MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            cond(false(),n,l) -> tail(nthtail(s(n),l))
            cond(true(),n,l) -> l
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            length(cons(x,l)) -> s(length(l))
            length(nil()) -> 0()
            nthtail(n,l) -> cond(ge(n,length(l)),n,l)
            tail(cons(x,l)) -> l
            tail(nil()) -> nil()
        - Signature:
            {cond/3,ge/2,length/1,nthtail/2,tail/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond,ge,length,nthtail,tail} and constructors {0,cons
            ,false,nil,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          cond#(false(),n,l) -> c_1(tail#(nthtail(s(n),l)),nthtail#(s(n),l))
          cond#(true(),n,l) -> c_2()
          ge#(u,0()) -> c_3()
          ge#(0(),s(v)) -> c_4()
          ge#(s(u),s(v)) -> c_5(ge#(u,v))
          length#(cons(x,l)) -> c_6(length#(l))
          length#(nil()) -> c_7()
          nthtail#(n,l) -> c_8(cond#(ge(n,length(l)),n,l),ge#(n,length(l)),length#(l))
          tail#(cons(x,l)) -> c_9()
          tail#(nil()) -> c_10()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(false(),n,l) -> c_1(tail#(nthtail(s(n),l)),nthtail#(s(n),l))
            cond#(true(),n,l) -> c_2()
            ge#(u,0()) -> c_3()
            ge#(0(),s(v)) -> c_4()
            ge#(s(u),s(v)) -> c_5(ge#(u,v))
            length#(cons(x,l)) -> c_6(length#(l))
            length#(nil()) -> c_7()
            nthtail#(n,l) -> c_8(cond#(ge(n,length(l)),n,l),ge#(n,length(l)),length#(l))
            tail#(cons(x,l)) -> c_9()
            tail#(nil()) -> c_10()
        - Weak TRS:
            cond(false(),n,l) -> tail(nthtail(s(n),l))
            cond(true(),n,l) -> l
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            length(cons(x,l)) -> s(length(l))
            length(nil()) -> 0()
            nthtail(n,l) -> cond(ge(n,length(l)),n,l)
            tail(cons(x,l)) -> l
            tail(nil()) -> nil()
        - Signature:
            {cond/3,ge/2,length/1,nthtail/2,tail/1,cond#/3,ge#/2,length#/1,nthtail#/2,tail#/1} / {0/0,cons/2,false/0
            ,nil/0,s/1,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/1,c_6/1,c_7/0,c_8/3,c_9/0,c_10/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond#,ge#,length#,nthtail#,tail#} and constructors {0
            ,cons,false,nil,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,3,4,7,9,10}
        by application of
          Pre({2,3,4,7,9,10}) = {1,5,6,8}.
        Here rules are labelled as follows:
          1: cond#(false(),n,l) -> c_1(tail#(nthtail(s(n),l)),nthtail#(s(n),l))
          2: cond#(true(),n,l) -> c_2()
          3: ge#(u,0()) -> c_3()
          4: ge#(0(),s(v)) -> c_4()
          5: ge#(s(u),s(v)) -> c_5(ge#(u,v))
          6: length#(cons(x,l)) -> c_6(length#(l))
          7: length#(nil()) -> c_7()
          8: nthtail#(n,l) -> c_8(cond#(ge(n,length(l)),n,l),ge#(n,length(l)),length#(l))
          9: tail#(cons(x,l)) -> c_9()
          10: tail#(nil()) -> c_10()
* Step 3: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(false(),n,l) -> c_1(tail#(nthtail(s(n),l)),nthtail#(s(n),l))
            ge#(s(u),s(v)) -> c_5(ge#(u,v))
            length#(cons(x,l)) -> c_6(length#(l))
            nthtail#(n,l) -> c_8(cond#(ge(n,length(l)),n,l),ge#(n,length(l)),length#(l))
        - Weak DPs:
            cond#(true(),n,l) -> c_2()
            ge#(u,0()) -> c_3()
            ge#(0(),s(v)) -> c_4()
            length#(nil()) -> c_7()
            tail#(cons(x,l)) -> c_9()
            tail#(nil()) -> c_10()
        - Weak TRS:
            cond(false(),n,l) -> tail(nthtail(s(n),l))
            cond(true(),n,l) -> l
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            length(cons(x,l)) -> s(length(l))
            length(nil()) -> 0()
            nthtail(n,l) -> cond(ge(n,length(l)),n,l)
            tail(cons(x,l)) -> l
            tail(nil()) -> nil()
        - Signature:
            {cond/3,ge/2,length/1,nthtail/2,tail/1,cond#/3,ge#/2,length#/1,nthtail#/2,tail#/1} / {0/0,cons/2,false/0
            ,nil/0,s/1,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/1,c_6/1,c_7/0,c_8/3,c_9/0,c_10/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond#,ge#,length#,nthtail#,tail#} and constructors {0
            ,cons,false,nil,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:cond#(false(),n,l) -> c_1(tail#(nthtail(s(n),l)),nthtail#(s(n),l))
             -->_2 nthtail#(n,l) -> c_8(cond#(ge(n,length(l)),n,l),ge#(n,length(l)),length#(l)):4
             -->_1 tail#(nil()) -> c_10():10
             -->_1 tail#(cons(x,l)) -> c_9():9
          
          2:S:ge#(s(u),s(v)) -> c_5(ge#(u,v))
             -->_1 ge#(0(),s(v)) -> c_4():7
             -->_1 ge#(u,0()) -> c_3():6
             -->_1 ge#(s(u),s(v)) -> c_5(ge#(u,v)):2
          
          3:S:length#(cons(x,l)) -> c_6(length#(l))
             -->_1 length#(nil()) -> c_7():8
             -->_1 length#(cons(x,l)) -> c_6(length#(l)):3
          
          4:S:nthtail#(n,l) -> c_8(cond#(ge(n,length(l)),n,l),ge#(n,length(l)),length#(l))
             -->_3 length#(nil()) -> c_7():8
             -->_2 ge#(0(),s(v)) -> c_4():7
             -->_2 ge#(u,0()) -> c_3():6
             -->_1 cond#(true(),n,l) -> c_2():5
             -->_3 length#(cons(x,l)) -> c_6(length#(l)):3
             -->_2 ge#(s(u),s(v)) -> c_5(ge#(u,v)):2
             -->_1 cond#(false(),n,l) -> c_1(tail#(nthtail(s(n),l)),nthtail#(s(n),l)):1
          
          5:W:cond#(true(),n,l) -> c_2()
             
          
          6:W:ge#(u,0()) -> c_3()
             
          
          7:W:ge#(0(),s(v)) -> c_4()
             
          
          8:W:length#(nil()) -> c_7()
             
          
          9:W:tail#(cons(x,l)) -> c_9()
             
          
          10:W:tail#(nil()) -> c_10()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          9: tail#(cons(x,l)) -> c_9()
          10: tail#(nil()) -> c_10()
          5: cond#(true(),n,l) -> c_2()
          6: ge#(u,0()) -> c_3()
          7: ge#(0(),s(v)) -> c_4()
          8: length#(nil()) -> c_7()
* Step 4: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(false(),n,l) -> c_1(tail#(nthtail(s(n),l)),nthtail#(s(n),l))
            ge#(s(u),s(v)) -> c_5(ge#(u,v))
            length#(cons(x,l)) -> c_6(length#(l))
            nthtail#(n,l) -> c_8(cond#(ge(n,length(l)),n,l),ge#(n,length(l)),length#(l))
        - Weak TRS:
            cond(false(),n,l) -> tail(nthtail(s(n),l))
            cond(true(),n,l) -> l
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            length(cons(x,l)) -> s(length(l))
            length(nil()) -> 0()
            nthtail(n,l) -> cond(ge(n,length(l)),n,l)
            tail(cons(x,l)) -> l
            tail(nil()) -> nil()
        - Signature:
            {cond/3,ge/2,length/1,nthtail/2,tail/1,cond#/3,ge#/2,length#/1,nthtail#/2,tail#/1} / {0/0,cons/2,false/0
            ,nil/0,s/1,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/1,c_6/1,c_7/0,c_8/3,c_9/0,c_10/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond#,ge#,length#,nthtail#,tail#} and constructors {0
            ,cons,false,nil,s,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:cond#(false(),n,l) -> c_1(tail#(nthtail(s(n),l)),nthtail#(s(n),l))
             -->_2 nthtail#(n,l) -> c_8(cond#(ge(n,length(l)),n,l),ge#(n,length(l)),length#(l)):4
          
          2:S:ge#(s(u),s(v)) -> c_5(ge#(u,v))
             -->_1 ge#(s(u),s(v)) -> c_5(ge#(u,v)):2
          
          3:S:length#(cons(x,l)) -> c_6(length#(l))
             -->_1 length#(cons(x,l)) -> c_6(length#(l)):3
          
          4:S:nthtail#(n,l) -> c_8(cond#(ge(n,length(l)),n,l),ge#(n,length(l)),length#(l))
             -->_3 length#(cons(x,l)) -> c_6(length#(l)):3
             -->_2 ge#(s(u),s(v)) -> c_5(ge#(u,v)):2
             -->_1 cond#(false(),n,l) -> c_1(tail#(nthtail(s(n),l)),nthtail#(s(n),l)):1
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          cond#(false(),n,l) -> c_1(nthtail#(s(n),l))
* Step 5: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(false(),n,l) -> c_1(nthtail#(s(n),l))
            ge#(s(u),s(v)) -> c_5(ge#(u,v))
            length#(cons(x,l)) -> c_6(length#(l))
            nthtail#(n,l) -> c_8(cond#(ge(n,length(l)),n,l),ge#(n,length(l)),length#(l))
        - Weak TRS:
            cond(false(),n,l) -> tail(nthtail(s(n),l))
            cond(true(),n,l) -> l
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            length(cons(x,l)) -> s(length(l))
            length(nil()) -> 0()
            nthtail(n,l) -> cond(ge(n,length(l)),n,l)
            tail(cons(x,l)) -> l
            tail(nil()) -> nil()
        - Signature:
            {cond/3,ge/2,length/1,nthtail/2,tail/1,cond#/3,ge#/2,length#/1,nthtail#/2,tail#/1} / {0/0,cons/2,false/0
            ,nil/0,s/1,true/0,c_1/1,c_2/0,c_3/0,c_4/0,c_5/1,c_6/1,c_7/0,c_8/3,c_9/0,c_10/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond#,ge#,length#,nthtail#,tail#} and constructors {0
            ,cons,false,nil,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          ge(u,0()) -> true()
          ge(0(),s(v)) -> false()
          ge(s(u),s(v)) -> ge(u,v)
          length(cons(x,l)) -> s(length(l))
          length(nil()) -> 0()
          cond#(false(),n,l) -> c_1(nthtail#(s(n),l))
          ge#(s(u),s(v)) -> c_5(ge#(u,v))
          length#(cons(x,l)) -> c_6(length#(l))
          nthtail#(n,l) -> c_8(cond#(ge(n,length(l)),n,l),ge#(n,length(l)),length#(l))
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          cond#(false(),n,l) -> c_1(nthtail#(s(n),l))
          ge#(s(u),s(v)) -> c_5(ge#(u,v))
          length#(cons(x,l)) -> c_6(length#(l))
          nthtail#(n,l) -> c_8(cond#(ge(n,length(l)),n,l),ge#(n,length(l)),length#(l))
      - Weak TRS:
          ge(u,0()) -> true()
          ge(0(),s(v)) -> false()
          ge(s(u),s(v)) -> ge(u,v)
          length(cons(x,l)) -> s(length(l))
          length(nil()) -> 0()
      - Signature:
          {cond/3,ge/2,length/1,nthtail/2,tail/1,cond#/3,ge#/2,length#/1,nthtail#/2,tail#/1} / {0/0,cons/2,false/0
          ,nil/0,s/1,true/0,c_1/1,c_2/0,c_3/0,c_4/0,c_5/1,c_6/1,c_7/0,c_8/3,c_9/0,c_10/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {cond#,ge#,length#,nthtail#,tail#} and constructors {0
          ,cons,false,nil,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE