MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            cond1(true(),x) -> cond2(even(x),x)
            cond2(false(),x) -> cond1(neq(x,0()),p(x))
            cond2(true(),x) -> cond1(neq(x,0()),div2(x))
            div2(0()) -> 0()
            div2(s(0())) -> 0()
            div2(s(s(x))) -> s(div2(x))
            even(0()) -> true()
            even(s(0())) -> false()
            even(s(s(x))) -> even(x)
            neq(0(),0()) -> false()
            neq(0(),s(x)) -> true()
            neq(s(x),0()) -> true()
            neq(s(x),s(y())) -> neq(x,y())
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {cond1/2,cond2/2,div2/1,even/1,neq/2,p/1} / {0/0,false/0,s/1,true/0,y/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond1,cond2,div2,even,neq,p} and constructors {0,false,s
            ,true,y}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          cond1#(true(),x) -> c_1(cond2#(even(x),x),even#(x))
          cond2#(false(),x) -> c_2(cond1#(neq(x,0()),p(x)),neq#(x,0()),p#(x))
          cond2#(true(),x) -> c_3(cond1#(neq(x,0()),div2(x)),neq#(x,0()),div2#(x))
          div2#(0()) -> c_4()
          div2#(s(0())) -> c_5()
          div2#(s(s(x))) -> c_6(div2#(x))
          even#(0()) -> c_7()
          even#(s(0())) -> c_8()
          even#(s(s(x))) -> c_9(even#(x))
          neq#(0(),0()) -> c_10()
          neq#(0(),s(x)) -> c_11()
          neq#(s(x),0()) -> c_12()
          neq#(s(x),s(y())) -> c_13(neq#(x,y()))
          p#(0()) -> c_14()
          p#(s(x)) -> c_15()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            cond1#(true(),x) -> c_1(cond2#(even(x),x),even#(x))
            cond2#(false(),x) -> c_2(cond1#(neq(x,0()),p(x)),neq#(x,0()),p#(x))
            cond2#(true(),x) -> c_3(cond1#(neq(x,0()),div2(x)),neq#(x,0()),div2#(x))
            div2#(0()) -> c_4()
            div2#(s(0())) -> c_5()
            div2#(s(s(x))) -> c_6(div2#(x))
            even#(0()) -> c_7()
            even#(s(0())) -> c_8()
            even#(s(s(x))) -> c_9(even#(x))
            neq#(0(),0()) -> c_10()
            neq#(0(),s(x)) -> c_11()
            neq#(s(x),0()) -> c_12()
            neq#(s(x),s(y())) -> c_13(neq#(x,y()))
            p#(0()) -> c_14()
            p#(s(x)) -> c_15()
        - Weak TRS:
            cond1(true(),x) -> cond2(even(x),x)
            cond2(false(),x) -> cond1(neq(x,0()),p(x))
            cond2(true(),x) -> cond1(neq(x,0()),div2(x))
            div2(0()) -> 0()
            div2(s(0())) -> 0()
            div2(s(s(x))) -> s(div2(x))
            even(0()) -> true()
            even(s(0())) -> false()
            even(s(s(x))) -> even(x)
            neq(0(),0()) -> false()
            neq(0(),s(x)) -> true()
            neq(s(x),0()) -> true()
            neq(s(x),s(y())) -> neq(x,y())
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {cond1/2,cond2/2,div2/1,even/1,neq/2,p/1,cond1#/2,cond2#/2,div2#/1,even#/1,neq#/2,p#/1} / {0/0,false/0,s/1
            ,true/0,y/0,c_1/2,c_2/3,c_3/3,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0,c_12/0,c_13/1,c_14/0,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond1#,cond2#,div2#,even#,neq#,p#} and constructors {0
            ,false,s,true,y}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          div2(0()) -> 0()
          div2(s(0())) -> 0()
          div2(s(s(x))) -> s(div2(x))
          even(0()) -> true()
          even(s(0())) -> false()
          even(s(s(x))) -> even(x)
          neq(0(),0()) -> false()
          neq(s(x),0()) -> true()
          p(0()) -> 0()
          p(s(x)) -> x
          cond1#(true(),x) -> c_1(cond2#(even(x),x),even#(x))
          cond2#(false(),x) -> c_2(cond1#(neq(x,0()),p(x)),neq#(x,0()),p#(x))
          cond2#(true(),x) -> c_3(cond1#(neq(x,0()),div2(x)),neq#(x,0()),div2#(x))
          div2#(0()) -> c_4()
          div2#(s(0())) -> c_5()
          div2#(s(s(x))) -> c_6(div2#(x))
          even#(0()) -> c_7()
          even#(s(0())) -> c_8()
          even#(s(s(x))) -> c_9(even#(x))
          neq#(0(),0()) -> c_10()
          neq#(0(),s(x)) -> c_11()
          neq#(s(x),0()) -> c_12()
          neq#(s(x),s(y())) -> c_13(neq#(x,y()))
          p#(0()) -> c_14()
          p#(s(x)) -> c_15()
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            cond1#(true(),x) -> c_1(cond2#(even(x),x),even#(x))
            cond2#(false(),x) -> c_2(cond1#(neq(x,0()),p(x)),neq#(x,0()),p#(x))
            cond2#(true(),x) -> c_3(cond1#(neq(x,0()),div2(x)),neq#(x,0()),div2#(x))
            div2#(0()) -> c_4()
            div2#(s(0())) -> c_5()
            div2#(s(s(x))) -> c_6(div2#(x))
            even#(0()) -> c_7()
            even#(s(0())) -> c_8()
            even#(s(s(x))) -> c_9(even#(x))
            neq#(0(),0()) -> c_10()
            neq#(0(),s(x)) -> c_11()
            neq#(s(x),0()) -> c_12()
            neq#(s(x),s(y())) -> c_13(neq#(x,y()))
            p#(0()) -> c_14()
            p#(s(x)) -> c_15()
        - Weak TRS:
            div2(0()) -> 0()
            div2(s(0())) -> 0()
            div2(s(s(x))) -> s(div2(x))
            even(0()) -> true()
            even(s(0())) -> false()
            even(s(s(x))) -> even(x)
            neq(0(),0()) -> false()
            neq(s(x),0()) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {cond1/2,cond2/2,div2/1,even/1,neq/2,p/1,cond1#/2,cond2#/2,div2#/1,even#/1,neq#/2,p#/1} / {0/0,false/0,s/1
            ,true/0,y/0,c_1/2,c_2/3,c_3/3,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0,c_12/0,c_13/1,c_14/0,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond1#,cond2#,div2#,even#,neq#,p#} and constructors {0
            ,false,s,true,y}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {4,5,7,8,10,11,12,13,14,15}
        by application of
          Pre({4,5,7,8,10,11,12,13,14,15}) = {1,2,3,6,9}.
        Here rules are labelled as follows:
          1: cond1#(true(),x) -> c_1(cond2#(even(x),x),even#(x))
          2: cond2#(false(),x) -> c_2(cond1#(neq(x,0()),p(x)),neq#(x,0()),p#(x))
          3: cond2#(true(),x) -> c_3(cond1#(neq(x,0()),div2(x)),neq#(x,0()),div2#(x))
          4: div2#(0()) -> c_4()
          5: div2#(s(0())) -> c_5()
          6: div2#(s(s(x))) -> c_6(div2#(x))
          7: even#(0()) -> c_7()
          8: even#(s(0())) -> c_8()
          9: even#(s(s(x))) -> c_9(even#(x))
          10: neq#(0(),0()) -> c_10()
          11: neq#(0(),s(x)) -> c_11()
          12: neq#(s(x),0()) -> c_12()
          13: neq#(s(x),s(y())) -> c_13(neq#(x,y()))
          14: p#(0()) -> c_14()
          15: p#(s(x)) -> c_15()
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            cond1#(true(),x) -> c_1(cond2#(even(x),x),even#(x))
            cond2#(false(),x) -> c_2(cond1#(neq(x,0()),p(x)),neq#(x,0()),p#(x))
            cond2#(true(),x) -> c_3(cond1#(neq(x,0()),div2(x)),neq#(x,0()),div2#(x))
            div2#(s(s(x))) -> c_6(div2#(x))
            even#(s(s(x))) -> c_9(even#(x))
        - Weak DPs:
            div2#(0()) -> c_4()
            div2#(s(0())) -> c_5()
            even#(0()) -> c_7()
            even#(s(0())) -> c_8()
            neq#(0(),0()) -> c_10()
            neq#(0(),s(x)) -> c_11()
            neq#(s(x),0()) -> c_12()
            neq#(s(x),s(y())) -> c_13(neq#(x,y()))
            p#(0()) -> c_14()
            p#(s(x)) -> c_15()
        - Weak TRS:
            div2(0()) -> 0()
            div2(s(0())) -> 0()
            div2(s(s(x))) -> s(div2(x))
            even(0()) -> true()
            even(s(0())) -> false()
            even(s(s(x))) -> even(x)
            neq(0(),0()) -> false()
            neq(s(x),0()) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {cond1/2,cond2/2,div2/1,even/1,neq/2,p/1,cond1#/2,cond2#/2,div2#/1,even#/1,neq#/2,p#/1} / {0/0,false/0,s/1
            ,true/0,y/0,c_1/2,c_2/3,c_3/3,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0,c_12/0,c_13/1,c_14/0,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond1#,cond2#,div2#,even#,neq#,p#} and constructors {0
            ,false,s,true,y}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:cond1#(true(),x) -> c_1(cond2#(even(x),x),even#(x))
             -->_2 even#(s(s(x))) -> c_9(even#(x)):5
             -->_1 cond2#(true(),x) -> c_3(cond1#(neq(x,0()),div2(x)),neq#(x,0()),div2#(x)):3
             -->_1 cond2#(false(),x) -> c_2(cond1#(neq(x,0()),p(x)),neq#(x,0()),p#(x)):2
             -->_2 even#(s(0())) -> c_8():9
             -->_2 even#(0()) -> c_7():8
          
          2:S:cond2#(false(),x) -> c_2(cond1#(neq(x,0()),p(x)),neq#(x,0()),p#(x))
             -->_3 p#(s(x)) -> c_15():15
             -->_3 p#(0()) -> c_14():14
             -->_2 neq#(s(x),0()) -> c_12():12
             -->_2 neq#(0(),0()) -> c_10():10
             -->_1 cond1#(true(),x) -> c_1(cond2#(even(x),x),even#(x)):1
          
          3:S:cond2#(true(),x) -> c_3(cond1#(neq(x,0()),div2(x)),neq#(x,0()),div2#(x))
             -->_3 div2#(s(s(x))) -> c_6(div2#(x)):4
             -->_2 neq#(s(x),0()) -> c_12():12
             -->_2 neq#(0(),0()) -> c_10():10
             -->_3 div2#(s(0())) -> c_5():7
             -->_3 div2#(0()) -> c_4():6
             -->_1 cond1#(true(),x) -> c_1(cond2#(even(x),x),even#(x)):1
          
          4:S:div2#(s(s(x))) -> c_6(div2#(x))
             -->_1 div2#(s(0())) -> c_5():7
             -->_1 div2#(0()) -> c_4():6
             -->_1 div2#(s(s(x))) -> c_6(div2#(x)):4
          
          5:S:even#(s(s(x))) -> c_9(even#(x))
             -->_1 even#(s(0())) -> c_8():9
             -->_1 even#(0()) -> c_7():8
             -->_1 even#(s(s(x))) -> c_9(even#(x)):5
          
          6:W:div2#(0()) -> c_4()
             
          
          7:W:div2#(s(0())) -> c_5()
             
          
          8:W:even#(0()) -> c_7()
             
          
          9:W:even#(s(0())) -> c_8()
             
          
          10:W:neq#(0(),0()) -> c_10()
             
          
          11:W:neq#(0(),s(x)) -> c_11()
             
          
          12:W:neq#(s(x),0()) -> c_12()
             
          
          13:W:neq#(s(x),s(y())) -> c_13(neq#(x,y()))
             
          
          14:W:p#(0()) -> c_14()
             
          
          15:W:p#(s(x)) -> c_15()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          13: neq#(s(x),s(y())) -> c_13(neq#(x,y()))
          11: neq#(0(),s(x)) -> c_11()
          14: p#(0()) -> c_14()
          15: p#(s(x)) -> c_15()
          10: neq#(0(),0()) -> c_10()
          12: neq#(s(x),0()) -> c_12()
          6: div2#(0()) -> c_4()
          7: div2#(s(0())) -> c_5()
          8: even#(0()) -> c_7()
          9: even#(s(0())) -> c_8()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            cond1#(true(),x) -> c_1(cond2#(even(x),x),even#(x))
            cond2#(false(),x) -> c_2(cond1#(neq(x,0()),p(x)),neq#(x,0()),p#(x))
            cond2#(true(),x) -> c_3(cond1#(neq(x,0()),div2(x)),neq#(x,0()),div2#(x))
            div2#(s(s(x))) -> c_6(div2#(x))
            even#(s(s(x))) -> c_9(even#(x))
        - Weak TRS:
            div2(0()) -> 0()
            div2(s(0())) -> 0()
            div2(s(s(x))) -> s(div2(x))
            even(0()) -> true()
            even(s(0())) -> false()
            even(s(s(x))) -> even(x)
            neq(0(),0()) -> false()
            neq(s(x),0()) -> true()
            p(0()) -> 0()
            p(s(x)) -> x
        - Signature:
            {cond1/2,cond2/2,div2/1,even/1,neq/2,p/1,cond1#/2,cond2#/2,div2#/1,even#/1,neq#/2,p#/1} / {0/0,false/0,s/1
            ,true/0,y/0,c_1/2,c_2/3,c_3/3,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0,c_12/0,c_13/1,c_14/0,c_15/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond1#,cond2#,div2#,even#,neq#,p#} and constructors {0
            ,false,s,true,y}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:cond1#(true(),x) -> c_1(cond2#(even(x),x),even#(x))
             -->_2 even#(s(s(x))) -> c_9(even#(x)):5
             -->_1 cond2#(true(),x) -> c_3(cond1#(neq(x,0()),div2(x)),neq#(x,0()),div2#(x)):3
             -->_1 cond2#(false(),x) -> c_2(cond1#(neq(x,0()),p(x)),neq#(x,0()),p#(x)):2
          
          2:S:cond2#(false(),x) -> c_2(cond1#(neq(x,0()),p(x)),neq#(x,0()),p#(x))
             -->_1 cond1#(true(),x) -> c_1(cond2#(even(x),x),even#(x)):1
          
          3:S:cond2#(true(),x) -> c_3(cond1#(neq(x,0()),div2(x)),neq#(x,0()),div2#(x))
             -->_3 div2#(s(s(x))) -> c_6(div2#(x)):4
             -->_1 cond1#(true(),x) -> c_1(cond2#(even(x),x),even#(x)):1
          
          4:S:div2#(s(s(x))) -> c_6(div2#(x))
             -->_1 div2#(s(s(x))) -> c_6(div2#(x)):4
          
          5:S:even#(s(s(x))) -> c_9(even#(x))
             -->_1 even#(s(s(x))) -> c_9(even#(x)):5
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          cond2#(false(),x) -> c_2(cond1#(neq(x,0()),p(x)))
          cond2#(true(),x) -> c_3(cond1#(neq(x,0()),div2(x)),div2#(x))
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          cond1#(true(),x) -> c_1(cond2#(even(x),x),even#(x))
          cond2#(false(),x) -> c_2(cond1#(neq(x,0()),p(x)))
          cond2#(true(),x) -> c_3(cond1#(neq(x,0()),div2(x)),div2#(x))
          div2#(s(s(x))) -> c_6(div2#(x))
          even#(s(s(x))) -> c_9(even#(x))
      - Weak TRS:
          div2(0()) -> 0()
          div2(s(0())) -> 0()
          div2(s(s(x))) -> s(div2(x))
          even(0()) -> true()
          even(s(0())) -> false()
          even(s(s(x))) -> even(x)
          neq(0(),0()) -> false()
          neq(s(x),0()) -> true()
          p(0()) -> 0()
          p(s(x)) -> x
      - Signature:
          {cond1/2,cond2/2,div2/1,even/1,neq/2,p/1,cond1#/2,cond2#/2,div2#/1,even#/1,neq#/2,p#/1} / {0/0,false/0,s/1
          ,true/0,y/0,c_1/2,c_2/1,c_3/2,c_4/0,c_5/0,c_6/1,c_7/0,c_8/0,c_9/1,c_10/0,c_11/0,c_12/0,c_13/1,c_14/0,c_15/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {cond1#,cond2#,div2#,even#,neq#,p#} and constructors {0
          ,false,s,true,y}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE