MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            a() -> c()
            a() -> d()
            div(x,y) -> div2(x,y,0())
            div2(x,y,i) -> if1(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i))
            if1(false(),b,x,y,i,j) -> if2(b,x,y,i,j)
            if1(true(),b,x,y,i,j) -> divZeroError()
            if2(false(),x,y,i,j) -> i
            if2(true(),x,y,i,j) -> div2(minus(x,y),y,j)
            ifPlus(false(),x,y,z) -> plusIter(x,s(y),s(z))
            ifPlus(true(),x,y,z) -> y
            inc(0()) -> 0()
            inc(s(i)) -> s(inc(i))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(0(),y) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            plus(x,y) -> plusIter(x,y,0())
            plusIter(x,y,z) -> ifPlus(le(x,z),x,y,z)
        - Signature:
            {a/0,div/2,div2/3,if1/6,if2/5,ifPlus/4,inc/1,le/2,minus/2,plus/2,plusIter/3} / {0/0,c/0,d/0,divZeroError/0
            ,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,div,div2,if1,if2,ifPlus,inc,le,minus,plus
            ,plusIter} and constructors {0,c,d,divZeroError,false,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          a#() -> c_1()
          a#() -> c_2()
          div#(x,y) -> c_3(div2#(x,y,0()))
          div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i)),le#(y,0()),le#(y,x),plus#(i,0()),inc#(i))
          if1#(false(),b,x,y,i,j) -> c_5(if2#(b,x,y,i,j))
          if1#(true(),b,x,y,i,j) -> c_6()
          if2#(false(),x,y,i,j) -> c_7()
          if2#(true(),x,y,i,j) -> c_8(div2#(minus(x,y),y,j),minus#(x,y))
          ifPlus#(false(),x,y,z) -> c_9(plusIter#(x,s(y),s(z)))
          ifPlus#(true(),x,y,z) -> c_10()
          inc#(0()) -> c_11()
          inc#(s(i)) -> c_12(inc#(i))
          le#(0(),y) -> c_13()
          le#(s(x),0()) -> c_14()
          le#(s(x),s(y)) -> c_15(le#(x,y))
          minus#(x,0()) -> c_16()
          minus#(0(),y) -> c_17()
          minus#(s(x),s(y)) -> c_18(minus#(x,y))
          plus#(x,y) -> c_19(plusIter#(x,y,0()))
          plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            a#() -> c_1()
            a#() -> c_2()
            div#(x,y) -> c_3(div2#(x,y,0()))
            div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i)),le#(y,0()),le#(y,x),plus#(i,0()),inc#(i))
            if1#(false(),b,x,y,i,j) -> c_5(if2#(b,x,y,i,j))
            if1#(true(),b,x,y,i,j) -> c_6()
            if2#(false(),x,y,i,j) -> c_7()
            if2#(true(),x,y,i,j) -> c_8(div2#(minus(x,y),y,j),minus#(x,y))
            ifPlus#(false(),x,y,z) -> c_9(plusIter#(x,s(y),s(z)))
            ifPlus#(true(),x,y,z) -> c_10()
            inc#(0()) -> c_11()
            inc#(s(i)) -> c_12(inc#(i))
            le#(0(),y) -> c_13()
            le#(s(x),0()) -> c_14()
            le#(s(x),s(y)) -> c_15(le#(x,y))
            minus#(x,0()) -> c_16()
            minus#(0(),y) -> c_17()
            minus#(s(x),s(y)) -> c_18(minus#(x,y))
            plus#(x,y) -> c_19(plusIter#(x,y,0()))
            plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z))
        - Weak TRS:
            a() -> c()
            a() -> d()
            div(x,y) -> div2(x,y,0())
            div2(x,y,i) -> if1(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i))
            if1(false(),b,x,y,i,j) -> if2(b,x,y,i,j)
            if1(true(),b,x,y,i,j) -> divZeroError()
            if2(false(),x,y,i,j) -> i
            if2(true(),x,y,i,j) -> div2(minus(x,y),y,j)
            ifPlus(false(),x,y,z) -> plusIter(x,s(y),s(z))
            ifPlus(true(),x,y,z) -> y
            inc(0()) -> 0()
            inc(s(i)) -> s(inc(i))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(0(),y) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            plus(x,y) -> plusIter(x,y,0())
            plusIter(x,y,z) -> ifPlus(le(x,z),x,y,z)
        - Signature:
            {a/0,div/2,div2/3,if1/6,if2/5,ifPlus/4,inc/1,le/2,minus/2,plus/2,plusIter/3,a#/0,div#/2,div2#/3,if1#/6
            ,if2#/5,ifPlus#/4,inc#/1,le#/2,minus#/2,plus#/2,plusIter#/3} / {0/0,c/0,d/0,divZeroError/0,false/0,s/1
            ,true/0,c_1/0,c_2/0,c_3/1,c_4/5,c_5/1,c_6/0,c_7/0,c_8/2,c_9/1,c_10/0,c_11/0,c_12/1,c_13/0,c_14/0,c_15/1
            ,c_16/0,c_17/0,c_18/1,c_19/1,c_20/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,div#,div2#,if1#,if2#,ifPlus#,inc#,le#,minus#,plus#
            ,plusIter#} and constructors {0,c,d,divZeroError,false,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          ifPlus(false(),x,y,z) -> plusIter(x,s(y),s(z))
          ifPlus(true(),x,y,z) -> y
          inc(0()) -> 0()
          inc(s(i)) -> s(inc(i))
          le(0(),y) -> true()
          le(s(x),0()) -> false()
          le(s(x),s(y)) -> le(x,y)
          minus(x,0()) -> x
          minus(0(),y) -> 0()
          minus(s(x),s(y)) -> minus(x,y)
          plus(x,y) -> plusIter(x,y,0())
          plusIter(x,y,z) -> ifPlus(le(x,z),x,y,z)
          a#() -> c_1()
          a#() -> c_2()
          div#(x,y) -> c_3(div2#(x,y,0()))
          div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i)),le#(y,0()),le#(y,x),plus#(i,0()),inc#(i))
          if1#(false(),b,x,y,i,j) -> c_5(if2#(b,x,y,i,j))
          if1#(true(),b,x,y,i,j) -> c_6()
          if2#(false(),x,y,i,j) -> c_7()
          if2#(true(),x,y,i,j) -> c_8(div2#(minus(x,y),y,j),minus#(x,y))
          ifPlus#(false(),x,y,z) -> c_9(plusIter#(x,s(y),s(z)))
          ifPlus#(true(),x,y,z) -> c_10()
          inc#(0()) -> c_11()
          inc#(s(i)) -> c_12(inc#(i))
          le#(0(),y) -> c_13()
          le#(s(x),0()) -> c_14()
          le#(s(x),s(y)) -> c_15(le#(x,y))
          minus#(x,0()) -> c_16()
          minus#(0(),y) -> c_17()
          minus#(s(x),s(y)) -> c_18(minus#(x,y))
          plus#(x,y) -> c_19(plusIter#(x,y,0()))
          plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            a#() -> c_1()
            a#() -> c_2()
            div#(x,y) -> c_3(div2#(x,y,0()))
            div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i)),le#(y,0()),le#(y,x),plus#(i,0()),inc#(i))
            if1#(false(),b,x,y,i,j) -> c_5(if2#(b,x,y,i,j))
            if1#(true(),b,x,y,i,j) -> c_6()
            if2#(false(),x,y,i,j) -> c_7()
            if2#(true(),x,y,i,j) -> c_8(div2#(minus(x,y),y,j),minus#(x,y))
            ifPlus#(false(),x,y,z) -> c_9(plusIter#(x,s(y),s(z)))
            ifPlus#(true(),x,y,z) -> c_10()
            inc#(0()) -> c_11()
            inc#(s(i)) -> c_12(inc#(i))
            le#(0(),y) -> c_13()
            le#(s(x),0()) -> c_14()
            le#(s(x),s(y)) -> c_15(le#(x,y))
            minus#(x,0()) -> c_16()
            minus#(0(),y) -> c_17()
            minus#(s(x),s(y)) -> c_18(minus#(x,y))
            plus#(x,y) -> c_19(plusIter#(x,y,0()))
            plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z))
        - Weak TRS:
            ifPlus(false(),x,y,z) -> plusIter(x,s(y),s(z))
            ifPlus(true(),x,y,z) -> y
            inc(0()) -> 0()
            inc(s(i)) -> s(inc(i))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(0(),y) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            plus(x,y) -> plusIter(x,y,0())
            plusIter(x,y,z) -> ifPlus(le(x,z),x,y,z)
        - Signature:
            {a/0,div/2,div2/3,if1/6,if2/5,ifPlus/4,inc/1,le/2,minus/2,plus/2,plusIter/3,a#/0,div#/2,div2#/3,if1#/6
            ,if2#/5,ifPlus#/4,inc#/1,le#/2,minus#/2,plus#/2,plusIter#/3} / {0/0,c/0,d/0,divZeroError/0,false/0,s/1
            ,true/0,c_1/0,c_2/0,c_3/1,c_4/5,c_5/1,c_6/0,c_7/0,c_8/2,c_9/1,c_10/0,c_11/0,c_12/1,c_13/0,c_14/0,c_15/1
            ,c_16/0,c_17/0,c_18/1,c_19/1,c_20/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,div#,div2#,if1#,if2#,ifPlus#,inc#,le#,minus#,plus#
            ,plusIter#} and constructors {0,c,d,divZeroError,false,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,6,7,10,11,13,14,16,17}
        by application of
          Pre({1,2,6,7,10,11,13,14,16,17}) = {4,5,8,12,15,18,20}.
        Here rules are labelled as follows:
          1: a#() -> c_1()
          2: a#() -> c_2()
          3: div#(x,y) -> c_3(div2#(x,y,0()))
          4: div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i))
                                ,le#(y,0())
                                ,le#(y,x)
                                ,plus#(i,0())
                                ,inc#(i))
          5: if1#(false(),b,x,y,i,j) -> c_5(if2#(b,x,y,i,j))
          6: if1#(true(),b,x,y,i,j) -> c_6()
          7: if2#(false(),x,y,i,j) -> c_7()
          8: if2#(true(),x,y,i,j) -> c_8(div2#(minus(x,y),y,j),minus#(x,y))
          9: ifPlus#(false(),x,y,z) -> c_9(plusIter#(x,s(y),s(z)))
          10: ifPlus#(true(),x,y,z) -> c_10()
          11: inc#(0()) -> c_11()
          12: inc#(s(i)) -> c_12(inc#(i))
          13: le#(0(),y) -> c_13()
          14: le#(s(x),0()) -> c_14()
          15: le#(s(x),s(y)) -> c_15(le#(x,y))
          16: minus#(x,0()) -> c_16()
          17: minus#(0(),y) -> c_17()
          18: minus#(s(x),s(y)) -> c_18(minus#(x,y))
          19: plus#(x,y) -> c_19(plusIter#(x,y,0()))
          20: plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            div#(x,y) -> c_3(div2#(x,y,0()))
            div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i)),le#(y,0()),le#(y,x),plus#(i,0()),inc#(i))
            if1#(false(),b,x,y,i,j) -> c_5(if2#(b,x,y,i,j))
            if2#(true(),x,y,i,j) -> c_8(div2#(minus(x,y),y,j),minus#(x,y))
            ifPlus#(false(),x,y,z) -> c_9(plusIter#(x,s(y),s(z)))
            inc#(s(i)) -> c_12(inc#(i))
            le#(s(x),s(y)) -> c_15(le#(x,y))
            minus#(s(x),s(y)) -> c_18(minus#(x,y))
            plus#(x,y) -> c_19(plusIter#(x,y,0()))
            plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z))
        - Weak DPs:
            a#() -> c_1()
            a#() -> c_2()
            if1#(true(),b,x,y,i,j) -> c_6()
            if2#(false(),x,y,i,j) -> c_7()
            ifPlus#(true(),x,y,z) -> c_10()
            inc#(0()) -> c_11()
            le#(0(),y) -> c_13()
            le#(s(x),0()) -> c_14()
            minus#(x,0()) -> c_16()
            minus#(0(),y) -> c_17()
        - Weak TRS:
            ifPlus(false(),x,y,z) -> plusIter(x,s(y),s(z))
            ifPlus(true(),x,y,z) -> y
            inc(0()) -> 0()
            inc(s(i)) -> s(inc(i))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(0(),y) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            plus(x,y) -> plusIter(x,y,0())
            plusIter(x,y,z) -> ifPlus(le(x,z),x,y,z)
        - Signature:
            {a/0,div/2,div2/3,if1/6,if2/5,ifPlus/4,inc/1,le/2,minus/2,plus/2,plusIter/3,a#/0,div#/2,div2#/3,if1#/6
            ,if2#/5,ifPlus#/4,inc#/1,le#/2,minus#/2,plus#/2,plusIter#/3} / {0/0,c/0,d/0,divZeroError/0,false/0,s/1
            ,true/0,c_1/0,c_2/0,c_3/1,c_4/5,c_5/1,c_6/0,c_7/0,c_8/2,c_9/1,c_10/0,c_11/0,c_12/1,c_13/0,c_14/0,c_15/1
            ,c_16/0,c_17/0,c_18/1,c_19/1,c_20/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,div#,div2#,if1#,if2#,ifPlus#,inc#,le#,minus#,plus#
            ,plusIter#} and constructors {0,c,d,divZeroError,false,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:div#(x,y) -> c_3(div2#(x,y,0()))
             -->_1 div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i))
                                      ,le#(y,0())
                                      ,le#(y,x)
                                      ,plus#(i,0())
                                      ,inc#(i)):2
          
          2:S:div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i))
                                 ,le#(y,0())
                                 ,le#(y,x)
                                 ,plus#(i,0())
                                 ,inc#(i))
             -->_4 plus#(x,y) -> c_19(plusIter#(x,y,0())):9
             -->_3 le#(s(x),s(y)) -> c_15(le#(x,y)):7
             -->_5 inc#(s(i)) -> c_12(inc#(i)):6
             -->_1 if1#(false(),b,x,y,i,j) -> c_5(if2#(b,x,y,i,j)):3
             -->_3 le#(s(x),0()) -> c_14():18
             -->_2 le#(s(x),0()) -> c_14():18
             -->_3 le#(0(),y) -> c_13():17
             -->_2 le#(0(),y) -> c_13():17
             -->_5 inc#(0()) -> c_11():16
             -->_1 if1#(true(),b,x,y,i,j) -> c_6():13
          
          3:S:if1#(false(),b,x,y,i,j) -> c_5(if2#(b,x,y,i,j))
             -->_1 if2#(true(),x,y,i,j) -> c_8(div2#(minus(x,y),y,j),minus#(x,y)):4
             -->_1 if2#(false(),x,y,i,j) -> c_7():14
          
          4:S:if2#(true(),x,y,i,j) -> c_8(div2#(minus(x,y),y,j),minus#(x,y))
             -->_2 minus#(s(x),s(y)) -> c_18(minus#(x,y)):8
             -->_2 minus#(0(),y) -> c_17():20
             -->_2 minus#(x,0()) -> c_16():19
             -->_1 div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i))
                                      ,le#(y,0())
                                      ,le#(y,x)
                                      ,plus#(i,0())
                                      ,inc#(i)):2
          
          5:S:ifPlus#(false(),x,y,z) -> c_9(plusIter#(x,s(y),s(z)))
             -->_1 plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z)):10
          
          6:S:inc#(s(i)) -> c_12(inc#(i))
             -->_1 inc#(0()) -> c_11():16
             -->_1 inc#(s(i)) -> c_12(inc#(i)):6
          
          7:S:le#(s(x),s(y)) -> c_15(le#(x,y))
             -->_1 le#(s(x),0()) -> c_14():18
             -->_1 le#(0(),y) -> c_13():17
             -->_1 le#(s(x),s(y)) -> c_15(le#(x,y)):7
          
          8:S:minus#(s(x),s(y)) -> c_18(minus#(x,y))
             -->_1 minus#(0(),y) -> c_17():20
             -->_1 minus#(x,0()) -> c_16():19
             -->_1 minus#(s(x),s(y)) -> c_18(minus#(x,y)):8
          
          9:S:plus#(x,y) -> c_19(plusIter#(x,y,0()))
             -->_1 plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z)):10
          
          10:S:plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z))
             -->_2 le#(s(x),0()) -> c_14():18
             -->_2 le#(0(),y) -> c_13():17
             -->_1 ifPlus#(true(),x,y,z) -> c_10():15
             -->_2 le#(s(x),s(y)) -> c_15(le#(x,y)):7
             -->_1 ifPlus#(false(),x,y,z) -> c_9(plusIter#(x,s(y),s(z))):5
          
          11:W:a#() -> c_1()
             
          
          12:W:a#() -> c_2()
             
          
          13:W:if1#(true(),b,x,y,i,j) -> c_6()
             
          
          14:W:if2#(false(),x,y,i,j) -> c_7()
             
          
          15:W:ifPlus#(true(),x,y,z) -> c_10()
             
          
          16:W:inc#(0()) -> c_11()
             
          
          17:W:le#(0(),y) -> c_13()
             
          
          18:W:le#(s(x),0()) -> c_14()
             
          
          19:W:minus#(x,0()) -> c_16()
             
          
          20:W:minus#(0(),y) -> c_17()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          12: a#() -> c_2()
          11: a#() -> c_1()
          13: if1#(true(),b,x,y,i,j) -> c_6()
          14: if2#(false(),x,y,i,j) -> c_7()
          19: minus#(x,0()) -> c_16()
          20: minus#(0(),y) -> c_17()
          16: inc#(0()) -> c_11()
          15: ifPlus#(true(),x,y,z) -> c_10()
          17: le#(0(),y) -> c_13()
          18: le#(s(x),0()) -> c_14()
* Step 5: SimplifyRHS MAYBE
    + Considered Problem:
        - Strict DPs:
            div#(x,y) -> c_3(div2#(x,y,0()))
            div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i)),le#(y,0()),le#(y,x),plus#(i,0()),inc#(i))
            if1#(false(),b,x,y,i,j) -> c_5(if2#(b,x,y,i,j))
            if2#(true(),x,y,i,j) -> c_8(div2#(minus(x,y),y,j),minus#(x,y))
            ifPlus#(false(),x,y,z) -> c_9(plusIter#(x,s(y),s(z)))
            inc#(s(i)) -> c_12(inc#(i))
            le#(s(x),s(y)) -> c_15(le#(x,y))
            minus#(s(x),s(y)) -> c_18(minus#(x,y))
            plus#(x,y) -> c_19(plusIter#(x,y,0()))
            plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z))
        - Weak TRS:
            ifPlus(false(),x,y,z) -> plusIter(x,s(y),s(z))
            ifPlus(true(),x,y,z) -> y
            inc(0()) -> 0()
            inc(s(i)) -> s(inc(i))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(0(),y) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            plus(x,y) -> plusIter(x,y,0())
            plusIter(x,y,z) -> ifPlus(le(x,z),x,y,z)
        - Signature:
            {a/0,div/2,div2/3,if1/6,if2/5,ifPlus/4,inc/1,le/2,minus/2,plus/2,plusIter/3,a#/0,div#/2,div2#/3,if1#/6
            ,if2#/5,ifPlus#/4,inc#/1,le#/2,minus#/2,plus#/2,plusIter#/3} / {0/0,c/0,d/0,divZeroError/0,false/0,s/1
            ,true/0,c_1/0,c_2/0,c_3/1,c_4/5,c_5/1,c_6/0,c_7/0,c_8/2,c_9/1,c_10/0,c_11/0,c_12/1,c_13/0,c_14/0,c_15/1
            ,c_16/0,c_17/0,c_18/1,c_19/1,c_20/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,div#,div2#,if1#,if2#,ifPlus#,inc#,le#,minus#,plus#
            ,plusIter#} and constructors {0,c,d,divZeroError,false,s,true}
    + Applied Processor:
        SimplifyRHS
    + Details:
        Consider the dependency graph
          1:S:div#(x,y) -> c_3(div2#(x,y,0()))
             -->_1 div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i))
                                      ,le#(y,0())
                                      ,le#(y,x)
                                      ,plus#(i,0())
                                      ,inc#(i)):2
          
          2:S:div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i))
                                 ,le#(y,0())
                                 ,le#(y,x)
                                 ,plus#(i,0())
                                 ,inc#(i))
             -->_4 plus#(x,y) -> c_19(plusIter#(x,y,0())):9
             -->_3 le#(s(x),s(y)) -> c_15(le#(x,y)):7
             -->_5 inc#(s(i)) -> c_12(inc#(i)):6
             -->_1 if1#(false(),b,x,y,i,j) -> c_5(if2#(b,x,y,i,j)):3
          
          3:S:if1#(false(),b,x,y,i,j) -> c_5(if2#(b,x,y,i,j))
             -->_1 if2#(true(),x,y,i,j) -> c_8(div2#(minus(x,y),y,j),minus#(x,y)):4
          
          4:S:if2#(true(),x,y,i,j) -> c_8(div2#(minus(x,y),y,j),minus#(x,y))
             -->_2 minus#(s(x),s(y)) -> c_18(minus#(x,y)):8
             -->_1 div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i))
                                      ,le#(y,0())
                                      ,le#(y,x)
                                      ,plus#(i,0())
                                      ,inc#(i)):2
          
          5:S:ifPlus#(false(),x,y,z) -> c_9(plusIter#(x,s(y),s(z)))
             -->_1 plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z)):10
          
          6:S:inc#(s(i)) -> c_12(inc#(i))
             -->_1 inc#(s(i)) -> c_12(inc#(i)):6
          
          7:S:le#(s(x),s(y)) -> c_15(le#(x,y))
             -->_1 le#(s(x),s(y)) -> c_15(le#(x,y)):7
          
          8:S:minus#(s(x),s(y)) -> c_18(minus#(x,y))
             -->_1 minus#(s(x),s(y)) -> c_18(minus#(x,y)):8
          
          9:S:plus#(x,y) -> c_19(plusIter#(x,y,0()))
             -->_1 plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z)):10
          
          10:S:plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z))
             -->_2 le#(s(x),s(y)) -> c_15(le#(x,y)):7
             -->_1 ifPlus#(false(),x,y,z) -> c_9(plusIter#(x,s(y),s(z))):5
          
        Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified:
          div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i)),le#(y,x),plus#(i,0()),inc#(i))
* Step 6: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            div#(x,y) -> c_3(div2#(x,y,0()))
            div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i)),le#(y,x),plus#(i,0()),inc#(i))
            if1#(false(),b,x,y,i,j) -> c_5(if2#(b,x,y,i,j))
            if2#(true(),x,y,i,j) -> c_8(div2#(minus(x,y),y,j),minus#(x,y))
            ifPlus#(false(),x,y,z) -> c_9(plusIter#(x,s(y),s(z)))
            inc#(s(i)) -> c_12(inc#(i))
            le#(s(x),s(y)) -> c_15(le#(x,y))
            minus#(s(x),s(y)) -> c_18(minus#(x,y))
            plus#(x,y) -> c_19(plusIter#(x,y,0()))
            plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z))
        - Weak TRS:
            ifPlus(false(),x,y,z) -> plusIter(x,s(y),s(z))
            ifPlus(true(),x,y,z) -> y
            inc(0()) -> 0()
            inc(s(i)) -> s(inc(i))
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            minus(x,0()) -> x
            minus(0(),y) -> 0()
            minus(s(x),s(y)) -> minus(x,y)
            plus(x,y) -> plusIter(x,y,0())
            plusIter(x,y,z) -> ifPlus(le(x,z),x,y,z)
        - Signature:
            {a/0,div/2,div2/3,if1/6,if2/5,ifPlus/4,inc/1,le/2,minus/2,plus/2,plusIter/3,a#/0,div#/2,div2#/3,if1#/6
            ,if2#/5,ifPlus#/4,inc#/1,le#/2,minus#/2,plus#/2,plusIter#/3} / {0/0,c/0,d/0,divZeroError/0,false/0,s/1
            ,true/0,c_1/0,c_2/0,c_3/1,c_4/4,c_5/1,c_6/0,c_7/0,c_8/2,c_9/1,c_10/0,c_11/0,c_12/1,c_13/0,c_14/0,c_15/1
            ,c_16/0,c_17/0,c_18/1,c_19/1,c_20/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,div#,div2#,if1#,if2#,ifPlus#,inc#,le#,minus#,plus#
            ,plusIter#} and constructors {0,c,d,divZeroError,false,s,true}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:div#(x,y) -> c_3(div2#(x,y,0()))
           -->_1 div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i)),le#(y,x),plus#(i,0()),inc#(i)):2
        
        2:S:div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i)),le#(y,x),plus#(i,0()),inc#(i))
           -->_3 plus#(x,y) -> c_19(plusIter#(x,y,0())):9
           -->_2 le#(s(x),s(y)) -> c_15(le#(x,y)):7
           -->_4 inc#(s(i)) -> c_12(inc#(i)):6
           -->_1 if1#(false(),b,x,y,i,j) -> c_5(if2#(b,x,y,i,j)):3
        
        3:S:if1#(false(),b,x,y,i,j) -> c_5(if2#(b,x,y,i,j))
           -->_1 if2#(true(),x,y,i,j) -> c_8(div2#(minus(x,y),y,j),minus#(x,y)):4
        
        4:S:if2#(true(),x,y,i,j) -> c_8(div2#(minus(x,y),y,j),minus#(x,y))
           -->_2 minus#(s(x),s(y)) -> c_18(minus#(x,y)):8
           -->_1 div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i)),le#(y,x),plus#(i,0()),inc#(i)):2
        
        5:S:ifPlus#(false(),x,y,z) -> c_9(plusIter#(x,s(y),s(z)))
           -->_1 plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z)):10
        
        6:S:inc#(s(i)) -> c_12(inc#(i))
           -->_1 inc#(s(i)) -> c_12(inc#(i)):6
        
        7:S:le#(s(x),s(y)) -> c_15(le#(x,y))
           -->_1 le#(s(x),s(y)) -> c_15(le#(x,y)):7
        
        8:S:minus#(s(x),s(y)) -> c_18(minus#(x,y))
           -->_1 minus#(s(x),s(y)) -> c_18(minus#(x,y)):8
        
        9:S:plus#(x,y) -> c_19(plusIter#(x,y,0()))
           -->_1 plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z)):10
        
        10:S:plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z))
           -->_2 le#(s(x),s(y)) -> c_15(le#(x,y)):7
           -->_1 ifPlus#(false(),x,y,z) -> c_9(plusIter#(x,s(y),s(z))):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,div#(x,y) -> c_3(div2#(x,y,0())))]
* Step 7: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          div2#(x,y,i) -> c_4(if1#(le(y,0()),le(y,x),x,y,plus(i,0()),inc(i)),le#(y,x),plus#(i,0()),inc#(i))
          if1#(false(),b,x,y,i,j) -> c_5(if2#(b,x,y,i,j))
          if2#(true(),x,y,i,j) -> c_8(div2#(minus(x,y),y,j),minus#(x,y))
          ifPlus#(false(),x,y,z) -> c_9(plusIter#(x,s(y),s(z)))
          inc#(s(i)) -> c_12(inc#(i))
          le#(s(x),s(y)) -> c_15(le#(x,y))
          minus#(s(x),s(y)) -> c_18(minus#(x,y))
          plus#(x,y) -> c_19(plusIter#(x,y,0()))
          plusIter#(x,y,z) -> c_20(ifPlus#(le(x,z),x,y,z),le#(x,z))
      - Weak TRS:
          ifPlus(false(),x,y,z) -> plusIter(x,s(y),s(z))
          ifPlus(true(),x,y,z) -> y
          inc(0()) -> 0()
          inc(s(i)) -> s(inc(i))
          le(0(),y) -> true()
          le(s(x),0()) -> false()
          le(s(x),s(y)) -> le(x,y)
          minus(x,0()) -> x
          minus(0(),y) -> 0()
          minus(s(x),s(y)) -> minus(x,y)
          plus(x,y) -> plusIter(x,y,0())
          plusIter(x,y,z) -> ifPlus(le(x,z),x,y,z)
      - Signature:
          {a/0,div/2,div2/3,if1/6,if2/5,ifPlus/4,inc/1,le/2,minus/2,plus/2,plusIter/3,a#/0,div#/2,div2#/3,if1#/6
          ,if2#/5,ifPlus#/4,inc#/1,le#/2,minus#/2,plus#/2,plusIter#/3} / {0/0,c/0,d/0,divZeroError/0,false/0,s/1
          ,true/0,c_1/0,c_2/0,c_3/1,c_4/4,c_5/1,c_6/0,c_7/0,c_8/2,c_9/1,c_10/0,c_11/0,c_12/1,c_13/0,c_14/0,c_15/1
          ,c_16/0,c_17/0,c_18/1,c_19/1,c_20/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {a#,div#,div2#,if1#,if2#,ifPlus#,inc#,le#,minus#,plus#
          ,plusIter#} and constructors {0,c,d,divZeroError,false,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE