MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            U11(tt(),L) -> U12(tt(),activate(L))
            U12(tt(),L) -> s(length(activate(L)))
            activate(X) -> X
            activate(n__zeros()) -> zeros()
            length(cons(N,L)) -> U11(tt(),activate(L))
            length(nil()) -> 0()
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {U11/2,U12/2,activate/1,length/1,zeros/0} / {0/0,cons/2,n__zeros/0,nil/0,s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11,U12,activate,length,zeros} and constructors {0,cons
            ,n__zeros,nil,s,tt}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L))
          U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L))
          activate#(X) -> c_3()
          activate#(n__zeros()) -> c_4(zeros#())
          length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)),activate#(L))
          length#(nil()) -> c_6()
          zeros#() -> c_7()
          zeros#() -> c_8()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L))
            U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L))
            activate#(X) -> c_3()
            activate#(n__zeros()) -> c_4(zeros#())
            length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)),activate#(L))
            length#(nil()) -> c_6()
            zeros#() -> c_7()
            zeros#() -> c_8()
        - Weak TRS:
            U11(tt(),L) -> U12(tt(),activate(L))
            U12(tt(),L) -> s(length(activate(L)))
            activate(X) -> X
            activate(n__zeros()) -> zeros()
            length(cons(N,L)) -> U11(tt(),activate(L))
            length(nil()) -> 0()
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {U11/2,U12/2,activate/1,length/1,zeros/0,U11#/2,U12#/2,activate#/1,length#/1,zeros#/0} / {0/0,cons/2
            ,n__zeros/0,nil/0,s/1,tt/0,c_1/2,c_2/2,c_3/0,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,activate#,length#,zeros#} and constructors {0
            ,cons,n__zeros,nil,s,tt}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          activate(X) -> X
          activate(n__zeros()) -> zeros()
          zeros() -> cons(0(),n__zeros())
          zeros() -> n__zeros()
          U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L))
          U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L))
          activate#(X) -> c_3()
          activate#(n__zeros()) -> c_4(zeros#())
          length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)),activate#(L))
          length#(nil()) -> c_6()
          zeros#() -> c_7()
          zeros#() -> c_8()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L))
            U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L))
            activate#(X) -> c_3()
            activate#(n__zeros()) -> c_4(zeros#())
            length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)),activate#(L))
            length#(nil()) -> c_6()
            zeros#() -> c_7()
            zeros#() -> c_8()
        - Weak TRS:
            activate(X) -> X
            activate(n__zeros()) -> zeros()
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {U11/2,U12/2,activate/1,length/1,zeros/0,U11#/2,U12#/2,activate#/1,length#/1,zeros#/0} / {0/0,cons/2
            ,n__zeros/0,nil/0,s/1,tt/0,c_1/2,c_2/2,c_3/0,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,activate#,length#,zeros#} and constructors {0
            ,cons,n__zeros,nil,s,tt}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {3,6,7,8}
        by application of
          Pre({3,6,7,8}) = {1,2,4,5}.
        Here rules are labelled as follows:
          1: U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L))
          2: U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L))
          3: activate#(X) -> c_3()
          4: activate#(n__zeros()) -> c_4(zeros#())
          5: length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)),activate#(L))
          6: length#(nil()) -> c_6()
          7: zeros#() -> c_7()
          8: zeros#() -> c_8()
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L))
            U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L))
            activate#(n__zeros()) -> c_4(zeros#())
            length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)),activate#(L))
        - Weak DPs:
            activate#(X) -> c_3()
            length#(nil()) -> c_6()
            zeros#() -> c_7()
            zeros#() -> c_8()
        - Weak TRS:
            activate(X) -> X
            activate(n__zeros()) -> zeros()
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {U11/2,U12/2,activate/1,length/1,zeros/0,U11#/2,U12#/2,activate#/1,length#/1,zeros#/0} / {0/0,cons/2
            ,n__zeros/0,nil/0,s/1,tt/0,c_1/2,c_2/2,c_3/0,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,activate#,length#,zeros#} and constructors {0
            ,cons,n__zeros,nil,s,tt}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {3}
        by application of
          Pre({3}) = {1,2,4}.
        Here rules are labelled as follows:
          1: U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L))
          2: U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L))
          3: activate#(n__zeros()) -> c_4(zeros#())
          4: length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)),activate#(L))
          5: activate#(X) -> c_3()
          6: length#(nil()) -> c_6()
          7: zeros#() -> c_7()
          8: zeros#() -> c_8()
* Step 5: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L))
            U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L))
            length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)),activate#(L))
        - Weak DPs:
            activate#(X) -> c_3()
            activate#(n__zeros()) -> c_4(zeros#())
            length#(nil()) -> c_6()
            zeros#() -> c_7()
            zeros#() -> c_8()
        - Weak TRS:
            activate(X) -> X
            activate(n__zeros()) -> zeros()
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {U11/2,U12/2,activate/1,length/1,zeros/0,U11#/2,U12#/2,activate#/1,length#/1,zeros#/0} / {0/0,cons/2
            ,n__zeros/0,nil/0,s/1,tt/0,c_1/2,c_2/2,c_3/0,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,activate#,length#,zeros#} and constructors {0
            ,cons,n__zeros,nil,s,tt}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L))
             -->_2 activate#(n__zeros()) -> c_4(zeros#()):5
             -->_1 U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L)):2
             -->_2 activate#(X) -> c_3():4
          
          2:S:U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L))
             -->_2 activate#(n__zeros()) -> c_4(zeros#()):5
             -->_1 length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)),activate#(L)):3
             -->_1 length#(nil()) -> c_6():6
             -->_2 activate#(X) -> c_3():4
          
          3:S:length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)),activate#(L))
             -->_2 activate#(n__zeros()) -> c_4(zeros#()):5
             -->_2 activate#(X) -> c_3():4
             -->_1 U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L)):1
          
          4:W:activate#(X) -> c_3()
             
          
          5:W:activate#(n__zeros()) -> c_4(zeros#())
             -->_1 zeros#() -> c_8():8
             -->_1 zeros#() -> c_7():7
          
          6:W:length#(nil()) -> c_6()
             
          
          7:W:zeros#() -> c_7()
             
          
          8:W:zeros#() -> c_8()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          6: length#(nil()) -> c_6()
          4: activate#(X) -> c_3()
          5: activate#(n__zeros()) -> c_4(zeros#())
          7: zeros#() -> c_7()
          8: zeros#() -> c_8()
* Step 6: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L))
            U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L))
            length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)),activate#(L))
        - Weak TRS:
            activate(X) -> X
            activate(n__zeros()) -> zeros()
            zeros() -> cons(0(),n__zeros())
            zeros() -> n__zeros()
        - Signature:
            {U11/2,U12/2,activate/1,length/1,zeros/0,U11#/2,U12#/2,activate#/1,length#/1,zeros#/0} / {0/0,cons/2
            ,n__zeros/0,nil/0,s/1,tt/0,c_1/2,c_2/2,c_3/0,c_4/1,c_5/2,c_6/0,c_7/0,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11#,U12#,activate#,length#,zeros#} and constructors {0
            ,cons,n__zeros,nil,s,tt}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L))
             -->_1 U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L)):2
          
          2:S:U12#(tt(),L) -> c_2(length#(activate(L)),activate#(L))
             -->_1 length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)),activate#(L)):3
          
          3:S:length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)),activate#(L))
             -->_1 U11#(tt(),L) -> c_1(U12#(tt(),activate(L)),activate#(L)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          U11#(tt(),L) -> c_1(U12#(tt(),activate(L)))
          U12#(tt(),L) -> c_2(length#(activate(L)))
          length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)))
* Step 7: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          U11#(tt(),L) -> c_1(U12#(tt(),activate(L)))
          U12#(tt(),L) -> c_2(length#(activate(L)))
          length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)))
      - Weak TRS:
          activate(X) -> X
          activate(n__zeros()) -> zeros()
          zeros() -> cons(0(),n__zeros())
          zeros() -> n__zeros()
      - Signature:
          {U11/2,U12/2,activate/1,length/1,zeros/0,U11#/2,U12#/2,activate#/1,length#/1,zeros#/0} / {0/0,cons/2
          ,n__zeros/0,nil/0,s/1,tt/0,c_1/1,c_2/1,c_3/0,c_4/1,c_5/1,c_6/0,c_7/0,c_8/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {U11#,U12#,activate#,length#,zeros#} and constructors {0
          ,cons,n__zeros,nil,s,tt}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE