X1,X2)
            activate(n__incr(X)) -> incr(X)
            activate(n__repItems(X)) -> repItems(X)
            activate(n__take(X1,X2)) -> take(X1,X2)
            activate(n__zip(X1,X2)) -> zip(X1,X2)
            cons(X1,X2) -> n__cons(X1,X2)
            incr(X) -> n__incr(X)
            oddNs() -> incr(pairNs())
            pairNs() -> cons(0(),n__incr(oddNs()))
            repItems(X) -> n__repItems(X)
            repItems(nil()) -> nil()
            take(X1,X2) -> n__take(X1,X2)
            take(0(),XS) -> nil()
            zip(X,nil()) -> nil()
            zip(X1,X2) -> n__zip(X1,X2)
            zip(nil(),XS) -> nil()
        - Signature:
            {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1
            ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2
            ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/0,c_12/0,c_13/0
            ,c_14/0,c_15/0,c_16/0,c_17/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail#
            ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          cons(X1,X2) -> n__cons(X1,X2)
          incr(X) -> n__incr(X)
          oddNs() -> incr(pairNs())
          pairNs() -> cons(0(),n__incr(oddNs()))
          activate#(X) -> c_1()
          activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
          activate#(n__incr(X)) -> c_3(incr#(X))
          activate#(n__repItems(X)) -> c_4(repItems#(X))
          activate#(n__take(X1,X2)) -> c_5(take#(X1,X2))
          activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2))
          cons#(X1,X2) -> c_7()
          incr#(X) -> c_8()
          oddNs#() -> c_9(incr#(pairNs()),pairNs#())
          pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#())
          repItems#(X) -> c_11()
          repItems#(nil()) -> c_12()
          take#(X1,X2) -> c_13()
          take#(0(),XS) -> c_14()
          zip#(X,nil()) -> c_15()
          zip#(X1,X2) -> c_16()
          zip#(nil(),XS) -> c_17()
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
            activate#(n__incr(X)) -> c_3(incr#(X))
            activate#(n__repItems(X)) -> c_4(repItems#(X))
            activate#(n__take(X1,X2)) -> c_5(take#(X1,X2))
            activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2))
            cons#(X1,X2) -> c_7()
            incr#(X) -> c_8()
            oddNs#() -> c_9(incr#(pairNs()),pairNs#())
            pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#())
            repItems#(X) -> c_11()
            repItems#(nil()) -> c_12()
            take#(X1,X2) -> c_13()
            take#(0(),XS) -> c_14()
            zip#(X,nil()) -> c_15()
            zip#(X1,X2) -> c_16()
            zip#(nil(),XS) -> c_17()
        - Weak TRS:
            cons(X1,X2) -> n__cons(X1,X2)
            incr(X) -> n__incr(X)
            oddNs() -> incr(pairNs())
            pairNs() -> cons(0(),n__incr(oddNs()))
        - Signature:
            {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1
            ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2
            ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/0,c_12/0,c_13/0
            ,c_14/0,c_15/0,c_16/0,c_17/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail#
            ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,7,8,11,12,13,14,15,16,17}
        by application of
          Pre({1,7,8,11,12,13,14,15,16,17}) = {2,3,4,5,6,9,10}.
        Here rules are labelled as follows:
          1: activate#(X) -> c_1()
          2: activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
          3: activate#(n__incr(X)) -> c_3(incr#(X))
          4: activate#(n__repItems(X)) -> c_4(repItems#(X))
          5: activate#(n__take(X1,X2)) -> c_5(take#(X1,X2))
          6: activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2))
          7: cons#(X1,X2) -> c_7()
          8: incr#(X) -> c_8()
          9: oddNs#() -> c_9(incr#(pairNs()),pairNs#())
          10: pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#())
          11: repItems#(X) -> c_11()
          12: repItems#(nil()) -> c_12()
          13: take#(X1,X2) -> c_13()
          14: take#(0(),XS) -> c_14()
          15: zip#(X,nil()) -> c_15()
          16: zip#(X1,X2) -> c_16()
          17: zip#(nil(),XS) -> c_17()
* Step 5: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
            activate#(n__incr(X)) -> c_3(incr#(X))
            activate#(n__repItems(X)) -> c_4(repItems#(X))
            activate#(n__take(X1,X2)) -> c_5(take#(X1,X2))
            activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2))
            oddNs#() -> c_9(incr#(pairNs()),pairNs#())
            pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#())
        - Weak DPs:
            activate#(X) -> c_1()
            cons#(X1,X2) -> c_7()
            incr#(X) -> c_8()
            repItems#(X) -> c_11()
            repItems#(nil()) -> c_12()
            take#(X1,X2) -> c_13()
            take#(0(),XS) -> c_14()
            zip#(X,nil()) -> c_15()
            zip#(X1,X2) -> c_16()
            zip#(nil(),XS) -> c_17()
        - Weak TRS:
            cons(X1,X2) -> n__cons(X1,X2)
            incr(X) -> n__incr(X)
            oddNs() -> incr(pairNs())
            pairNs() -> cons(0(),n__incr(oddNs()))
        - Signature:
            {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1
            ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2
            ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/0,c_12/0,c_13/0
            ,c_14/0,c_15/0,c_16/0,c_17/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail#
            ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,3,4,5}
        by application of
          Pre({1,2,3,4,5}) = {}.
        Here rules are labelled as follows:
          1: activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
          2: activate#(n__incr(X)) -> c_3(incr#(X))
          3: activate#(n__repItems(X)) -> c_4(repItems#(X))
          4: activate#(n__take(X1,X2)) -> c_5(take#(X1,X2))
          5: activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2))
          6: oddNs#() -> c_9(incr#(pairNs()),pairNs#())
          7: pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#())
          8: activate#(X) -> c_1()
          9: cons#(X1,X2) -> c_7()
          10: incr#(X) -> c_8()
          11: repItems#(X) -> c_11()
          12: repItems#(nil()) -> c_12()
          13: take#(X1,X2) -> c_13()
          14: take#(0(),XS) -> c_14()
          15: zip#(X,nil()) -> c_15()
          16: zip#(X1,X2) -> c_16()
          17: zip#(nil(),XS) -> c_17()
* Step 6: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            oddNs#() -> c_9(incr#(pairNs()),pairNs#())
            pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#())
        - Weak DPs:
            activate#(X) -> c_1()
            activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
            activate#(n__incr(X)) -> c_3(incr#(X))
            activate#(n__repItems(X)) -> c_4(repItems#(X))
            activate#(n__take(X1,X2)) -> c_5(take#(X1,X2))
            activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2))
            cons#(X1,X2) -> c_7()
            incr#(X) -> c_8()
            repItems#(X) -> c_11()
            repItems#(nil()) -> c_12()
            take#(X1,X2) -> c_13()
            take#(0(),XS) -> c_14()
            zip#(X,nil()) -> c_15()
            zip#(X1,X2) -> c_16()
            zip#(nil(),XS) -> c_17()
        - Weak TRS:
            cons(X1,X2) -> n__cons(X1,X2)
            incr(X) -> n__incr(X)
            oddNs() -> incr(pairNs())
            pairNs() -> cons(0(),n__incr(oddNs()))
        - Signature:
            {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1
            ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2
            ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/0,c_12/0,c_13/0
            ,c_14/0,c_15/0,c_16/0,c_17/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail#
            ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:oddNs#() -> c_9(incr#(pairNs()),pairNs#())
             -->_2 pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#()):2
             -->_1 incr#(X) -> c_8():10
          
          2:S:pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#())
             -->_1 cons#(X1,X2) -> c_7():9
             -->_2 oddNs#() -> c_9(incr#(pairNs()),pairNs#()):1
          
          3:W:activate#(X) -> c_1()
             
          
          4:W:activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
             -->_1 cons#(X1,X2) -> c_7():9
          
          5:W:activate#(n__incr(X)) -> c_3(incr#(X))
             -->_1 incr#(X) -> c_8():10
          
          6:W:activate#(n__repItems(X)) -> c_4(repItems#(X))
             -->_1 repItems#(nil()) -> c_12():12
             -->_1 repItems#(X) -> c_11():11
          
          7:W:activate#(n__take(X1,X2)) -> c_5(take#(X1,X2))
             -->_1 take#(0(),XS) -> c_14():14
             -->_1 take#(X1,X2) -> c_13():13
          
          8:W:activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2))
             -->_1 zip#(nil(),XS) -> c_17():17
             -->_1 zip#(X1,X2) -> c_16():16
             -->_1 zip#(X,nil()) -> c_15():15
          
          9:W:cons#(X1,X2) -> c_7()
             
          
          10:W:incr#(X) -> c_8()
             
          
          11:W:repItems#(X) -> c_11()
             
          
          12:W:repItems#(nil()) -> c_12()
             
          
          13:W:take#(X1,X2) -> c_13()
             
          
          14:W:take#(0(),XS) -> c_14()
             
          
          15:W:zip#(X,nil()) -> c_15()
             
          
          16:W:zip#(X1,X2) -> c_16()
             
          
          17:W:zip#(nil(),XS) -> c_17()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          8: activate#(n__zip(X1,X2)) -> c_6(zip#(X1,X2))
          15: zip#(X,nil()) -> c_15()
          16: zip#(X1,X2) -> c_16()
          17: zip#(nil(),XS) -> c_17()
          7: activate#(n__take(X1,X2)) -> c_5(take#(X1,X2))
          13: take#(X1,X2) -> c_13()
          14: take#(0(),XS) -> c_14()
          6: activate#(n__repItems(X)) -> c_4(repItems#(X))
          11: repItems#(X) -> c_11()
          12: repItems#(nil()) -> c_12()
          5: activate#(n__incr(X)) -> c_3(incr#(X))
          4: activate#(n__cons(X1,X2)) -> c_2(cons#(X1,X2))
          3: activate#(X) -> c_1()
          10: incr#(X) -> c_8()
          9: cons#(X1,X2) -> c_7()
* Step 7: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            oddNs#() -> c_9(incr#(pairNs()),pairNs#())
            pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#())
        - Weak TRS:
            cons(X1,X2) -> n__cons(X1,X2)
            incr(X) -> n__incr(X)
            oddNs() -> incr(pairNs())
            pairNs() -> cons(0(),n__incr(oddNs()))
        - Signature:
            {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1
            ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2
            ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/2,c_10/2,c_11/0,c_12/0,c_13/0
            ,c_14/0,c_15/0,c_16/0,c_17/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail#
            ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:oddNs#() -> c_9(incr#(pairNs()),pairNs#())
             -->_2 pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#()):2
          
          2:S:pairNs#() -> c_10(cons#(0(),n__incr(oddNs())),oddNs#())
             -->_2 oddNs#() -> c_9(incr#(pairNs()),pairNs#()):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          oddNs#() -> c_9(pairNs#())
          pairNs#() -> c_10(oddNs#())
* Step 8: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            oddNs#() -> c_9(pairNs#())
            pairNs#() -> c_10(oddNs#())
        - Weak TRS:
            cons(X1,X2) -> n__cons(X1,X2)
            incr(X) -> n__incr(X)
            oddNs() -> incr(pairNs())
            pairNs() -> cons(0(),n__incr(oddNs()))
        - Signature:
            {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1
            ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2
            ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/1,c_10/1,c_11/0,c_12/0,c_13/0
            ,c_14/0,c_15/0,c_16/0,c_17/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail#
            ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          oddNs#() -> c_9(pairNs#())
          pairNs#() -> c_10(oddNs#())
* Step 9: WeightGap MAYBE
    + Considered Problem:
        - Strict DPs:
            oddNs#() -> c_9(pairNs#())
            pairNs#() -> c_10(oddNs#())
        - Signature:
            {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1
            ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2
            ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/1,c_10/1,c_11/0,c_12/0,c_13/0
            ,c_14/0,c_15/0,c_16/0,c_17/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail#
            ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,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_9) = {1},
            uargs(c_10) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                      p(0) = [0]         
               p(activate) = [0]         
                   p(cons) = [0]         
                   p(incr) = [0]         
                p(n__cons) = [0]         
                p(n__incr) = [0]         
            p(n__repItems) = [0]         
                p(n__take) = [0]         
                 p(n__zip) = [0]         
                    p(nil) = [0]         
                  p(oddNs) = [0]         
                   p(pair) = [0]         
                 p(pairNs) = [0]         
               p(repItems) = [0]         
                      p(s) = [0]         
                   p(tail) = [0]         
                   p(take) = [0]         
                    p(zip) = [0]         
              p(activate#) = [0]         
                  p(cons#) = [0]         
                  p(incr#) = [0]         
                 p(oddNs#) = [0]         
                p(pairNs#) = [3]         
              p(repItems#) = [0]         
                  p(tail#) = [0]         
                  p(take#) = [0]         
                   p(zip#) = [0]         
                    p(c_1) = [0]         
                    p(c_2) = [0]         
                    p(c_3) = [0]         
                    p(c_4) = [0]         
                    p(c_5) = [0]         
                    p(c_6) = [0]         
                    p(c_7) = [0]         
                    p(c_8) = [0]         
                    p(c_9) = [1] x1 + [0]
                   p(c_10) = [1] x1 + [0]
                   p(c_11) = [0]         
                   p(c_12) = [0]         
                   p(c_13) = [0]         
                   p(c_14) = [0]         
                   p(c_15) = [0]         
                   p(c_16) = [0]         
                   p(c_17) = [0]         
          
          Following rules are strictly oriented:
          pairNs#() = [3]           
                    > [0]           
                    = c_10(oddNs#())
          
          
          Following rules are (at-least) weakly oriented:
          oddNs#() =  [0]           
                   >= [3]           
                   =  c_9(pairNs#())
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 10: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          oddNs#() -> c_9(pairNs#())
      - Weak DPs:
          pairNs#() -> c_10(oddNs#())
      - Signature:
          {activate/1,cons/2,incr/1,oddNs/0,pairNs/0,repItems/1,tail/1,take/2,zip/2,activate#/1,cons#/2,incr#/1
          ,oddNs#/0,pairNs#/0,repItems#/1,tail#/1,take#/2,zip#/2} / {0/0,n__cons/2,n__incr/1,n__repItems/1,n__take/2
          ,n__zip/2,nil/0,pair/2,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1,c_7/0,c_8/0,c_9/1,c_10/1,c_11/0,c_12/0,c_13/0
          ,c_14/0,c_15/0,c_16/0,c_17/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {activate#,cons#,incr#,oddNs#,pairNs#,repItems#,tail#
          ,take#,zip#} and constructors {0,n__cons,n__incr,n__repItems,n__take,n__zip,nil,pair,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE