MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            minus(X,0()) -> 0()
            minus(s(X),s(Y)) -> minus(X,Y)
            quot(0(),s(Y)) -> 0()
            quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
            zWquot(X1,X2) -> n__zWquot(X1,X2)
            zWquot(XS,nil()) -> nil()
            zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
            zWquot(nil(),XS) -> nil()
        - Signature:
            {activate/1,from/1,minus/2,quot/2,sel/2,zWquot/2} / {0/0,cons/2,n__from/1,n__zWquot/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,from,minus,quot,sel,zWquot} and constructors {0
            ,cons,n__from,n__zWquot,nil,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          activate#(X) -> c_1()
          activate#(n__from(X)) -> c_2(from#(X))
          activate#(n__zWquot(X1,X2)) -> c_3(zWquot#(X1,X2))
          from#(X) -> c_4()
          from#(X) -> c_5()
          minus#(X,0()) -> c_6()
          minus#(s(X),s(Y)) -> c_7(minus#(X,Y))
          quot#(0(),s(Y)) -> c_8()
          quot#(s(X),s(Y)) -> c_9(quot#(minus(X,Y),s(Y)),minus#(X,Y))
          sel#(0(),cons(X,XS)) -> c_10()
          sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
          zWquot#(X1,X2) -> c_12()
          zWquot#(XS,nil()) -> c_13()
          zWquot#(cons(X,XS),cons(Y,YS)) -> c_14(quot#(X,Y),activate#(XS),activate#(YS))
          zWquot#(nil(),XS) -> c_15()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__from(X)) -> c_2(from#(X))
            activate#(n__zWquot(X1,X2)) -> c_3(zWquot#(X1,X2))
            from#(X) -> c_4()
            from#(X) -> c_5()
            minus#(X,0()) -> c_6()
            minus#(s(X),s(Y)) -> c_7(minus#(X,Y))
            quot#(0(),s(Y)) -> c_8()
            quot#(s(X),s(Y)) -> c_9(quot#(minus(X,Y),s(Y)),minus#(X,Y))
            sel#(0(),cons(X,XS)) -> c_10()
            sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
            zWquot#(X1,X2) -> c_12()
            zWquot#(XS,nil()) -> c_13()
            zWquot#(cons(X,XS),cons(Y,YS)) -> c_14(quot#(X,Y),activate#(XS),activate#(YS))
            zWquot#(nil(),XS) -> c_15()
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            minus(X,0()) -> 0()
            minus(s(X),s(Y)) -> minus(X,Y)
            quot(0(),s(Y)) -> 0()
            quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
            zWquot(X1,X2) -> n__zWquot(X1,X2)
            zWquot(XS,nil()) -> nil()
            zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
            zWquot(nil(),XS) -> nil()
        - Signature:
            {activate/1,from/1,minus/2,quot/2,sel/2,zWquot/2,activate#/1,from#/1,minus#/2,quot#/2,sel#/2
            ,zWquot#/2} / {0/0,cons/2,n__from/1,n__zWquot/2,nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/0,c_5/0,c_6/0,c_7/1,c_8/0
            ,c_9/2,c_10/0,c_11/2,c_12/0,c_13/0,c_14/3,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,from#,minus#,quot#,sel#
            ,zWquot#} and constructors {0,cons,n__from,n__zWquot,nil,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate(X) -> X
          activate(n__from(X)) -> from(X)
          activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
          from(X) -> cons(X,n__from(s(X)))
          from(X) -> n__from(X)
          minus(X,0()) -> 0()
          minus(s(X),s(Y)) -> minus(X,Y)
          quot(0(),s(Y)) -> 0()
          quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
          zWquot(X1,X2) -> n__zWquot(X1,X2)
          zWquot(XS,nil()) -> nil()
          zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
          zWquot(nil(),XS) -> nil()
          activate#(X) -> c_1()
          activate#(n__from(X)) -> c_2(from#(X))
          activate#(n__zWquot(X1,X2)) -> c_3(zWquot#(X1,X2))
          from#(X) -> c_4()
          from#(X) -> c_5()
          minus#(X,0()) -> c_6()
