WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            A() -> c21()
            A() -> c22()
            GE(z0,0()) -> c18()
            GE(0(),s(z0)) -> c19()
            GE(s(z0),s(z1)) -> c20(GE(z0,z1))
            HEAD(cons(z0,z1)) -> c15()
            HEAD(nil()) -> c14()
            IFPROD(false(),z0,z1) -> c4(PRODITER(tail(z0),times(z1,head(z0))),TAIL(z0))
            IFPROD(false(),z0,z1) -> c5(PRODITER(tail(z0),times(z1,head(z0))),TIMES(z1,head(z0)),HEAD(z0))
            IFPROD(true(),z0,z1) -> c3()
            IFTIMES(false(),z0,z1,z2,z3) -> c11(TIMESITER(z0,z1,plus(z1,z2),s(z3)),PLUS(z1,z2))
            IFTIMES(true(),z0,z1,z2,z3) -> c10()
            ISEMPTY(cons(z0,z1)) -> c13()
            ISEMPTY(nil()) -> c12()
            PLUS(0(),z0) -> c6()
            PLUS(s(z0),z1) -> c7(PLUS(z0,z1))
            PROD(z0) -> c1(PRODITER(z0,s(0())))
            PRODITER(z0,z1) -> c2(IFPROD(isempty(z0),z0,z1),ISEMPTY(z0))
            TAIL(cons(z0,z1)) -> c17()
            TAIL(nil()) -> c16()
            TIMES(z0,z1) -> c8(TIMESITER(z0,z1,0(),0()))
            TIMESITER(z0,z1,z2,z3) -> c9(IFTIMES(ge(z3,z0),z0,z1,z2,z3),GE(z3,z0))
        - Weak TRS:
            a() -> b()
            a() -> c()
            ge(z0,0()) -> true()
            ge(0(),s(z0)) -> false()
            ge(s(z0),s(z1)) -> ge(z0,z1)
            head(cons(z0,z1)) -> z0
            head(nil()) -> error()
            ifProd(false(),z0,z1) -> prodIter(tail(z0),times(z1,head(z0)))
            ifProd(true(),z0,z1) -> z1
            ifTimes(false(),z0,z1,z2,z3) -> timesIter(z0,z1,plus(z1,z2),s(z3))
            ifTimes(true(),z0,z1,z2,z3) -> z2
            isempty(cons(z0,z1)) -> false()
            isempty(nil()) -> true()
            plus(0(),z0) -> z0
            plus(s(z0),z1) -> s(plus(z0,z1))
            prod(z0) -> prodIter(z0,s(0()))
            prodIter(z0,z1) -> ifProd(isempty(z0),z0,z1)
            tail(cons(z0,z1)) -> z1
            tail(nil()) -> nil()
            times(z0,z1) -> timesIter(z0,z1,0(),0())
            timesIter(z0,z1,z2,z3) -> ifTimes(ge(z3,z0),z0,z1,z2,z3)
        - Signature:
            {A/0,GE/2,HEAD/1,IFPROD/3,IFTIMES/5,ISEMPTY/1,PLUS/2,PROD/1,PRODITER/2,TAIL/1,TIMES/2,TIMESITER/4,a/0,ge/2
            ,head/1,ifProd/3,ifTimes/5,isempty/1,plus/2,prod/1,prodIter/2,tail/1,times/2,timesIter/4} / {0/0,b/0,c/0
            ,c1/1,c10/0,c11/2,c12/0,c13/0,c14/0,c15/0,c16/0,c17/0,c18/0,c19/0,c2/2,c20/1,c21/0,c22/0,c3/0,c4/2,c5/3,c6/0
            ,c7/1,c8/1,c9/2,cons/2,error/0,false/0,nil/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {A,GE,HEAD,IFPROD,IFTIMES,ISEMPTY,PLUS,PROD,PRODITER,TAIL
            ,TIMES,TIMESITER,a,ge,head,ifProd,ifTimes,isempty,plus,prod,prodIter,tail,times
            ,timesIter} and constructors {0,b,c,c1,c10,c11,c12,c13,c14,c15,c16,c17,c18,c19,c2,c20,c21,c22,c3,c4,c5,c6,c7
            ,c8,c9,cons,error,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            A() -> c21()
            A() -> c22()
            GE(z0,0()) -> c18()
            GE(0(),s(z0)) -> c19()
            GE(s(z0),s(z1)) -> c20(GE(z0,z1))
            HEAD(cons(z0,z1)) -> c15()
            HEAD(nil()) -> c14()
            IFPROD(false(),z0,z1) -> c4(PRODITER(tail(z0),times(z1,head(z0))),TAIL(z0))
            IFPROD(false(),z0,z1) -> c5(PRODITER(tail(z0),times(z1,head(z0))),TIMES(z1,head(z0)),HEAD(z0))
            IFPROD(true(),z0,z1) -> c3()
            IFTIMES(false(),z0,z1,z2,z3) -> c11(TIMESITER(z0,z1,plus(z1,z2),s(z3)),PLUS(z1,z2))
            IFTIMES(true(),z0,z1,z2,z3) -> c10()
            ISEMPTY(cons(z0,z1)) -> c13()
            ISEMPTY(nil()) -> c12()
            PLUS(0(),z0) -> c6()
            PLUS(s(z0),z1) -> c7(PLUS(z0,z1))
            PROD(z0) -> c1(PRODITER(z0,s(0())))
            PRODITER(z0,z1) -> c2(IFPROD(isempty(z0),z0,z1),ISEMPTY(z0))
            TAIL(cons(z0,z1)) -> c17()
            TAIL(nil()) -> c16()
            TIMES(z0,z1) -> c8(TIMESITER(z0,z1,0(),0()))
            TIMESITER(z0,z1,z2,z3) -> c9(IFTIMES(ge(z3,z0),z0,z1,z2,z3),GE(z3,z0))
        - Weak TRS:
            a() -> b()
            a() -> c()
            ge(z0,0()) -> true()
            ge(0(),s(z0)) -> false()
            ge(s(z0),s(z1)) -> ge(z0,z1)
            head(cons(z0,z1)) -> z0
            head(nil()) -> error()
            ifProd(false(),z0,z1) -> prodIter(tail(z0),times(z1,head(z0)))
            ifProd(true(),z0,z1) -> z1
            ifTimes(false(),z0,z1,z2,z3) -> timesIter(z0,z1,plus(z1,z2),s(z3))
            ifTimes(true(),z0,z1,z2,z3) -> z2
            isempty(cons(z0,z1)) -> false()
            isempty(nil()) -> true()
            plus(0(),z0) -> z0
            plus(s(z0),z1) -> s(plus(z0,z1))
            prod(z0) -> prodIter(z0,s(0()))
            prodIter(z0,z1) -> ifProd(isempty(z0),z0,z1)
            tail(cons(z0,z1)) -> z1
            tail(nil()) -> nil()
            times(z0,z1) -> timesIter(z0,z1,0(),0())
            timesIter(z0,z1,z2,z3) -> ifTimes(ge(z3,z0),z0,z1,z2,z3)
        - Signature:
            {A/0,GE/2,HEAD/1,IFPROD/3,IFTIMES/5,ISEMPTY/1,PLUS/2,PROD/1,PRODITER/2,TAIL/1,TIMES/2,TIMESITER/4,a/0,ge/2
            ,head/1,ifProd/3,ifTimes/5,isempty/1,plus/2,prod/1,prodIter/2,tail/1,times/2,timesIter/4} / {0/0,b/0,c/0
            ,c1/1,c10/0,c11/2,c12/0,c13/0,c14/0,c15/0,c16/0,c17/0,c18/0,c19/0,c2/2,c20/1,c21/0,c22/0,c3/0,c4/2,c5/3,c6/0
            ,c7/1,c8/1,c9/2,cons/2,error/0,false/0,nil/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {A,GE,HEAD,IFPROD,IFTIMES,ISEMPTY,PLUS,PROD,PRODITER,TAIL
            ,TIMES,TIMESITER,a,ge,head,ifProd,ifTimes,isempty,plus,prod,prodIter,tail,times
            ,timesIter} and constructors {0,b,c,c1,c10,c11,c12,c13,c14,c15,c16,c17,c18,c19,c2,c20,c21,c22,c3,c4,c5,c6,c7
            ,c8,c9,cons,error,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            A() -> c21()
            A() -> c22()
            GE(z0,0()) -> c18()
            GE(0(),s(z0)) -> c19()
            GE(s(z0),s(z1)) -> c20(GE(z0,z1))
            HEAD(cons(z0,z1)) -> c15()
            HEAD(nil()) -> c14()
            IFPROD(false(),z0,z1) -> c4(PRODITER(tail(z0),times(z1,head(z0))),TAIL(z0))
            IFPROD(false(),z0,z1) -> c5(PRODITER(tail(z0),times(z1,head(z0))),TIMES(z1,head(z0)),HEAD(z0))
            IFPROD(true(),z0,z1) -> c3()
            IFTIMES(false(),z0,z1,z2,z3) -> c11(TIMESITER(z0,z1,plus(z1,z2),s(z3)),PLUS(z1,z2))
            IFTIMES(true(),z0,z1,z2,z3) -> c10()
            ISEMPTY(cons(z0,z1)) -> c13()
            ISEMPTY(nil()) -> c12()
            PLUS(0(),z0) -> c6()
            PLUS(s(z0),z1) -> c7(PLUS(z0,z1))
            PROD(z0) -> c1(PRODITER(z0,s(0())))
            PRODITER(z0,z1) -> c2(IFPROD(isempty(z0),z0,z1),ISEMPTY(z0))
            TAIL(cons(z0,z1)) -> c17()
            TAIL(nil()) -> c16()
            TIMES(z0,z1) -> c8(TIMESITER(z0,z1,0(),0()))
            TIMESITER(z0,z1,z2,z3) -> c9(IFTIMES(ge(z3,z0),z0,z1,z2,z3),GE(z3,z0))
        - Weak TRS:
            a() -> b()
            a() -> c()
            ge(z0,0()) -> true()
            ge(0(),s(z0)) -> false()
            ge(s(z0),s(z1)) -> ge(z0,z1)
            head(cons(z0,z1)) -> z0
            head(nil()) -> error()
            ifProd(false(),z0,z1) -> prodIter(tail(z0),times(z1,head(z0)))
            ifProd(true(),z0,z1) -> z1
            ifTimes(false(),z0,z1,z2,z3) -> timesIter(z0,z1,plus(z1,z2),s(z3))
            ifTimes(true(),z0,z1,z2,z3) -> z2
            isempty(cons(z0,z1)) -> false()
            isempty(nil()) -> true()
            plus(0(),z0) -> z0
            plus(s(z0),z1) -> s(plus(z0,z1))
            prod(z0) -> prodIter(z0,s(0()))
            prodIter(z0,z1) -> ifProd(isempty(z0),z0,z1)
            tail(cons(z0,z1)) -> z1
            tail(nil()) -> nil()
            times(z0,z1) -> timesIter(z0,z1,0(),0())
            timesIter(z0,z1,z2,z3) -> ifTimes(ge(z3,z0),z0,z1,z2,z3)
        - Signature:
            {A/0,GE/2,HEAD/1,IFPROD/3,IFTIMES/5,ISEMPTY/1,PLUS/2,PROD/1,PRODITER/2,TAIL/1,TIMES/2,TIMESITER/4,a/0,ge/2
            ,head/1,ifProd/3,ifTimes/5,isempty/1,plus/2,prod/1,prodIter/2,tail/1,times/2,timesIter/4} / {0/0,b/0,c/0
            ,c1/1,c10/0,c11/2,c12/0,c13/0,c14/0,c15/0,c16/0,c17/0,c18/0,c19/0,c2/2,c20/1,c21/0,c22/0,c3/0,c4/2,c5/3,c6/0
            ,c7/1,c8/1,c9/2,cons/2,error/0,false/0,nil/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {A,GE,HEAD,IFPROD,IFTIMES,ISEMPTY,PLUS,PROD,PRODITER,TAIL
            ,TIMES,TIMESITER,a,ge,head,ifProd,ifTimes,isempty,plus,prod,prodIter,tail,times
            ,timesIter} and constructors {0,b,c,c1,c10,c11,c12,c13,c14,c15,c16,c17,c18,c19,c2,c20,c21,c22,c3,c4,c5,c6,c7
            ,c8,c9,cons,error,false,nil,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          GE(x,y){x -> s(x),y -> s(y)} =
            GE(s(x),s(y)) ->^+ c20(GE(x,y))
              = C[GE(x,y) = GE(x,y){}]

WORST_CASE(Omega(n^1),?)