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_ = WIDP}
    + Details:
        We add the following weak innermost dependency pairs:
        
        Strict DPs
          U11#(tt(),L) -> c_1(U12#(tt(),activate(L)))
          U12#(tt(),L) -> c_2(length#(activate(L)))
          activate#(X) -> c_3()
          activate#(n__zeros()) -> c_4(zeros#())
          length#(cons(N,L)) -> c_5(U11#(tt(),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)))
            U12#(tt(),L) -> c_2(length#(activate(L)))
            activate#(X) -> c_3()
            activate#(n__zeros()) -> c_4(zeros#())
            length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)))
            length#(nil()) -> c_6()
            zeros#() -> c_7()
            zeros#() -> c_8()
        - 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,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:
        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)))
          U12#(tt(),L) -> c_2(length#(activate(L)))
          activate#(X) -> c_3()
          activate#(n__zeros()) -> c_4(zeros#())
          length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)))
          length#(nil()) -> c_6()
          zeros#() -> c_7()
          zeros#() -> c_8()
* Step 3: WeightGap MAYBE
    + Considered Problem:
        - Strict DPs:
            U11#(tt(),L) -> c_1(U12#(tt(),activate(L)))
            U12#(tt(),L) -> c_2(length#(activate(L)))
            activate#(X) -> c_3()
            activate#(n__zeros()) -> c_4(zeros#())
            length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)))
            length#(nil()) -> c_6()
            zeros#() -> c_7()
            zeros#() -> c_8()
        - Strict 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:
        WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnTrs}
    + Details:
        The weightgap principle applies using the following constant growth matrix-interpretation:
          We apply a matrix interpretation of kind constructor based matrix interpretation:
          The following argument positions are considered usable:
            uargs(U11#) = {2},
            uargs(U12#) = {2},
            uargs(length#) = {1},
            uargs(c_1) = {1},
            uargs(c_2) = {1},
            uargs(c_4) = {1},
            uargs(c_5) = {1}
          
          Following symbols are considered usable:
            all
          TcT has computed the following interpretation:
                    p(0) = [0]                  
                  p(U11) = [1] x1 + [0]         
                  p(U12) = [0]                  
             p(activate) = [1] x1 + [11]        
                 p(cons) = [1] x1 + [1] x2 + [0]
               p(length) = [0]                  
             p(n__zeros) = [0]                  
                  p(nil) = [0]                  
                    p(s) = [1] x1 + [0]         
                   p(tt) = [0]                  
                p(zeros) = [2]                  
                 p(U11#) = [1] x2 + [0]         
                 p(U12#) = [1] x2 + [0]         
            p(activate#) = [0]                  
              p(length#) = [1] x1 + [0]         
               p(zeros#) = [0]                  
                  p(c_1) = [1] x1 + [0]         
                  p(c_2) = [1] x1 + [0]         
                  p(c_3) = [0]                  
                  p(c_4) = [1] x1 + [0]         
                  p(c_5) = [1] x1 + [0]         
                  p(c_6) = [0]                  
                  p(c_7) = [0]                  
                  p(c_8) = [0]                  
          
          Following rules are strictly oriented:
                   activate(X) = [1] X + [11]        
                               > [1] X + [0]         
                               = X                   
          
          activate(n__zeros()) = [11]                
                               > [2]                 
                               = zeros()             
          
                       zeros() = [2]                 
                               > [0]                 
                               = cons(0(),n__zeros())
          
                       zeros() = [2]                 
                               > [0]                 
                               = n__zeros()          
          
          
          Following rules are (at-least) weakly oriented:
                   U11#(tt(),L) =  [1] L + [0]                
                                >= [1] L + [11]               
                                =  c_1(U12#(tt(),activate(L)))
          
                   U12#(tt(),L) =  [1] L + [0]                
                                >= [1] L + [11]               
                                =  c_2(length#(activate(L)))  
          
                   activate#(X) =  [0]                        
                                >= [0]                        
                                =  c_3()                      
          
          activate#(n__zeros()) =  [0]                        
                                >= [0]                        
                                =  c_4(zeros#())              
          
             length#(cons(N,L)) =  [1] L + [1] N + [0]        
                                >= [1] L + [11]               
                                =  c_5(U11#(tt(),activate(L)))
          
                 length#(nil()) =  [0]                        
                                >= [0]                        
                                =  c_6()                      
          
                       zeros#() =  [0]                        
                                >= [0]                        
                                =  c_7()                      
          
                       zeros#() =  [0]                        
                                >= [0]                        
                                =  c_8()                      
          
        Further, it can be verified that all rules not oriented are covered by the weightgap condition.
* Step 4: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            U11#(tt(),L) -> c_1(U12#(tt(),activate(L)))
            U12#(tt(),L) -> c_2(length#(activate(L)))
            activate#(X) -> c_3()
            activate#(n__zeros()) -> c_4(zeros#())
            length#(cons(N,L)) -> c_5(U11#(tt(),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_1/1,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:
        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}) = {2,4}.
        Here rules are labelled as follows:
          1: U11#(tt(),L) -> c_1(U12#(tt(),activate(L)))
          2: U12#(tt(),L) -> c_2(length#(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)))
          6: length#(nil()) -> c_6()
          7: zeros#() -> c_7()
          8: zeros#() -> c_8()
* Step 5: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            U11#(tt(),L) -> c_1(U12#(tt(),activate(L)))
            U12#(tt(),L) -> c_2(length#(activate(L)))
            activate#(n__zeros()) -> c_4(zeros#())
            length#(cons(N,L)) -> c_5(U11#(tt(),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_1/1,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:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {3}
        by application of
          Pre({3}) = {}.
        Here rules are labelled as follows:
          1: U11#(tt(),L) -> c_1(U12#(tt(),activate(L)))
          2: U12#(tt(),L) -> c_2(length#(activate(L)))
          3: activate#(n__zeros()) -> c_4(zeros#())
          4: length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)))
          5: activate#(X) -> c_3()
          6: length#(nil()) -> c_6()
          7: zeros#() -> c_7()
          8: zeros#() -> c_8()
* Step 6: RemoveWeakSuffixes 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 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_1/1,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:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:U11#(tt(),L) -> c_1(U12#(tt(),activate(L)))
             -->_1 U12#(tt(),L) -> c_2(length#(activate(L))):2
          
          2:S:U12#(tt(),L) -> c_2(length#(activate(L)))
             -->_1 length#(cons(N,L)) -> c_5(U11#(tt(),activate(L))):3
             -->_1 length#(nil()) -> c_6():6
          
          3:S:length#(cons(N,L)) -> c_5(U11#(tt(),activate(L)))
             -->_1 U11#(tt(),L) -> c_1(U12#(tt(),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.
          5: activate#(n__zeros()) -> c_4(zeros#())
          7: zeros#() -> c_7()
          8: zeros#() -> c_8()
          4: activate#(X) -> c_3()
          6: length#(nil()) -> c_6()
* 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