          minus#(s(X),s(Y)) -> c_7(minus#(X,Y))
          quot#(0(),s(Y)) -> c_8()
          quot#(s(X),s(Y)) -> c_9(quot#(minus(X,Y),s(Y)),minus#(X,Y))
          sel#(0(),cons(X,XS)) -> c_10()
          sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
          zWquot#(X1,X2) -> c_12()
          zWquot#(XS,nil()) -> c_13()
          zWquot#(cons(X,XS),cons(Y,YS)) -> c_14(quot#(X,Y),activate#(XS),activate#(YS))
          zWquot#(nil(),XS) -> c_15()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__from(X)) -> c_2(from#(X))
            activate#(n__zWquot(X1,X2)) -> c_3(zWquot#(X1,X2))
            from#(X) -> c_4()
            from#(X) -> c_5()
            minus#(X,0()) -> c_6()
            minus#(s(X),s(Y)) -> c_7(minus#(X,Y))
            quot#(0(),s(Y)) -> c_8()
            quot#(s(X),s(Y)) -> c_9(quot#(minus(X,Y),s(Y)),minus#(X,Y))
            sel#(0(),cons(X,XS)) -> c_10()
            sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
            zWquot#(X1,X2) -> c_12()
            zWquot#(XS,nil()) -> c_13()
            zWquot#(cons(X,XS),cons(Y,YS)) -> c_14(quot#(X,Y),activate#(XS),activate#(YS))
            zWquot#(nil(),XS) -> c_15()
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            minus(X,0()) -> 0()
            minus(s(X),s(Y)) -> minus(X,Y)
            quot(0(),s(Y)) -> 0()
            quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
            zWquot(X1,X2) -> n__zWquot(X1,X2)
            zWquot(XS,nil()) -> nil()
            zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
            zWquot(nil(),XS) -> nil()
        - Signature:
            {activate/1,from/1,minus/2,quot/2,sel/2,zWquot/2,activate#/1,from#/1,minus#/2,quot#/2,sel#/2
            ,zWquot#/2} / {0/0,cons/2,n__from/1,n__zWquot/2,nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/0,c_5/0,c_6/0,c_7/1,c_8/0
            ,c_9/2,c_10/0,c_11/2,c_12/0,c_13/0,c_14/3,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,from#,minus#,quot#,sel#
            ,zWquot#} and constructors {0,cons,n__from,n__zWquot,nil,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4,5,6,8,10,12,13,15}
        by application of
          Pre({1,4,5,6,8,10,12,13,15}) = {2,3,7,9,11,14}.
        Here rules are labelled as follows:
          1: activate#(X) -> c_1()
          2: activate#(n__from(X)) -> c_2(from#(X))
          3: activate#(n__zWquot(X1,X2)) -> c_3(zWquot#(X1,X2))
          4: from#(X) -> c_4()
          5: from#(X) -> c_5()
          6: minus#(X,0()) -> c_6()
          7: minus#(s(X),s(Y)) -> c_7(minus#(X,Y))
          8: quot#(0(),s(Y)) -> c_8()
          9: quot#(s(X),s(Y)) -> c_9(quot#(minus(X,Y),s(Y)),minus#(X,Y))
          10: sel#(0(),cons(X,XS)) -> c_10()
          11: sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
          12: zWquot#(X1,X2) -> c_12()
          13: zWquot#(XS,nil()) -> c_13()
          14: zWquot#(cons(X,XS),cons(Y,YS)) -> c_14(quot#(X,Y),activate#(XS),activate#(YS))
          15: zWquot#(nil(),XS) -> c_15()
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__from(X)) -> c_2(from#(X))
            activate#(n__zWquot(X1,X2)) -> c_3(zWquot#(X1,X2))
            minus#(s(X),s(Y)) -> c_7(minus#(X,Y))
            quot#(s(X),s(Y)) -> c_9(quot#(minus(X,Y),s(Y)),minus#(X,Y))
            sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
            zWquot#(cons(X,XS),cons(Y,YS)) -> c_14(quot#(X,Y),activate#(XS),activate#(YS))
        - Weak DPs:
            activate#(X) -> c_1()
            from#(X) -> c_4()
            from#(X) -> c_5()
            minus#(X,0()) -> c_6()
            quot#(0(),s(Y)) -> c_8()
            sel#(0(),cons(X,XS)) -> c_10()
            zWquot#(X1,X2) -> c_12()
            zWquot#(XS,nil()) -> c_13()
            zWquot#(nil(),XS) -> c_15()
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            minus(X,0()) -> 0()
            minus(s(X),s(Y)) -> minus(X,Y)
            quot(0(),s(Y)) -> 0()
            quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
            zWquot(X1,X2) -> n__zWquot(X1,X2)
            zWquot(XS,nil()) -> nil()
            zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
            zWquot(nil(),XS) -> nil()
        - Signature:
            {activate/1,from/1,minus/2,quot/2,sel/2,zWquot/2,activate#/1,from#/1,minus#/2,quot#/2,sel#/2
            ,zWquot#/2} / {0/0,cons/2,n__from/1,n__zWquot/2,nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/0,c_5/0,c_6/0,c_7/1,c_8/0
            ,c_9/2,c_10/0,c_11/2,c_12/0,c_13/0,c_14/3,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,from#,minus#,quot#,sel#
            ,zWquot#} and constructors {0,cons,n__from,n__zWquot,nil,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {5,6}.
        Here rules are labelled as follows:
          1: activate#(n__from(X)) -> c_2(from#(X))
          2: activate#(n__zWquot(X1,X2)) -> c_3(zWquot#(X1,X2))
          3: minus#(s(X),s(Y)) -> c_7(minus#(X,Y))
          4: quot#(s(X),s(Y)) -> c_9(quot#(minus(X,Y),s(Y)),minus#(X,Y))
          5: sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
          6: zWquot#(cons(X,XS),cons(Y,YS)) -> c_14(quot#(X,Y),activate#(XS),activate#(YS))
          7: activate#(X) -> c_1()
          8: from#(X) -> c_4()
          9: from#(X) -> c_5()
          10: minus#(X,0()) -> c_6()
          11: quot#(0(),s(Y)) -> c_8()
          12: sel#(0(),cons(X,XS)) -> c_10()
          13: zWquot#(X1,X2) -> c_12()
          14: zWquot#(XS,nil()) -> c_13()
          15: zWquot#(nil(),XS) -> c_15()
* Step 5: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__zWquot(X1,X2)) -> c_3(zWquot#(X1,X2))
            minus#(s(X),s(Y)) -> c_7(minus#(X,Y))
            quot#(s(X),s(Y)) -> c_9(quot#(minus(X,Y),s(Y)),minus#(X,Y))
            sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
            zWquot#(cons(X,XS),cons(Y,YS)) -> c_14(quot#(X,Y),activate#(XS),activate#(YS))
        - Weak DPs:
            activate#(X) -> c_1()
            activate#(n__from(X)) -> c_2(from#(X))
            from#(X) -> c_4()
            from#(X) -> c_5()
            minus#(X,0()) -> c_6()
            quot#(0(),s(Y)) -> c_8()
            sel#(0(),cons(X,XS)) -> c_10()
            zWquot#(X1,X2) -> c_12()
            zWquot#(XS,nil()) -> c_13()
            zWquot#(nil(),XS) -> c_15()
        - Weak TRS:
            activate(X) -> X
            activate(n__from(X)) -> from(X)
            activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
            from(X) -> cons(X,n__from(s(X)))
            from(X) -> n__from(X)
            minus(X,0()) -> 0()
            minus(s(X),s(Y)) -> minus(X,Y)
            quot(0(),s(Y)) -> 0()
            quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
            zWquot(X1,X2) -> n__zWquot(X1,X2)
            zWquot(XS,nil()) -> nil()
            zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
            zWquot(nil(),XS) -> nil()
        - Signature:
            {activate/1,from/1,minus/2,quot/2,sel/2,zWquot/2,activate#/1,from#/1,minus#/2,quot#/2,sel#/2
            ,zWquot#/2} / {0/0,cons/2,n__from/1,n__zWquot/2,nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/0,c_5/0,c_6/0,c_7/1,c_8/0
            ,c_9/2,c_10/0,c_11/2,c_12/0,c_13/0,c_14/3,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,from#,minus#,quot#,sel#
            ,zWquot#} and constructors {0,cons,n__from,n__zWquot,nil,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:activate#(n__zWquot(X1,X2)) -> c_3(zWquot#(X1,X2))
             -->_1 zWquot#(cons(X,XS),cons(Y,YS)) -> c_14(quot#(X,Y),activate#(XS),activate#(YS)):5
             -->_1 zWquot#(nil(),XS) -> c_15():15
             -->_1 zWquot#(XS,nil()) -> c_13():14
             -->_1 zWquot#(X1,X2) -> c_12():13
          
          2:S:minus#(s(X),s(Y)) -> c_7(minus#(X,Y))
             -->_1 minus#(X,0()) -> c_6():10
             -->_1 minus#(s(X),s(Y)) -> c_7(minus#(X,Y)):2
          
          3:S:quot#(s(X),s(Y)) -> c_9(quot#(minus(X,Y),s(Y)),minus#(X,Y))
             -->_1 quot#(0(),s(Y)) -> c_8():11
             -->_2 minus#(X,0()) -> c_6():10
             -->_1 quot#(s(X),s(Y)) -> c_9(quot#(minus(X,Y),s(Y)),minus#(X,Y)):3
             -->_2 minus#(s(X),s(Y)) -> c_7(minus#(X,Y)):2
          
          4:S:sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
             -->_2 activate#(n__from(X)) -> c_2(from#(X)):7
             -->_1 sel#(0(),cons(X,XS)) -> c_10():12
             -->_2 activate#(X) -> c_1():6
             -->_1 sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS)):4
             -->_2 activate#(n__zWquot(X1,X2)) -> c_3(zWquot#(X1,X2)):1
          
          5:S:zWquot#(cons(X,XS),cons(Y,YS)) -> c_14(quot#(X,Y),activate#(XS),activate#(YS))
             -->_3 activate#(n__from(X)) -> c_2(from#(X)):7
             -->_2 activate#(n__from(X)) -> c_2(from#(X)):7
             -->_1 quot#(0(),s(Y)) -> c_8():11
             -->_3 activate#(X) -> c_1():6
             -->_2 activate#(X) -> c_1():6
             -->_1 quot#(s(X),s(Y)) -> c_9(quot#(minus(X,Y),s(Y)),minus#(X,Y)):3
             -->_3 activate#(n__zWquot(X1,X2)) -> c_3(zWquot#(X1,X2)):1
             -->_2 activate#(n__zWquot(X1,X2)) -> c_3(zWquot#(X1,X2)):1
          
          6:W:activate#(X) -> c_1()
             
          
          7:W:activate#(n__from(X)) -> c_2(from#(X))
             -->_1 from#(X) -> c_5():9
             -->_1 from#(X) -> c_4():8
          
          8:W:from#(X) -> c_4()
             
          
          9:W:from#(X) -> c_5()
             
          
          10:W:minus#(X,0()) -> c_6()
             
          
          11:W:quot#(0(),s(Y)) -> c_8()
             
          
          12:W:sel#(0(),cons(X,XS)) -> c_10()
             
          
          13:W:zWquot#(X1,X2) -> c_12()
             
          
          14:W:zWquot#(XS,nil()) -> c_13()
             
          
          15:W:zWquot#(nil(),XS) -> c_15()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          12: sel#(0(),cons(X,XS)) -> c_10()
          13: zWquot#(X1,X2) -> c_12()
          14: zWquot#(XS,nil()) -> c_13()
          15: zWquot#(nil(),XS) -> c_15()
          10: minus#(X,0()) -> c_6()
          6: activate#(X) -> c_1()
          11: quot#(0(),s(Y)) -> c_8()
          7: activate#(n__from(X)) -> c_2(from#(X))
          8: from#(X) -> c_4()
          9: from#(X) -> c_5()
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          activate#(n__zWquot(X1,X2)) -> c_3(zWquot#(X1,X2))
          minus#(s(X),s(Y)) -> c_7(minus#(X,Y))
          quot#(s(X),s(Y)) -> c_9(quot#(minus(X,Y),s(Y)),minus#(X,Y))
          sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
          zWquot#(cons(X,XS),cons(Y,YS)) -> c_14(quot#(X,Y),activate#(XS),activate#(YS))
      - Weak TRS:
          activate(X) -> X
          activate(n__from(X)) -> from(X)
          activate(n__zWquot(X1,X2)) -> zWquot(X1,X2)
          from(X) -> cons(X,n__from(s(X)))
          from(X) -> n__from(X)
          minus(X,0()) -> 0()
          minus(s(X),s(Y)) -> minus(X,Y)
          quot(0(),s(Y)) -> 0()
          quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y)))
          zWquot(X1,X2) -> n__zWquot(X1,X2)
          zWquot(XS,nil()) -> nil()
          zWquot(cons(X,XS),cons(Y,YS)) -> cons(quot(X,Y),n__zWquot(activate(XS),activate(YS)))
          zWquot(nil(),XS) -> nil()
      - Signature:
          {activate/1,from/1,minus/2,quot/2,sel/2,zWquot/2,activate#/1,from#/1,minus#/2,quot#/2,sel#/2
          ,zWquot#/2} / {0/0,cons/2,n__from/1,n__zWquot/2,nil/0,s/1,c_1/0,c_2/1,c_3/1,c_4/0,c_5/0,c_6/0,c_7/1,c_8/0
          ,c_9/2,c_10/0,c_11/2,c_12/0,c_13/0,c_14/3,c_15/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {activate#,from#,minus#,quot#,sel#
          ,zWquot#} and constructors {0,cons,n__from,n__zWquot,nil,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE