MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            cond(false(),x,y,z) -> 0()
            cond(true(),x,y,z) -> s(d(x,s(y),plus(s(y),z)))
            d(x,s(y),z) -> cond(ge(x,z),x,y,z)
            div(x,s(y)) -> d(x,s(y),0())
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
        - Signature:
            {cond/4,d/3,div/2,ge/2,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond,d,div,ge,plus} and constructors {0,false,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          cond#(false(),x,y,z) -> c_1()
          cond#(true(),x,y,z) -> c_2(d#(x,s(y),plus(s(y),z)),plus#(s(y),z))
          d#(x,s(y),z) -> c_3(cond#(ge(x,z),x,y,z),ge#(x,z))
          div#(x,s(y)) -> c_4(d#(x,s(y),0()))
          ge#(u,0()) -> c_5()
          ge#(0(),s(v)) -> c_6()
          ge#(s(u),s(v)) -> c_7(ge#(u,v))
          plus#(n,0()) -> c_8()
          plus#(n,s(m)) -> c_9(plus#(n,m))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(false(),x,y,z) -> c_1()
            cond#(true(),x,y,z) -> c_2(d#(x,s(y),plus(s(y),z)),plus#(s(y),z))
            d#(x,s(y),z) -> c_3(cond#(ge(x,z),x,y,z),ge#(x,z))
            div#(x,s(y)) -> c_4(d#(x,s(y),0()))
            ge#(u,0()) -> c_5()
            ge#(0(),s(v)) -> c_6()
            ge#(s(u),s(v)) -> c_7(ge#(u,v))
            plus#(n,0()) -> c_8()
            plus#(n,s(m)) -> c_9(plus#(n,m))
        - Weak TRS:
            cond(false(),x,y,z) -> 0()
            cond(true(),x,y,z) -> s(d(x,s(y),plus(s(y),z)))
            d(x,s(y),z) -> cond(ge(x,z),x,y,z)
            div(x,s(y)) -> d(x,s(y),0())
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
        - Signature:
            {cond/4,d/3,div/2,ge/2,plus/2,cond#/4,d#/3,div#/2,ge#/2,plus#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/2,c_3/2
            ,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond#,d#,div#,ge#,plus#} and constructors {0,false,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)
          plus(n,0()) -> n
          plus(n,s(m)) -> s(plus(n,m))
          cond#(false(),x,y,z) -> c_1()
          cond#(true(),x,y,z) -> c_2(d#(x,s(y),plus(s(y),z)),plus#(s(y),z))
          d#(x,s(y),z) -> c_3(cond#(ge(x,z),x,y,z),ge#(x,z))
          div#(x,s(y)) -> c_4(d#(x,s(y),0()))
          ge#(u,0()) -> c_5()
          ge#(0(),s(v)) -> c_6()
          ge#(s(u),s(v)) -> c_7(ge#(u,v))
          plus#(n,0()) -> c_8()
          plus#(n,s(m)) -> c_9(plus#(n,m))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(false(),x,y,z) -> c_1()
            cond#(true(),x,y,z) -> c_2(d#(x,s(y),plus(s(y),z)),plus#(s(y),z))
            d#(x,s(y),z) -> c_3(cond#(ge(x,z),x,y,z),ge#(x,z))
            div#(x,s(y)) -> c_4(d#(x,s(y),0()))
            ge#(u,0()) -> c_5()
            ge#(0(),s(v)) -> c_6()
            ge#(s(u),s(v)) -> c_7(ge#(u,v))
            plus#(n,0()) -> c_8()
            plus#(n,s(m)) -> c_9(plus#(n,m))
        - Weak TRS:
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
        - Signature:
            {cond/4,d/3,div/2,ge/2,plus/2,cond#/4,d#/3,div#/2,ge#/2,plus#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/2,c_3/2
            ,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond#,d#,div#,ge#,plus#} and constructors {0,false,s
            ,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,5,6,8}
        by application of
          Pre({1,5,6,8}) = {2,3,7,9}.
        Here rules are labelled as follows:
          1: cond#(false(),x,y,z) -> c_1()
          2: cond#(true(),x,y,z) -> c_2(d#(x,s(y),plus(s(y),z)),plus#(s(y),z))
          3: d#(x,s(y),z) -> c_3(cond#(ge(x,z),x,y,z),ge#(x,z))
          4: div#(x,s(y)) -> c_4(d#(x,s(y),0()))
          5: ge#(u,0()) -> c_5()
          6: ge#(0(),s(v)) -> c_6()
          7: ge#(s(u),s(v)) -> c_7(ge#(u,v))
          8: plus#(n,0()) -> c_8()
          9: plus#(n,s(m)) -> c_9(plus#(n,m))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(true(),x,y,z) -> c_2(d#(x,s(y),plus(s(y),z)),plus#(s(y),z))
            d#(x,s(y),z) -> c_3(cond#(ge(x,z),x,y,z),ge#(x,z))
            div#(x,s(y)) -> c_4(d#(x,s(y),0()))
            ge#(s(u),s(v)) -> c_7(ge#(u,v))
            plus#(n,s(m)) -> c_9(plus#(n,m))
        - Weak DPs:
            cond#(false(),x,y,z) -> c_1()
            ge#(u,0()) -> c_5()
            ge#(0(),s(v)) -> c_6()
            plus#(n,0()) -> c_8()
        - Weak TRS:
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
        - Signature:
            {cond/4,d/3,div/2,ge/2,plus/2,cond#/4,d#/3,div#/2,ge#/2,plus#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/2,c_3/2
            ,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond#,d#,div#,ge#,plus#} and constructors {0,false,s
            ,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:cond#(true(),x,y,z) -> c_2(d#(x,s(y),plus(s(y),z)),plus#(s(y),z))
             -->_2 plus#(n,s(m)) -> c_9(plus#(n,m)):5
             -->_1 d#(x,s(y),z) -> c_3(cond#(ge(x,z),x,y,z),ge#(x,z)):2
             -->_2 plus#(n,0()) -> c_8():9
          
          2:S:d#(x,s(y),z) -> c_3(cond#(ge(x,z),x,y,z),ge#(x,z))
             -->_2 ge#(s(u),s(v)) -> c_7(ge#(u,v)):4
             -->_2 ge#(0(),s(v)) -> c_6():8
             -->_2 ge#(u,0()) -> c_5():7
             -->_1 cond#(false(),x,y,z) -> c_1():6
             -->_1 cond#(true(),x,y,z) -> c_2(d#(x,s(y),plus(s(y),z)),plus#(s(y),z)):1
          
          3:S:div#(x,s(y)) -> c_4(d#(x,s(y),0()))
             -->_1 d#(x,s(y),z) -> c_3(cond#(ge(x,z),x,y,z),ge#(x,z)):2
          
          4:S:ge#(s(u),s(v)) -> c_7(ge#(u,v))
             -->_1 ge#(0(),s(v)) -> c_6():8
             -->_1 ge#(u,0()) -> c_5():7
             -->_1 ge#(s(u),s(v)) -> c_7(ge#(u,v)):4
          
          5:S:plus#(n,s(m)) -> c_9(plus#(n,m))
             -->_1 plus#(n,0()) -> c_8():9
             -->_1 plus#(n,s(m)) -> c_9(plus#(n,m)):5
          
          6:W:cond#(false(),x,y,z) -> c_1()
             
          
          7:W:ge#(u,0()) -> c_5()
             
          
          8:W:ge#(0(),s(v)) -> c_6()
             
          
          9:W:plus#(n,0()) -> c_8()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          6: cond#(false(),x,y,z) -> c_1()
          7: ge#(u,0()) -> c_5()
          8: ge#(0(),s(v)) -> c_6()
          9: plus#(n,0()) -> c_8()
* Step 5: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            cond#(true(),x,y,z) -> c_2(d#(x,s(y),plus(s(y),z)),plus#(s(y),z))
            d#(x,s(y),z) -> c_3(cond#(ge(x,z),x,y,z),ge#(x,z))
            div#(x,s(y)) -> c_4(d#(x,s(y),0()))
            ge#(s(u),s(v)) -> c_7(ge#(u,v))
            plus#(n,s(m)) -> c_9(plus#(n,m))
        - Weak TRS:
            ge(u,0()) -> true()
            ge(0(),s(v)) -> false()
            ge(s(u),s(v)) -> ge(u,v)
            plus(n,0()) -> n
            plus(n,s(m)) -> s(plus(n,m))
        - Signature:
            {cond/4,d/3,div/2,ge/2,plus/2,cond#/4,d#/3,div#/2,ge#/2,plus#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/2,c_3/2
            ,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {cond#,d#,div#,ge#,plus#} and constructors {0,false,s
            ,true}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:cond#(true(),x,y,z) -> c_2(d#(x,s(y),plus(s(y),z)),plus#(s(y),z))
           -->_2 plus#(n,s(m)) -> c_9(plus#(n,m)):5
           -->_1 d#(x,s(y),z) -> c_3(cond#(ge(x,z),x,y,z),ge#(x,z)):2
        
        2:S:d#(x,s(y),z) -> c_3(cond#(ge(x,z),x,y,z),ge#(x,z))
           -->_2 ge#(s(u),s(v)) -> c_7(ge#(u,v)):4
           -->_1 cond#(true(),x,y,z) -> c_2(d#(x,s(y),plus(s(y),z)),plus#(s(y),z)):1
        
        3:S:div#(x,s(y)) -> c_4(d#(x,s(y),0()))
           -->_1 d#(x,s(y),z) -> c_3(cond#(ge(x,z),x,y,z),ge#(x,z)):2
        
        4:S:ge#(s(u),s(v)) -> c_7(ge#(u,v))
           -->_1 ge#(s(u),s(v)) -> c_7(ge#(u,v)):4
        
        5:S:plus#(n,s(m)) -> c_9(plus#(n,m))
           -->_1 plus#(n,s(m)) -> c_9(plus#(n,m)):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).
        
        [(3,div#(x,s(y)) -> c_4(d#(x,s(y),0())))]
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          cond#(true(),x,y,z) -> c_2(d#(x,s(y),plus(s(y),z)),plus#(s(y),z))
          d#(x,s(y),z) -> c_3(cond#(ge(x,z),x,y,z),ge#(x,z))
          ge#(s(u),s(v)) -> c_7(ge#(u,v))
          plus#(n,s(m)) -> c_9(plus#(n,m))
      - Weak TRS:
          ge(u,0()) -> true()
          ge(0(),s(v)) -> false()
          ge(s(u),s(v)) -> ge(u,v)
          plus(n,0()) -> n
          plus(n,s(m)) -> s(plus(n,m))
      - Signature:
          {cond/4,d/3,div/2,ge/2,plus/2,cond#/4,d#/3,div#/2,ge#/2,plus#/2} / {0/0,false/0,s/1,true/0,c_1/0,c_2/2,c_3/2
          ,c_4/1,c_5/0,c_6/0,c_7/1,c_8/0,c_9/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {cond#,d#,div#,ge#,plus#} and constructors {0,false,s
          ,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE