WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            DIV(z0,z1) -> c8(QUOT(z0,z1,0()))
            IF(false(),z0,s(z1),z2) -> c12(QUOT(minus(z0,s(z1)),s(z1),z2),MINUS(z0,s(z1)))
            IF(true(),z0,z1,z2) -> c11(P(z2))
            MINUS(z0,0()) -> c1()
            MINUS(0(),z0) -> c()
            MINUS(s(z0),s(z1)) -> c2(MINUS(z0,z1))
            P(s(z0)) -> c7()
            PLUS(0(),z0) -> c3()
            PLUS(s(z0),z1) -> c4(PLUS(z0,s(z1)))
            QUOT(z0,z1,z2) -> c10(IF(zero(z0),z0,z1,plus(z2,s(0()))),PLUS(z2,s(0())))
            QUOT(z0,z1,z2) -> c9(IF(zero(z0),z0,z1,plus(z2,s(0()))),ZERO(z0))
            ZERO(0()) -> c6()
            ZERO(s(z0)) -> c5()
        - Weak TRS:
            div(z0,z1) -> quot(z0,z1,0())
            if(false(),z0,s(z1),z2) -> quot(minus(z0,s(z1)),s(z1),z2)
            if(true(),z0,z1,z2) -> p(z2)
            minus(z0,0()) -> z0
            minus(0(),z0) -> 0()
            minus(s(z0),s(z1)) -> minus(z0,z1)
            p(s(z0)) -> z0
            plus(0(),z0) -> z0
            plus(s(z0),z1) -> plus(z0,s(z1))
            quot(z0,z1,z2) -> if(zero(z0),z0,z1,plus(z2,s(0())))
            zero(0()) -> true()
            zero(s(z0)) -> false()
        - Signature:
            {DIV/2,IF/4,MINUS/2,P/1,PLUS/2,QUOT/3,ZERO/1,div/2,if/4,minus/2,p/1,plus/2,quot/3,zero/1} / {0/0,c/0,c1/0
            ,c10/2,c11/1,c12/2,c2/1,c3/0,c4/1,c5/0,c6/0,c7/0,c8/1,c9/2,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {DIV,IF,MINUS,P,PLUS,QUOT,ZERO,div,if,minus,p,plus,quot
            ,zero} and constructors {0,c,c1,c10,c11,c12,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) -> c8(QUOT(z0,z1,0()))
            IF(false(),z0,s(z1),z2) -> c12(QUOT(minus(z0,s(z1)),s(z1),z2),MINUS(z0,s(z1)))
            IF(true(),z0,z1,z2) -> c11(P(z2))
            MINUS(z0,0()) -> c1()
            MINUS(0(),z0) -> c()
            MINUS(s(z0),s(z1)) -> c2(MINUS(z0,z1))
            P(s(z0)) -> c7()
            PLUS(0(),z0) -> c3()
            PLUS(s(z0),z1) -> c4(PLUS(z0,s(z1)))
            QUOT(z0,z1,z2) -> c10(IF(zero(z0),z0,z1,plus(z2,s(0()))),PLUS(z2,s(0())))
            QUOT(z0,z1,z2) -> c9(IF(zero(z0),z0,z1,plus(z2,s(0()))),ZERO(z0))
            ZERO(0()) -> c6()
            ZERO(s(z0)) -> c5()
        - Weak TRS:
            div(z0,z1) -> quot(z0,z1,0())
            if(false(),z0,s(z1),z2) -> quot(minus(z0,s(z1)),s(z1),z2)
            if(true(),z0,z1,z2) -> p(z2)
            minus(z0,0()) -> z0
            minus(0(),z0) -> 0()
            minus(s(z0),s(z1)) -> minus(z0,z1)
            p(s(z0)) -> z0
            plus(0(),z0) -> z0
            plus(s(z0),z1) -> plus(z0,s(z1))
            quot(z0,z1,z2) -> if(zero(z0),z0,z1,plus(z2,s(0())))
            zero(0()) -> true()
            zero(s(z0)) -> false()
        - Signature:
            {DIV/2,IF/4,MINUS/2,P/1,PLUS/2,QUOT/3,ZERO/1,div/2,if/4,minus/2,p/1,plus/2,quot/3,zero/1} / {0/0,c/0,c1/0
            ,c10/2,c11/1,c12/2,c2/1,c3/0,c4/1,c5/0,c6/0,c7/0,c8/1,c9/2,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {DIV,IF,MINUS,P,PLUS,QUOT,ZERO,div,if,minus,p,plus,quot
            ,zero} and constructors {0,c,c1,c10,c11,c12,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) -> c8(QUOT(z0,z1,0()))
            IF(false(),z0,s(z1),z2) -> c12(QUOT(minus(z0,s(z1)),s(z1),z2),MINUS(z0,s(z1)))
            IF(true(),z0,z1,z2) -> c11(P(z2))
            MINUS(z0,0()) -> c1()
            MINUS(0(),z0) -> c()
            MINUS(s(z0),s(z1)) -> c2(MINUS(z0,z1))
            P(s(z0)) -> c7()
            PLUS(0(),z0) -> c3()
            PLUS(s(z0),z1) -> c4(PLUS(z0,s(z1)))
            QUOT(z0,z1,z2) -> c10(IF(zero(z0),z0,z1,plus(z2,s(0()))),PLUS(z2,s(0())))
            QUOT(z0,z1,z2) -> c9(IF(zero(z0),z0,z1,plus(z2,s(0()))),ZERO(z0))
            ZERO(0()) -> c6()
            ZERO(s(z0)) -> c5()
        - Weak TRS:
            div(z0,z1) -> quot(z0,z1,0())
            if(false(),z0,s(z1),z2) -> quot(minus(z0,s(z1)),s(z1),z2)
            if(true(),z0,z1,z2) -> p(z2)
            minus(z0,0()) -> z0
            minus(0(),z0) -> 0()
            minus(s(z0),s(z1)) -> minus(z0,z1)
            p(s(z0)) -> z0
            plus(0(),z0) -> z0
            plus(s(z0),z1) -> plus(z0,s(z1))
            quot(z0,z1,z2) -> if(zero(z0),z0,z1,plus(z2,s(0())))
            zero(0()) -> true()
            zero(s(z0)) -> false()
        - Signature:
            {DIV/2,IF/4,MINUS/2,P/1,PLUS/2,QUOT/3,ZERO/1,div/2,if/4,minus/2,p/1,plus/2,quot/3,zero/1} / {0/0,c/0,c1/0
            ,c10/2,c11/1,c12/2,c2/1,c3/0,c4/1,c5/0,c6/0,c7/0,c8/1,c9/2,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {DIV,IF,MINUS,P,PLUS,QUOT,ZERO,div,if,minus,p,plus,quot
            ,zero} and constructors {0,c,c1,c10,c11,c12,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:
          MINUS(x,y){x -> s(x),y -> s(y)} =
            MINUS(s(x),s(y)) ->^+ c2(MINUS(x,y))
              = C[MINUS(x,y) = MINUS(x,y){}]

WORST_CASE(Omega(n^1),?)