MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            conv(x) -> conviter(x,cons(0(),nil()))
            conviter(x,l) -> if(zero(x),x,l)
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            if(false(),x,l) -> conviter(half(x),cons(lastbit(x),l))
            if(true(),x,l) -> l
            lastbit(0()) -> 0()
            lastbit(s(0())) -> s(0())
            lastbit(s(s(x))) -> lastbit(x)
            zero(0()) -> true()
            zero(s(x)) -> false()
        - Signature:
            {conv/1,conviter/2,half/1,if/3,lastbit/1,zero/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {conv,conviter,half,if,lastbit,zero} and constructors {0
            ,cons,false,nil,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          conv#(x) -> c_1(conviter#(x,cons(0(),nil())))
          conviter#(x,l) -> c_2(if#(zero(x),x,l),zero#(x))
          half#(0()) -> c_3()
          half#(s(0())) -> c_4()
          half#(s(s(x))) -> c_5(half#(x))
          if#(false(),x,l) -> c_6(conviter#(half(x),cons(lastbit(x),l)),half#(x),lastbit#(x))
          if#(true(),x,l) -> c_7()
          lastbit#(0()) -> c_8()
          lastbit#(s(0())) -> c_9()
          lastbit#(s(s(x))) -> c_10(lastbit#(x))
          zero#(0()) -> c_11()
          zero#(s(x)) -> c_12()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            conv#(x) -> c_1(conviter#(x,cons(0(),nil())))
            conviter#(x,l) -> c_2(if#(zero(x),x,l),zero#(x))
            half#(0()) -> c_3()
            half#(s(0())) -> c_4()
            half#(s(s(x))) -> c_5(half#(x))
            if#(false(),x,l) -> c_6(conviter#(half(x),cons(lastbit(x),l)),half#(x),lastbit#(x))
            if#(true(),x,l) -> c_7()
            lastbit#(0()) -> c_8()
            lastbit#(s(0())) -> c_9()
            lastbit#(s(s(x))) -> c_10(lastbit#(x))
            zero#(0()) -> c_11()
            zero#(s(x)) -> c_12()
        - Weak TRS:
            conv(x) -> conviter(x,cons(0(),nil()))
            conviter(x,l) -> if(zero(x),x,l)
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            if(false(),x,l) -> conviter(half(x),cons(lastbit(x),l))
            if(true(),x,l) -> l
            lastbit(0()) -> 0()
            lastbit(s(0())) -> s(0())
            lastbit(s(s(x))) -> lastbit(x)
            zero(0()) -> true()
            zero(s(x)) -> false()
        - Signature:
            {conv/1,conviter/2,half/1,if/3,lastbit/1,zero/1,conv#/1,conviter#/2,half#/1,if#/3,lastbit#/1,zero#/1} / {0/0
            ,cons/2,false/0,nil/0,s/1,true/0,c_1/1,c_2/2,c_3/0,c_4/0,c_5/1,c_6/3,c_7/0,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {conv#,conviter#,half#,if#,lastbit#
            ,zero#} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          half(0()) -> 0()
          half(s(0())) -> 0()
          half(s(s(x))) -> s(half(x))
          lastbit(0()) -> 0()
          lastbit(s(0())) -> s(0())
          lastbit(s(s(x))) -> lastbit(x)
          zero(0()) -> true()
          zero(s(x)) -> false()
          conv#(x) -> c_1(conviter#(x,cons(0(),nil())))
          conviter#(x,l) -> c_2(if#(zero(x),x,l),zero#(x))
          half#(0()) -> c_3()
          half#(s(0())) -> c_4()
          half#(s(s(x))) -> c_5(half#(x))
          if#(false(),x,l) -> c_6(conviter#(half(x),cons(lastbit(x),l)),half#(x),lastbit#(x))
          if#(true(),x,l) -> c_7()
          lastbit#(0()) -> c_8()
          lastbit#(s(0())) -> c_9()
          lastbit#(s(s(x))) -> c_10(lastbit#(x))
          zero#(0()) -> c_11()
          zero#(s(x)) -> c_12()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            conv#(x) -> c_1(conviter#(x,cons(0(),nil())))
            conviter#(x,l) -> c_2(if#(zero(x),x,l),zero#(x))
            half#(0()) -> c_3()
            half#(s(0())) -> c_4()
            half#(s(s(x))) -> c_5(half#(x))
            if#(false(),x,l) -> c_6(conviter#(half(x),cons(lastbit(x),l)),half#(x),lastbit#(x))
            if#(true(),x,l) -> c_7()
            lastbit#(0()) -> c_8()
            lastbit#(s(0())) -> c_9()
            lastbit#(s(s(x))) -> c_10(lastbit#(x))
            zero#(0()) -> c_11()
            zero#(s(x)) -> c_12()
        - Weak TRS:
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            lastbit(0()) -> 0()
            lastbit(s(0())) -> s(0())
            lastbit(s(s(x))) -> lastbit(x)
            zero(0()) -> true()
            zero(s(x)) -> false()
        - Signature:
            {conv/1,conviter/2,half/1,if/3,lastbit/1,zero/1,conv#/1,conviter#/2,half#/1,if#/3,lastbit#/1,zero#/1} / {0/0
            ,cons/2,false/0,nil/0,s/1,true/0,c_1/1,c_2/2,c_3/0,c_4/0,c_5/1,c_6/3,c_7/0,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {conv#,conviter#,half#,if#,lastbit#
            ,zero#} 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
          {3,4,7,8,9,11,12}
        by application of
          Pre({3,4,7,8,9,11,12}) = {2,5,6,10}.
        Here rules are labelled as follows:
          1: conv#(x) -> c_1(conviter#(x,cons(0(),nil())))
          2: conviter#(x,l) -> c_2(if#(zero(x),x,l),zero#(x))
          3: half#(0()) -> c_3()
          4: half#(s(0())) -> c_4()
          5: half#(s(s(x))) -> c_5(half#(x))
          6: if#(false(),x,l) -> c_6(conviter#(half(x),cons(lastbit(x),l)),half#(x),lastbit#(x))
          7: if#(true(),x,l) -> c_7()
          8: lastbit#(0()) -> c_8()
          9: lastbit#(s(0())) -> c_9()
          10: lastbit#(s(s(x))) -> c_10(lastbit#(x))
          11: zero#(0()) -> c_11()
          12: zero#(s(x)) -> c_12()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            conv#(x) -> c_1(conviter#(x,cons(0(),nil())))
            conviter#(x,l) -> c_2(if#(zero(x),x,l),zero#(x))
            half#(s(s(x))) -> c_5(half#(x))
            if#(false(),x,l) -> c_6(conviter#(half(x),cons(lastbit(x),l)),half#(x),lastbit#(x))
            lastbit#(s(s(x))) -> c_10(lastbit#(x))
        - Weak DPs:
            half#(0()) -> c_3()
            half#(s(0())) -> c_4()
            if#(true(),x,l) -> c_7()
            lastbit#(0()) -> c_8()
            lastbit#(s(0())) -> c_9()
            zero#(0()) -> c_11()
            zero#(s(x)) -> c_12()
        - Weak TRS:
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            lastbit(0()) -> 0()
            lastbit(s(0())) -> s(0())
            lastbit(s(s(x))) -> lastbit(x)
            zero(0()) -> true()
            zero(s(x)) -> false()
        - Signature:
            {conv/1,conviter/2,half/1,if/3,lastbit/1,zero/1,conv#/1,conviter#/2,half#/1,if#/3,lastbit#/1,zero#/1} / {0/0
            ,cons/2,false/0,nil/0,s/1,true/0,c_1/1,c_2/2,c_3/0,c_4/0,c_5/1,c_6/3,c_7/0,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {conv#,conviter#,half#,if#,lastbit#
            ,zero#} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:conv#(x) -> c_1(conviter#(x,cons(0(),nil())))
             -->_1 conviter#(x,l) -> c_2(if#(zero(x),x,l),zero#(x)):2
          
          2:S:conviter#(x,l) -> c_2(if#(zero(x),x,l),zero#(x))
             -->_1 if#(false(),x,l) -> c_6(conviter#(half(x),cons(lastbit(x),l)),half#(x),lastbit#(x)):4
             -->_2 zero#(s(x)) -> c_12():12
             -->_2 zero#(0()) -> c_11():11
             -->_1 if#(true(),x,l) -> c_7():8
          
          3:S:half#(s(s(x))) -> c_5(half#(x))
             -->_1 half#(s(0())) -> c_4():7
             -->_1 half#(0()) -> c_3():6
             -->_1 half#(s(s(x))) -> c_5(half#(x)):3
          
          4:S:if#(false(),x,l) -> c_6(conviter#(half(x),cons(lastbit(x),l)),half#(x),lastbit#(x))
             -->_3 lastbit#(s(s(x))) -> c_10(lastbit#(x)):5
             -->_3 lastbit#(s(0())) -> c_9():10
             -->_3 lastbit#(0()) -> c_8():9
             -->_2 half#(s(0())) -> c_4():7
             -->_2 half#(0()) -> c_3():6
             -->_2 half#(s(s(x))) -> c_5(half#(x)):3
             -->_1 conviter#(x,l) -> c_2(if#(zero(x),x,l),zero#(x)):2
          
          5:S:lastbit#(s(s(x))) -> c_10(lastbit#(x))
             -->_1 lastbit#(s(0())) -> c_9():10
             -->_1 lastbit#(0()) -> c_8():9
             -->_1 lastbit#(s(s(x))) -> c_10(lastbit#(x)):5
          
          6:W:half#(0()) -> c_3()
             
          
          7:W:half#(s(0())) -> c_4()
             
          
          8:W:if#(true(),x,l) -> c_7()
             
          
          9:W:lastbit#(0()) -> c_8()
             
          
          10:W:lastbit#(s(0())) -> c_9()
             
          
          11:W:zero#(0()) -> c_11()
             
          
          12:W:zero#(s(x)) -> c_12()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          8: if#(true(),x,l) -> c_7()
          11: zero#(0()) -> c_11()
          12: zero#(s(x)) -> c_12()
          6: half#(0()) -> c_3()
          7: half#(s(0())) -> c_4()
          9: lastbit#(0()) -> c_8()
          10: lastbit#(s(0())) -> c_9()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            conv#(x) -> c_1(conviter#(x,cons(0(),nil())))
            conviter#(x,l) -> c_2(if#(zero(x),x,l),zero#(x))
            half#(s(s(x))) -> c_5(half#(x))
            if#(false(),x,l) -> c_6(conviter#(half(x),cons(lastbit(x),l)),half#(x),lastbit#(x))
            lastbit#(s(s(x))) -> c_10(lastbit#(x))
        - Weak TRS:
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            lastbit(0()) -> 0()
            lastbit(s(0())) -> s(0())
            lastbit(s(s(x))) -> lastbit(x)
            zero(0()) -> true()
            zero(s(x)) -> false()
        - Signature:
            {conv/1,conviter/2,half/1,if/3,lastbit/1,zero/1,conv#/1,conviter#/2,half#/1,if#/3,lastbit#/1,zero#/1} / {0/0
            ,cons/2,false/0,nil/0,s/1,true/0,c_1/1,c_2/2,c_3/0,c_4/0,c_5/1,c_6/3,c_7/0,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {conv#,conviter#,half#,if#,lastbit#
            ,zero#} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:conv#(x) -> c_1(conviter#(x,cons(0(),nil())))
             -->_1 conviter#(x,l) -> c_2(if#(zero(x),x,l),zero#(x)):2
          
          2:S:conviter#(x,l) -> c_2(if#(zero(x),x,l),zero#(x))
             -->_1 if#(false(),x,l) -> c_6(conviter#(half(x),cons(lastbit(x),l)),half#(x),lastbit#(x)):4
          
          3:S:half#(s(s(x))) -> c_5(half#(x))
             -->_1 half#(s(s(x))) -> c_5(half#(x)):3
          
          4:S:if#(false(),x,l) -> c_6(conviter#(half(x),cons(lastbit(x),l)),half#(x),lastbit#(x))
             -->_3 lastbit#(s(s(x))) -> c_10(lastbit#(x)):5
             -->_2 half#(s(s(x))) -> c_5(half#(x)):3
             -->_1 conviter#(x,l) -> c_2(if#(zero(x),x,l),zero#(x)):2
          
          5:S:lastbit#(s(s(x))) -> c_10(lastbit#(x))
             -->_1 lastbit#(s(s(x))) -> c_10(lastbit#(x)):5
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          conviter#(x,l) -> c_2(if#(zero(x),x,l))
* Step 6: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            conv#(x) -> c_1(conviter#(x,cons(0(),nil())))
            conviter#(x,l) -> c_2(if#(zero(x),x,l))
            half#(s(s(x))) -> c_5(half#(x))
            if#(false(),x,l) -> c_6(conviter#(half(x),cons(lastbit(x),l)),half#(x),lastbit#(x))
            lastbit#(s(s(x))) -> c_10(lastbit#(x))
        - Weak TRS:
            half(0()) -> 0()
            half(s(0())) -> 0()
            half(s(s(x))) -> s(half(x))
            lastbit(0()) -> 0()
            lastbit(s(0())) -> s(0())
            lastbit(s(s(x))) -> lastbit(x)
            zero(0()) -> true()
            zero(s(x)) -> false()
        - Signature:
            {conv/1,conviter/2,half/1,if/3,lastbit/1,zero/1,conv#/1,conviter#/2,half#/1,if#/3,lastbit#/1,zero#/1} / {0/0
            ,cons/2,false/0,nil/0,s/1,true/0,c_1/1,c_2/1,c_3/0,c_4/0,c_5/1,c_6/3,c_7/0,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {conv#,conviter#,half#,if#,lastbit#
            ,zero#} and constructors {0,cons,false,nil,s,true}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:conv#(x) -> c_1(conviter#(x,cons(0(),nil())))
           -->_1 conviter#(x,l) -> c_2(if#(zero(x),x,l)):2
        
        2:S:conviter#(x,l) -> c_2(if#(zero(x),x,l))
           -->_1 if#(false(),x,l) -> c_6(conviter#(half(x),cons(lastbit(x),l)),half#(x),lastbit#(x)):4
        
        3:S:half#(s(s(x))) -> c_5(half#(x))
           -->_1 half#(s(s(x))) -> c_5(half#(x)):3
        
        4:S:if#(false(),x,l) -> c_6(conviter#(half(x),cons(lastbit(x),l)),half#(x),lastbit#(x))
           -->_3 lastbit#(s(s(x))) -> c_10(lastbit#(x)):5
           -->_2 half#(s(s(x))) -> c_5(half#(x)):3
           -->_1 conviter#(x,l) -> c_2(if#(zero(x),x,l)):2
        
        5:S:lastbit#(s(s(x))) -> c_10(lastbit#(x))
           -->_1 lastbit#(s(s(x))) -> c_10(lastbit#(x)):5
        
        
        Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts).
        
        [(1,conv#(x) -> c_1(conviter#(x,cons(0(),nil()))))]
* Step 7: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          conviter#(x,l) -> c_2(if#(zero(x),x,l))
          half#(s(s(x))) -> c_5(half#(x))
          if#(false(),x,l) -> c_6(conviter#(half(x),cons(lastbit(x),l)),half#(x),lastbit#(x))
          lastbit#(s(s(x))) -> c_10(lastbit#(x))
      - Weak TRS:
          half(0()) -> 0()
          half(s(0())) -> 0()
          half(s(s(x))) -> s(half(x))
          lastbit(0()) -> 0()
          lastbit(s(0())) -> s(0())
          lastbit(s(s(x))) -> lastbit(x)
          zero(0()) -> true()
          zero(s(x)) -> false()
      - Signature:
          {conv/1,conviter/2,half/1,if/3,lastbit/1,zero/1,conv#/1,conviter#/2,half#/1,if#/3,lastbit#/1,zero#/1} / {0/0
          ,cons/2,false/0,nil/0,s/1,true/0,c_1/1,c_2/1,c_3/0,c_4/0,c_5/1,c_6/3,c_7/0,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {conv#,conviter#,half#,if#,lastbit#
          ,zero#} and constructors {0,cons,false,nil,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE