MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            activate(X) -> X
            activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
            activate(n__fib1(X1,X2)) -> fib1(activate(X1),activate(X2))
            add(X1,X2) -> n__add(X1,X2)
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            fib(N) -> sel(N,fib1(s(0()),s(0())))
            fib1(X,Y) -> cons(X,n__fib1(Y,n__add(X,Y)))
            fib1(X1,X2) -> n__fib1(X1,X2)
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
        - Signature:
            {activate/1,add/2,fib/1,fib1/2,sel/2} / {0/0,cons/2,n__add/2,n__fib1/2,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate,add,fib,fib1,sel} and constructors {0,cons
            ,n__add,n__fib1,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          activate#(X) -> c_1()
          activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
          activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
          add#(X1,X2) -> c_4()
          add#(0(),X) -> c_5()
          add#(s(X),Y) -> c_6(add#(X,Y))
          fib#(N) -> c_7(sel#(N,fib1(s(0()),s(0()))),fib1#(s(0()),s(0())))
          fib1#(X,Y) -> c_8()
          fib1#(X1,X2) -> c_9()
          sel#(0(),cons(X,XS)) -> c_10()
          sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            add#(X1,X2) -> c_4()
            add#(0(),X) -> c_5()
            add#(s(X),Y) -> c_6(add#(X,Y))
            fib#(N) -> c_7(sel#(N,fib1(s(0()),s(0()))),fib1#(s(0()),s(0())))
            fib1#(X,Y) -> c_8()
            fib1#(X1,X2) -> c_9()
            sel#(0(),cons(X,XS)) -> c_10()
            sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
        - Weak TRS:
            activate(X) -> X
            activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
            activate(n__fib1(X1,X2)) -> fib1(activate(X1),activate(X2))
            add(X1,X2) -> n__add(X1,X2)
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            fib(N) -> sel(N,fib1(s(0()),s(0())))
            fib1(X,Y) -> cons(X,n__fib1(Y,n__add(X,Y)))
            fib1(X1,X2) -> n__fib1(X1,X2)
            sel(0(),cons(X,XS)) -> X
            sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
        - Signature:
            {activate/1,add/2,fib/1,fib1/2,sel/2,activate#/1,add#/2,fib#/1,fib1#/2,sel#/2} / {0/0,cons/2,n__add/2
            ,n__fib1/2,s/1,c_1/0,c_2/3,c_3/3,c_4/0,c_5/0,c_6/1,c_7/2,c_8/0,c_9/0,c_10/0,c_11/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,add#,fib#,fib1#,sel#} and constructors {0,cons
            ,n__add,n__fib1,s}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate(X) -> X
          activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
          activate(n__fib1(X1,X2)) -> fib1(activate(X1),activate(X2))
          add(X1,X2) -> n__add(X1,X2)
          add(0(),X) -> X
          add(s(X),Y) -> s(add(X,Y))
          fib1(X,Y) -> cons(X,n__fib1(Y,n__add(X,Y)))
          fib1(X1,X2) -> n__fib1(X1,X2)
          activate#(X) -> c_1()
          activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
          activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
          add#(X1,X2) -> c_4()
          add#(0(),X) -> c_5()
          add#(s(X),Y) -> c_6(add#(X,Y))
          fib#(N) -> c_7(sel#(N,fib1(s(0()),s(0()))),fib1#(s(0()),s(0())))
          fib1#(X,Y) -> c_8()
          fib1#(X1,X2) -> c_9()
          sel#(0(),cons(X,XS)) -> c_10()
          sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(X) -> c_1()
            activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            add#(X1,X2) -> c_4()
            add#(0(),X) -> c_5()
            add#(s(X),Y) -> c_6(add#(X,Y))
            fib#(N) -> c_7(sel#(N,fib1(s(0()),s(0()))),fib1#(s(0()),s(0())))
            fib1#(X,Y) -> c_8()
            fib1#(X1,X2) -> c_9()
            sel#(0(),cons(X,XS)) -> c_10()
            sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
        - Weak TRS:
            activate(X) -> X
            activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
            activate(n__fib1(X1,X2)) -> fib1(activate(X1),activate(X2))
            add(X1,X2) -> n__add(X1,X2)
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            fib1(X,Y) -> cons(X,n__fib1(Y,n__add(X,Y)))
            fib1(X1,X2) -> n__fib1(X1,X2)
        - Signature:
            {activate/1,add/2,fib/1,fib1/2,sel/2,activate#/1,add#/2,fib#/1,fib1#/2,sel#/2} / {0/0,cons/2,n__add/2
            ,n__fib1/2,s/1,c_1/0,c_2/3,c_3/3,c_4/0,c_5/0,c_6/1,c_7/2,c_8/0,c_9/0,c_10/0,c_11/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,add#,fib#,fib1#,sel#} and constructors {0,cons
            ,n__add,n__fib1,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,4,5,8,9,10}
        by application of
          Pre({1,4,5,8,9,10}) = {2,3,6,7,11}.
        Here rules are labelled as follows:
          1: activate#(X) -> c_1()
          2: activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
          3: activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
          4: add#(X1,X2) -> c_4()
          5: add#(0(),X) -> c_5()
          6: add#(s(X),Y) -> c_6(add#(X,Y))
          7: fib#(N) -> c_7(sel#(N,fib1(s(0()),s(0()))),fib1#(s(0()),s(0())))
          8: fib1#(X,Y) -> c_8()
          9: fib1#(X1,X2) -> c_9()
          10: sel#(0(),cons(X,XS)) -> c_10()
          11: sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            add#(s(X),Y) -> c_6(add#(X,Y))
            fib#(N) -> c_7(sel#(N,fib1(s(0()),s(0()))),fib1#(s(0()),s(0())))
            sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
        - Weak DPs:
            activate#(X) -> c_1()
            add#(X1,X2) -> c_4()
            add#(0(),X) -> c_5()
            fib1#(X,Y) -> c_8()
            fib1#(X1,X2) -> c_9()
            sel#(0(),cons(X,XS)) -> c_10()
        - Weak TRS:
            activate(X) -> X
            activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
            activate(n__fib1(X1,X2)) -> fib1(activate(X1),activate(X2))
            add(X1,X2) -> n__add(X1,X2)
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            fib1(X,Y) -> cons(X,n__fib1(Y,n__add(X,Y)))
            fib1(X1,X2) -> n__fib1(X1,X2)
        - Signature:
            {activate/1,add/2,fib/1,fib1/2,sel/2,activate#/1,add#/2,fib#/1,fib1#/2,sel#/2} / {0/0,cons/2,n__add/2
            ,n__fib1/2,s/1,c_1/0,c_2/3,c_3/3,c_4/0,c_5/0,c_6/1,c_7/2,c_8/0,c_9/0,c_10/0,c_11/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,add#,fib#,fib1#,sel#} and constructors {0,cons
            ,n__add,n__fib1,s}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
             -->_1 add#(s(X),Y) -> c_6(add#(X,Y)):3
             -->_3 activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):2
             -->_2 activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):2
             -->_1 add#(0(),X) -> c_5():8
             -->_1 add#(X1,X2) -> c_4():7
             -->_3 activate#(X) -> c_1():6
             -->_2 activate#(X) -> c_1():6
             -->_3 activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
             -->_2 activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
          
          2:S:activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
             -->_1 fib1#(X1,X2) -> c_9():10
             -->_1 fib1#(X,Y) -> c_8():9
             -->_3 activate#(X) -> c_1():6
             -->_2 activate#(X) -> c_1():6
             -->_3 activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):2
             -->_2 activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):2
             -->_3 activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
             -->_2 activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
          
          3:S:add#(s(X),Y) -> c_6(add#(X,Y))
             -->_1 add#(0(),X) -> c_5():8
             -->_1 add#(X1,X2) -> c_4():7
             -->_1 add#(s(X),Y) -> c_6(add#(X,Y)):3
          
          4:S:fib#(N) -> c_7(sel#(N,fib1(s(0()),s(0()))),fib1#(s(0()),s(0())))
             -->_1 sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS)):5
             -->_1 sel#(0(),cons(X,XS)) -> c_10():11
             -->_2 fib1#(X1,X2) -> c_9():10
             -->_2 fib1#(X,Y) -> c_8():9
          
          5:S:sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
             -->_1 sel#(0(),cons(X,XS)) -> c_10():11
             -->_2 activate#(X) -> c_1():6
             -->_1 sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS)):5
             -->_2 activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):2
             -->_2 activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
          
          6:W:activate#(X) -> c_1()
             
          
          7:W:add#(X1,X2) -> c_4()
             
          
          8:W:add#(0(),X) -> c_5()
             
          
          9:W:fib1#(X,Y) -> c_8()
             
          
          10:W:fib1#(X1,X2) -> c_9()
             
          
          11:W:sel#(0(),cons(X,XS)) -> c_10()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          11: sel#(0(),cons(X,XS)) -> c_10()
          6: activate#(X) -> c_1()
          9: fib1#(X,Y) -> c_8()
          10: fib1#(X1,X2) -> c_9()
          7: add#(X1,X2) -> c_4()
          8: add#(0(),X) -> c_5()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            add#(s(X),Y) -> c_6(add#(X,Y))
            fib#(N) -> c_7(sel#(N,fib1(s(0()),s(0()))),fib1#(s(0()),s(0())))
            sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
        - Weak TRS:
            activate(X) -> X
            activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
            activate(n__fib1(X1,X2)) -> fib1(activate(X1),activate(X2))
            add(X1,X2) -> n__add(X1,X2)
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            fib1(X,Y) -> cons(X,n__fib1(Y,n__add(X,Y)))
            fib1(X1,X2) -> n__fib1(X1,X2)
        - Signature:
            {activate/1,add/2,fib/1,fib1/2,sel/2,activate#/1,add#/2,fib#/1,fib1#/2,sel#/2} / {0/0,cons/2,n__add/2
            ,n__fib1/2,s/1,c_1/0,c_2/3,c_3/3,c_4/0,c_5/0,c_6/1,c_7/2,c_8/0,c_9/0,c_10/0,c_11/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,add#,fib#,fib1#,sel#} and constructors {0,cons
            ,n__add,n__fib1,s}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
             -->_1 add#(s(X),Y) -> c_6(add#(X,Y)):3
             -->_3 activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):2
             -->_2 activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):2
             -->_3 activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
             -->_2 activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
          
          2:S:activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
             -->_3 activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):2
             -->_2 activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):2
             -->_3 activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
             -->_2 activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
          
          3:S:add#(s(X),Y) -> c_6(add#(X,Y))
             -->_1 add#(s(X),Y) -> c_6(add#(X,Y)):3
          
          4:S:fib#(N) -> c_7(sel#(N,fib1(s(0()),s(0()))),fib1#(s(0()),s(0())))
             -->_1 sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS)):5
          
          5:S:sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
             -->_1 sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS)):5
             -->_2 activate#(n__fib1(X1,X2)) -> c_3(fib1#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):2
             -->_2 activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          activate#(n__fib1(X1,X2)) -> c_3(activate#(X1),activate#(X2))
          fib#(N) -> c_7(sel#(N,fib1(s(0()),s(0()))))
* Step 6: NaturalMI MAYBE
    + Considered Problem:
        - Strict DPs:
            activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
            activate#(n__fib1(X1,X2)) -> c_3(activate#(X1),activate#(X2))
            add#(s(X),Y) -> c_6(add#(X,Y))
            fib#(N) -> c_7(sel#(N,fib1(s(0()),s(0()))))
            sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
        - Weak TRS:
            activate(X) -> X
            activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
            activate(n__fib1(X1,X2)) -> fib1(activate(X1),activate(X2))
            add(X1,X2) -> n__add(X1,X2)
            add(0(),X) -> X
            add(s(X),Y) -> s(add(X,Y))
            fib1(X,Y) -> cons(X,n__fib1(Y,n__add(X,Y)))
            fib1(X1,X2) -> n__fib1(X1,X2)
        - Signature:
            {activate/1,add/2,fib/1,fib1/2,sel/2,activate#/1,add#/2,fib#/1,fib1#/2,sel#/2} / {0/0,cons/2,n__add/2
            ,n__fib1/2,s/1,c_1/0,c_2/3,c_3/2,c_4/0,c_5/0,c_6/1,c_7/1,c_8/0,c_9/0,c_10/0,c_11/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {activate#,add#,fib#,fib1#,sel#} and constructors {0,cons
            ,n__add,n__fib1,s}
    + Applied Processor:
        NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules}
    + Details:
        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) = {1,2,3},
          uargs(c_3) = {1,2},
          uargs(c_6) = {1},
          uargs(c_7) = {1},
          uargs(c_11) = {1,2}
        
        Following symbols are considered usable:
          {activate#,add#,fib#,fib1#,sel#}
        TcT has computed the following interpretation:
                  p(0) = [0]                           
           p(activate) = [4] x1 + [6]                  
                p(add) = [0]                           
               p(cons) = [0]                           
                p(fib) = [0]                           
               p(fib1) = [5] x1 + [0]                  
             p(n__add) = [3]                           
            p(n__fib1) = [0]                           
                  p(s) = [5]                           
                p(sel) = [0]                           
          p(activate#) = [0]                           
               p(add#) = [0]                           
               p(fib#) = [11]                          
              p(fib1#) = [0]                           
               p(sel#) = [2]                           
                p(c_1) = [0]                           
                p(c_2) = [1] x1 + [4] x2 + [2] x3 + [0]
                p(c_3) = [4] x1 + [1] x2 + [0]         
                p(c_4) = [1]                           
                p(c_5) = [0]                           
                p(c_6) = [8] x1 + [0]                  
                p(c_7) = [1] x1 + [5]                  
                p(c_8) = [0]                           
                p(c_9) = [0]                           
               p(c_10) = [0]                           
               p(c_11) = [1] x1 + [1] x2 + [0]         
        
        Following rules are strictly oriented:
        fib#(N) = [11]                            
                > [7]                             
                = c_7(sel#(N,fib1(s(0()),s(0()))))
        
        
        Following rules are (at-least) weakly oriented:
         activate#(n__add(X1,X2)) =  [0]                                                             
                                  >= [0]                                                             
                                  =  c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
        
        activate#(n__fib1(X1,X2)) =  [0]                                                             
                                  >= [0]                                                             
                                  =  c_3(activate#(X1),activate#(X2))                                
        
                     add#(s(X),Y) =  [0]                                                             
                                  >= [0]                                                             
                                  =  c_6(add#(X,Y))                                                  
        
            sel#(s(N),cons(X,XS)) =  [2]                                                             
                                  >= [2]                                                             
                                  =  c_11(sel#(N,activate(XS)),activate#(XS))                        
        
* Step 7: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          activate#(n__add(X1,X2)) -> c_2(add#(activate(X1),activate(X2)),activate#(X1),activate#(X2))
          activate#(n__fib1(X1,X2)) -> c_3(activate#(X1),activate#(X2))
          add#(s(X),Y) -> c_6(add#(X,Y))
          sel#(s(N),cons(X,XS)) -> c_11(sel#(N,activate(XS)),activate#(XS))
      - Weak DPs:
          fib#(N) -> c_7(sel#(N,fib1(s(0()),s(0()))))
      - Weak TRS:
          activate(X) -> X
          activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
          activate(n__fib1(X1,X2)) -> fib1(activate(X1),activate(X2))
          add(X1,X2) -> n__add(X1,X2)
          add(0(),X) -> X
          add(s(X),Y) -> s(add(X,Y))
          fib1(X,Y) -> cons(X,n__fib1(Y,n__add(X,Y)))
          fib1(X1,X2) -> n__fib1(X1,X2)
      - Signature:
          {activate/1,add/2,fib/1,fib1/2,sel/2,activate#/1,add#/2,fib#/1,fib1#/2,sel#/2} / {0/0,cons/2,n__add/2
          ,n__fib1/2,s/1,c_1/0,c_2/3,c_3/2,c_4/0,c_5/0,c_6/1,c_7/1,c_8/0,c_9/0,c_10/0,c_11/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {activate#,add#,fib#,fib1#,sel#} and constructors {0,cons
          ,n__add,n__fib1,s}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE