MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            a__U11(X1,X2) -> U11(X1,X2)
            a__U11(tt(),L) -> a__U12(tt(),L)
            a__U12(X1,X2) -> U12(X1,X2)
            a__U12(tt(),L) -> s(a__length(mark(L)))
            a__length(X) -> length(X)
            a__length(cons(N,L)) -> a__U11(tt(),L)
            a__length(nil()) -> 0()
            a__zeros() -> cons(0(),zeros())
            a__zeros() -> zeros()
            mark(0()) -> 0()
            mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
            mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(length(X)) -> a__length(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
            mark(tt()) -> tt()
            mark(zeros()) -> a__zeros()
        - Signature:
            {a__U11/2,a__U12/2,a__length/1,a__zeros/0,mark/1} / {0/0,U11/2,U12/2,cons/2,length/1,nil/0,s/1,tt/0,zeros/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__U11,a__U12,a__length,a__zeros
            ,mark} and constructors {0,U11,U12,cons,length,nil,s,tt,zeros}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          a__U11#(X1,X2) -> c_1()
          a__U11#(tt(),L) -> c_2(a__U12#(tt(),L))
          a__U12#(X1,X2) -> c_3()
          a__U12#(tt(),L) -> c_4(a__length#(mark(L)),mark#(L))
          a__length#(X) -> c_5()
          a__length#(cons(N,L)) -> c_6(a__U11#(tt(),L))
          a__length#(nil()) -> c_7()
          a__zeros#() -> c_8()
          a__zeros#() -> c_9()
          mark#(0()) -> c_10()
          mark#(U11(X1,X2)) -> c_11(a__U11#(mark(X1),X2),mark#(X1))
          mark#(U12(X1,X2)) -> c_12(a__U12#(mark(X1),X2),mark#(X1))
          mark#(cons(X1,X2)) -> c_13(mark#(X1))
          mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X))
          mark#(nil()) -> c_15()
          mark#(s(X)) -> c_16(mark#(X))
          mark#(tt()) -> c_17()
          mark#(zeros()) -> c_18(a__zeros#())
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            a__U11#(X1,X2) -> c_1()
            a__U11#(tt(),L) -> c_2(a__U12#(tt(),L))
            a__U12#(X1,X2) -> c_3()
            a__U12#(tt(),L) -> c_4(a__length#(mark(L)),mark#(L))
            a__length#(X) -> c_5()
            a__length#(cons(N,L)) -> c_6(a__U11#(tt(),L))
            a__length#(nil()) -> c_7()
            a__zeros#() -> c_8()
            a__zeros#() -> c_9()
            mark#(0()) -> c_10()
            mark#(U11(X1,X2)) -> c_11(a__U11#(mark(X1),X2),mark#(X1))
            mark#(U12(X1,X2)) -> c_12(a__U12#(mark(X1),X2),mark#(X1))
            mark#(cons(X1,X2)) -> c_13(mark#(X1))
            mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X))
            mark#(nil()) -> c_15()
            mark#(s(X)) -> c_16(mark#(X))
            mark#(tt()) -> c_17()
            mark#(zeros()) -> c_18(a__zeros#())
        - Weak TRS:
            a__U11(X1,X2) -> U11(X1,X2)
            a__U11(tt(),L) -> a__U12(tt(),L)
            a__U12(X1,X2) -> U12(X1,X2)
            a__U12(tt(),L) -> s(a__length(mark(L)))
            a__length(X) -> length(X)
            a__length(cons(N,L)) -> a__U11(tt(),L)
            a__length(nil()) -> 0()
            a__zeros() -> cons(0(),zeros())
            a__zeros() -> zeros()
            mark(0()) -> 0()
            mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
            mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(length(X)) -> a__length(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
            mark(tt()) -> tt()
            mark(zeros()) -> a__zeros()
        - Signature:
            {a__U11/2,a__U12/2,a__length/1,a__zeros/0,mark/1,a__U11#/2,a__U12#/2,a__length#/1,a__zeros#/0
            ,mark#/1} / {0/0,U11/2,U12/2,cons/2,length/1,nil/0,s/1,tt/0,zeros/0,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/1
            ,c_7/0,c_8/0,c_9/0,c_10/0,c_11/2,c_12/2,c_13/1,c_14/2,c_15/0,c_16/1,c_17/0,c_18/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__U11#,a__U12#,a__length#,a__zeros#
            ,mark#} and constructors {0,U11,U12,cons,length,nil,s,tt,zeros}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,5,7,8,9,10,15,17}
        by application of
          Pre({1,3,5,7,8,9,10,15,17}) = {2,4,6,11,12,13,14,16,18}.
        Here rules are labelled as follows:
          1: a__U11#(X1,X2) -> c_1()
          2: a__U11#(tt(),L) -> c_2(a__U12#(tt(),L))
          3: a__U12#(X1,X2) -> c_3()
          4: a__U12#(tt(),L) -> c_4(a__length#(mark(L)),mark#(L))
          5: a__length#(X) -> c_5()
          6: a__length#(cons(N,L)) -> c_6(a__U11#(tt(),L))
          7: a__length#(nil()) -> c_7()
          8: a__zeros#() -> c_8()
          9: a__zeros#() -> c_9()
          10: mark#(0()) -> c_10()
          11: mark#(U11(X1,X2)) -> c_11(a__U11#(mark(X1),X2),mark#(X1))
          12: mark#(U12(X1,X2)) -> c_12(a__U12#(mark(X1),X2),mark#(X1))
          13: mark#(cons(X1,X2)) -> c_13(mark#(X1))
          14: mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X))
          15: mark#(nil()) -> c_15()
          16: mark#(s(X)) -> c_16(mark#(X))
          17: mark#(tt()) -> c_17()
          18: mark#(zeros()) -> c_18(a__zeros#())
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            a__U11#(tt(),L) -> c_2(a__U12#(tt(),L))
            a__U12#(tt(),L) -> c_4(a__length#(mark(L)),mark#(L))
            a__length#(cons(N,L)) -> c_6(a__U11#(tt(),L))
            mark#(U11(X1,X2)) -> c_11(a__U11#(mark(X1),X2),mark#(X1))
            mark#(U12(X1,X2)) -> c_12(a__U12#(mark(X1),X2),mark#(X1))
            mark#(cons(X1,X2)) -> c_13(mark#(X1))
            mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X))
            mark#(s(X)) -> c_16(mark#(X))
            mark#(zeros()) -> c_18(a__zeros#())
        - Weak DPs:
            a__U11#(X1,X2) -> c_1()
            a__U12#(X1,X2) -> c_3()
            a__length#(X) -> c_5()
            a__length#(nil()) -> c_7()
            a__zeros#() -> c_8()
            a__zeros#() -> c_9()
            mark#(0()) -> c_10()
            mark#(nil()) -> c_15()
            mark#(tt()) -> c_17()
        - Weak TRS:
            a__U11(X1,X2) -> U11(X1,X2)
            a__U11(tt(),L) -> a__U12(tt(),L)
            a__U12(X1,X2) -> U12(X1,X2)
            a__U12(tt(),L) -> s(a__length(mark(L)))
            a__length(X) -> length(X)
            a__length(cons(N,L)) -> a__U11(tt(),L)
            a__length(nil()) -> 0()
            a__zeros() -> cons(0(),zeros())
            a__zeros() -> zeros()
            mark(0()) -> 0()
            mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
            mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(length(X)) -> a__length(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
            mark(tt()) -> tt()
            mark(zeros()) -> a__zeros()
        - Signature:
            {a__U11/2,a__U12/2,a__length/1,a__zeros/0,mark/1,a__U11#/2,a__U12#/2,a__length#/1,a__zeros#/0
            ,mark#/1} / {0/0,U11/2,U12/2,cons/2,length/1,nil/0,s/1,tt/0,zeros/0,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/1
            ,c_7/0,c_8/0,c_9/0,c_10/0,c_11/2,c_12/2,c_13/1,c_14/2,c_15/0,c_16/1,c_17/0,c_18/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__U11#,a__U12#,a__length#,a__zeros#
            ,mark#} and constructors {0,U11,U12,cons,length,nil,s,tt,zeros}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {9}
        by application of
          Pre({9}) = {2,4,5,6,7,8}.
        Here rules are labelled as follows:
          1: a__U11#(tt(),L) -> c_2(a__U12#(tt(),L))
          2: a__U12#(tt(),L) -> c_4(a__length#(mark(L)),mark#(L))
          3: a__length#(cons(N,L)) -> c_6(a__U11#(tt(),L))
          4: mark#(U11(X1,X2)) -> c_11(a__U11#(mark(X1),X2),mark#(X1))
          5: mark#(U12(X1,X2)) -> c_12(a__U12#(mark(X1),X2),mark#(X1))
          6: mark#(cons(X1,X2)) -> c_13(mark#(X1))
          7: mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X))
          8: mark#(s(X)) -> c_16(mark#(X))
          9: mark#(zeros()) -> c_18(a__zeros#())
          10: a__U11#(X1,X2) -> c_1()
          11: a__U12#(X1,X2) -> c_3()
          12: a__length#(X) -> c_5()
          13: a__length#(nil()) -> c_7()
          14: a__zeros#() -> c_8()
          15: a__zeros#() -> c_9()
          16: mark#(0()) -> c_10()
          17: mark#(nil()) -> c_15()
          18: mark#(tt()) -> c_17()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            a__U11#(tt(),L) -> c_2(a__U12#(tt(),L))
            a__U12#(tt(),L) -> c_4(a__length#(mark(L)),mark#(L))
            a__length#(cons(N,L)) -> c_6(a__U11#(tt(),L))
            mark#(U11(X1,X2)) -> c_11(a__U11#(mark(X1),X2),mark#(X1))
            mark#(U12(X1,X2)) -> c_12(a__U12#(mark(X1),X2),mark#(X1))
            mark#(cons(X1,X2)) -> c_13(mark#(X1))
            mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X))
            mark#(s(X)) -> c_16(mark#(X))
        - Weak DPs:
            a__U11#(X1,X2) -> c_1()
            a__U12#(X1,X2) -> c_3()
            a__length#(X) -> c_5()
            a__length#(nil()) -> c_7()
            a__zeros#() -> c_8()
            a__zeros#() -> c_9()
            mark#(0()) -> c_10()
            mark#(nil()) -> c_15()
            mark#(tt()) -> c_17()
            mark#(zeros()) -> c_18(a__zeros#())
        - Weak TRS:
            a__U11(X1,X2) -> U11(X1,X2)
            a__U11(tt(),L) -> a__U12(tt(),L)
            a__U12(X1,X2) -> U12(X1,X2)
            a__U12(tt(),L) -> s(a__length(mark(L)))
            a__length(X) -> length(X)
            a__length(cons(N,L)) -> a__U11(tt(),L)
            a__length(nil()) -> 0()
            a__zeros() -> cons(0(),zeros())
            a__zeros() -> zeros()
            mark(0()) -> 0()
            mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
            mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(length(X)) -> a__length(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(mark(X))
            mark(tt()) -> tt()
            mark(zeros()) -> a__zeros()
        - Signature:
            {a__U11/2,a__U12/2,a__length/1,a__zeros/0,mark/1,a__U11#/2,a__U12#/2,a__length#/1,a__zeros#/0
            ,mark#/1} / {0/0,U11/2,U12/2,cons/2,length/1,nil/0,s/1,tt/0,zeros/0,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/1
            ,c_7/0,c_8/0,c_9/0,c_10/0,c_11/2,c_12/2,c_13/1,c_14/2,c_15/0,c_16/1,c_17/0,c_18/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__U11#,a__U12#,a__length#,a__zeros#
            ,mark#} and constructors {0,U11,U12,cons,length,nil,s,tt,zeros}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:a__U11#(tt(),L) -> c_2(a__U12#(tt(),L))
             -->_1 a__U12#(tt(),L) -> c_4(a__length#(mark(L)),mark#(L)):2
             -->_1 a__U12#(X1,X2) -> c_3():10
          
          2:S:a__U12#(tt(),L) -> c_4(a__length#(mark(L)),mark#(L))
             -->_2 mark#(zeros()) -> c_18(a__zeros#()):18
             -->_2 mark#(s(X)) -> c_16(mark#(X)):8
             -->_2 mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)):7
             -->_2 mark#(cons(X1,X2)) -> c_13(mark#(X1)):6
             -->_2 mark#(U12(X1,X2)) -> c_12(a__U12#(mark(X1),X2),mark#(X1)):5
             -->_2 mark#(U11(X1,X2)) -> c_11(a__U11#(mark(X1),X2),mark#(X1)):4
             -->_1 a__length#(cons(N,L)) -> c_6(a__U11#(tt(),L)):3
             -->_2 mark#(tt()) -> c_17():17
             -->_2 mark#(nil()) -> c_15():16
             -->_2 mark#(0()) -> c_10():15
             -->_1 a__length#(nil()) -> c_7():12
             -->_1 a__length#(X) -> c_5():11
          
          3:S:a__length#(cons(N,L)) -> c_6(a__U11#(tt(),L))
             -->_1 a__U11#(X1,X2) -> c_1():9
             -->_1 a__U11#(tt(),L) -> c_2(a__U12#(tt(),L)):1
          
          4:S:mark#(U11(X1,X2)) -> c_11(a__U11#(mark(X1),X2),mark#(X1))
             -->_2 mark#(zeros()) -> c_18(a__zeros#()):18
             -->_2 mark#(s(X)) -> c_16(mark#(X)):8
             -->_2 mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)):7
             -->_2 mark#(cons(X1,X2)) -> c_13(mark#(X1)):6
             -->_2 mark#(U12(X1,X2)) -> c_12(a__U12#(mark(X1),X2),mark#(X1)):5
             -->_2 mark#(tt()) -> c_17():17
             -->_2 mark#(nil()) -> c_15():16
             -->_2 mark#(0()) -> c_10():15
             -->_1 a__U11#(X1,X2) -> c_1():9
             -->_2 mark#(U11(X1,X2)) -> c_11(a__U11#(mark(X1),X2),mark#(X1)):4
             -->_1 a__U11#(tt(),L) -> c_2(a__U12#(tt(),L)):1
          
          5:S:mark#(U12(X1,X2)) -> c_12(a__U12#(mark(X1),X2),mark#(X1))
             -->_2 mark#(zeros()) -> c_18(a__zeros#()):18
             -->_2 mark#(s(X)) -> c_16(mark#(X)):8
             -->_2 mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)):7
             -->_2 mark#(cons(X1,X2)) -> c_13(mark#(X1)):6
             -->_2 mark#(tt()) -> c_17():17
             -->_2 mark#(nil()) -> c_15():16
             -->_2 mark#(0()) -> c_10():15
             -->_1 a__U12#(X1,X2) -> c_3():10
             -->_2 mark#(U12(X1,X2)) -> c_12(a__U12#(mark(X1),X2),mark#(X1)):5
             -->_2 mark#(U11(X1,X2)) -> c_11(a__U11#(mark(X1),X2),mark#(X1)):4
             -->_1 a__U12#(tt(),L) -> c_4(a__length#(mark(L)),mark#(L)):2
          
          6:S:mark#(cons(X1,X2)) -> c_13(mark#(X1))
             -->_1 mark#(zeros()) -> c_18(a__zeros#()):18
             -->_1 mark#(s(X)) -> c_16(mark#(X)):8
             -->_1 mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)):7
             -->_1 mark#(tt()) -> c_17():17
             -->_1 mark#(nil()) -> c_15():16
             -->_1 mark#(0()) -> c_10():15
             -->_1 mark#(cons(X1,X2)) -> c_13(mark#(X1)):6
             -->_1 mark#(U12(X1,X2)) -> c_12(a__U12#(mark(X1),X2),mark#(X1)):5
             -->_1 mark#(U11(X1,X2)) -> c_11(a__U11#(mark(X1),X2),mark#(X1)):4
          
          7:S:mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X))
             -->_2 mark#(zeros()) -> c_18(a__zeros#()):18
             -->_2 mark#(s(X)) -> c_16(mark#(X)):8
             -->_2 mark#(tt()) -> c_17():17
             -->_2 mark#(nil()) -> c_15():16
             -->_2 mark#(0()) -> c_10():15
             -->_1 a__length#(nil()) -> c_7():12
             -->_1 a__length#(X) -> c_5():11
             -->_2 mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)):7
             -->_2 mark#(cons(X1,X2)) -> c_13(mark#(X1)):6
             -->_2 mark#(U12(X1,X2)) -> c_12(a__U12#(mark(X1),X2),mark#(X1)):5
             -->_2 mark#(U11(X1,X2)) -> c_11(a__U11#(mark(X1),X2),mark#(X1)):4
             -->_1 a__length#(cons(N,L)) -> c_6(a__U11#(tt(),L)):3
          
          8:S:mark#(s(X)) -> c_16(mark#(X))
             -->_1 mark#(zeros()) -> c_18(a__zeros#()):18
             -->_1 mark#(tt()) -> c_17():17
             -->_1 mark#(nil()) -> c_15():16
             -->_1 mark#(0()) -> c_10():15
             -->_1 mark#(s(X)) -> c_16(mark#(X)):8
             -->_1 mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X)):7
             -->_1 mark#(cons(X1,X2)) -> c_13(mark#(X1)):6
             -->_1 mark#(U12(X1,X2)) -> c_12(a__U12#(mark(X1),X2),mark#(X1)):5
             -->_1 mark#(U11(X1,X2)) -> c_11(a__U11#(mark(X1),X2),mark#(X1)):4
          
          9:W:a__U11#(X1,X2) -> c_1()
             
          
          10:W:a__U12#(X1,X2) -> c_3()
             
          
          11:W:a__length#(X) -> c_5()
             
          
          12:W:a__length#(nil()) -> c_7()
             
          
          13:W:a__zeros#() -> c_8()
             
          
          14:W:a__zeros#() -> c_9()
             
          
          15:W:mark#(0()) -> c_10()
             
          
          16:W:mark#(nil()) -> c_15()
             
          
          17:W:mark#(tt()) -> c_17()
             
          
          18:W:mark#(zeros()) -> c_18(a__zeros#())
             -->_1 a__zeros#() -> c_9():14
             -->_1 a__zeros#() -> c_8():13
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          9: a__U11#(X1,X2) -> c_1()
          10: a__U12#(X1,X2) -> c_3()
          11: a__length#(X) -> c_5()
          12: a__length#(nil()) -> c_7()
          15: mark#(0()) -> c_10()
          16: mark#(nil()) -> c_15()
          17: mark#(tt()) -> c_17()
          18: mark#(zeros()) -> c_18(a__zeros#())
          13: a__zeros#() -> c_8()
          14: a__zeros#() -> c_9()
* Step 5: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          a__U11#(tt(),L) -> c_2(a__U12#(tt(),L))
          a__U12#(tt(),L) -> c_4(a__length#(mark(L)),mark#(L))
          a__length#(cons(N,L)) -> c_6(a__U11#(tt(),L))
          mark#(U11(X1,X2)) -> c_11(a__U11#(mark(X1),X2),mark#(X1))
          mark#(U12(X1,X2)) -> c_12(a__U12#(mark(X1),X2),mark#(X1))
          mark#(cons(X1,X2)) -> c_13(mark#(X1))
          mark#(length(X)) -> c_14(a__length#(mark(X)),mark#(X))
          mark#(s(X)) -> c_16(mark#(X))
      - Weak TRS:
          a__U11(X1,X2) -> U11(X1,X2)
          a__U11(tt(),L) -> a__U12(tt(),L)
          a__U12(X1,X2) -> U12(X1,X2)
          a__U12(tt(),L) -> s(a__length(mark(L)))
          a__length(X) -> length(X)
          a__length(cons(N,L)) -> a__U11(tt(),L)
          a__length(nil()) -> 0()
          a__zeros() -> cons(0(),zeros())
          a__zeros() -> zeros()
          mark(0()) -> 0()
          mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
          mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
          mark(cons(X1,X2)) -> cons(mark(X1),X2)
          mark(length(X)) -> a__length(mark(X))
          mark(nil()) -> nil()
          mark(s(X)) -> s(mark(X))
          mark(tt()) -> tt()
          mark(zeros()) -> a__zeros()
      - Signature:
          {a__U11/2,a__U12/2,a__length/1,a__zeros/0,mark/1,a__U11#/2,a__U12#/2,a__length#/1,a__zeros#/0
          ,mark#/1} / {0/0,U11/2,U12/2,cons/2,length/1,nil/0,s/1,tt/0,zeros/0,c_1/0,c_2/1,c_3/0,c_4/2,c_5/0,c_6/1
          ,c_7/0,c_8/0,c_9/0,c_10/0,c_11/2,c_12/2,c_13/1,c_14/2,c_15/0,c_16/1,c_17/0,c_18/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {a__U11#,a__U12#,a__length#,a__zeros#
          ,mark#} and constructors {0,U11,U12,cons,length,nil,s,tt,zeros}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE