WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            DIV(z0,z1,z2) -> c1(IF(lt(z0,z1),z0,z1,inc(z2)),LT(z0,z1))
            DIV(z0,z1,z2) -> c2(IF(lt(z0,z1),z0,z1,inc(z2)),INC(z2))
            DIVISION(z0,z1) -> c(DIV(z0,z1,0()))
            IF(false(),z0,s(z1),z2) -> c4(DIV(minus(z0,s(z1)),s(z1),z2),MINUS(z0,s(z1)))
            IF(true(),z0,z1,z2) -> c3()
            INC(0()) -> c10()
            INC(s(z0)) -> c11(INC(z0))
            LT(z0,0()) -> c7()
            LT(0(),s(z0)) -> c8()
            LT(s(z0),s(z1)) -> c9(LT(z0,z1))
            MINUS(z0,0()) -> c5()
            MINUS(s(z0),s(z1)) -> c6(MINUS(z0,z1))
        - Weak TRS:
            div(z0,z1,z2) -> if(lt(z0,z1),z0,z1,inc(z2))
            division(z0,z1) -> div(z0,z1,0())
            if(false(),z0,s(z1),z2) -> div(minus(z0,s(z1)),s(z1),z2)
            if(true(),z0,z1,z2) -> z2
            inc(0()) -> s(0())
            inc(s(z0)) -> s(inc(z0))
            lt(z0,0()) -> false()
            lt(0(),s(z0)) -> true()
            lt(s(z0),s(z1)) -> lt(z0,z1)
            minus(z0,0()) -> z0
            minus(s(z0),s(z1)) -> minus(z0,z1)
        - Signature:
            {DIV/3,DIVISION/2,IF/4,INC/1,LT/2,MINUS/2,div/3,division/2,if/4,inc/1,lt/2,minus/2} / {0/0,c/1,c1/2,c10/0
            ,c11/1,c2/2,c3/0,c4/2,c5/0,c6/1,c7/0,c8/0,c9/1,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {DIV,DIVISION,IF,INC,LT,MINUS,div,division,if,inc,lt
            ,minus} and constructors {0,c,c1,c10,c11,c2,c3,c4,c5,c6,c7,c8,c9,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            DIV(z0,z1,z2) -> c1(IF(lt(z0,z1),z0,z1,inc(z2)),LT(z0,z1))
            DIV(z0,z1,z2) -> c2(IF(lt(z0,z1),z0,z1,inc(z2)),INC(z2))
            DIVISION(z0,z1) -> c(DIV(z0,z1,0()))
            IF(false(),z0,s(z1),z2) -> c4(DIV(minus(z0,s(z1)),s(z1),z2),MINUS(z0,s(z1)))
            IF(true(),z0,z1,z2) -> c3()
            INC(0()) -> c10()
            INC(s(z0)) -> c11(INC(z0))
            LT(z0,0()) -> c7()
            LT(0(),s(z0)) -> c8()
            LT(s(z0),s(z1)) -> c9(LT(z0,z1))
            MINUS(z0,0()) -> c5()
            MINUS(s(z0),s(z1)) -> c6(MINUS(z0,z1))
        - Weak TRS:
            div(z0,z1,z2) -> if(lt(z0,z1),z0,z1,inc(z2))
            division(z0,z1) -> div(z0,z1,0())
            if(false(),z0,s(z1),z2) -> div(minus(z0,s(z1)),s(z1),z2)
            if(true(),z0,z1,z2) -> z2
            inc(0()) -> s(0())
            inc(s(z0)) -> s(inc(z0))
            lt(z0,0()) -> false()
            lt(0(),s(z0)) -> true()
            lt(s(z0),s(z1)) -> lt(z0,z1)
            minus(z0,0()) -> z0
            minus(s(z0),s(z1)) -> minus(z0,z1)
        - Signature:
            {DIV/3,DIVISION/2,IF/4,INC/1,LT/2,MINUS/2,div/3,division/2,if/4,inc/1,lt/2,minus/2} / {0/0,c/1,c1/2,c10/0
            ,c11/1,c2/2,c3/0,c4/2,c5/0,c6/1,c7/0,c8/0,c9/1,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {DIV,DIVISION,IF,INC,LT,MINUS,div,division,if,inc,lt
            ,minus} and constructors {0,c,c1,c10,c11,c2,c3,c4,c5,c6,c7,c8,c9,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            DIV(z0,z1,z2) -> c1(IF(lt(z0,z1),z0,z1,inc(z2)),LT(z0,z1))
            DIV(z0,z1,z2) -> c2(IF(lt(z0,z1),z0,z1,inc(z2)),INC(z2))
            DIVISION(z0,z1) -> c(DIV(z0,z1,0()))
            IF(false(),z0,s(z1),z2) -> c4(DIV(minus(z0,s(z1)),s(z1),z2),MINUS(z0,s(z1)))
            IF(true(),z0,z1,z2) -> c3()
            INC(0()) -> c10()
            INC(s(z0)) -> c11(INC(z0))
            LT(z0,0()) -> c7()
            LT(0(),s(z0)) -> c8()
            LT(s(z0),s(z1)) -> c9(LT(z0,z1))
            MINUS(z0,0()) -> c5()
            MINUS(s(z0),s(z1)) -> c6(MINUS(z0,z1))
        - Weak TRS:
            div(z0,z1,z2) -> if(lt(z0,z1),z0,z1,inc(z2))
            division(z0,z1) -> div(z0,z1,0())
            if(false(),z0,s(z1),z2) -> div(minus(z0,s(z1)),s(z1),z2)
            if(true(),z0,z1,z2) -> z2
            inc(0()) -> s(0())
            inc(s(z0)) -> s(inc(z0))
            lt(z0,0()) -> false()
            lt(0(),s(z0)) -> true()
            lt(s(z0),s(z1)) -> lt(z0,z1)
            minus(z0,0()) -> z0
            minus(s(z0),s(z1)) -> minus(z0,z1)
        - Signature:
            {DIV/3,DIVISION/2,IF/4,INC/1,LT/2,MINUS/2,div/3,division/2,if/4,inc/1,lt/2,minus/2} / {0/0,c/1,c1/2,c10/0
            ,c11/1,c2/2,c3/0,c4/2,c5/0,c6/1,c7/0,c8/0,c9/1,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {DIV,DIVISION,IF,INC,LT,MINUS,div,division,if,inc,lt
            ,minus} and constructors {0,c,c1,c10,c11,c2,c3,c4,c5,c6,c7,c8,c9,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          INC(x){x -> s(x)} =
            INC(s(x)) ->^+ c11(INC(x))
              = C[INC(x) = INC(x){}]

WORST_CASE(Omega(n^1),?)