* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__U11(X1,X2,X3) -> U11(X1,X2,X3)
            a__U11(tt(),V1,V2) -> a__U12(a__isNatKind(V1),V1,V2)
            a__U12(X1,X2,X3) -> U12(X1,X2,X3)
            a__U12(tt(),V1,V2) -> a__U13(a__isNatKind(V2),V1,V2)
            a__U13(X1,X2,X3) -> U13(X1,X2,X3)
            a__U13(tt(),V1,V2) -> a__U14(a__isNatKind(V2),V1,V2)
            a__U14(X1,X2,X3) -> U14(X1,X2,X3)
            a__U14(tt(),V1,V2) -> a__U15(a__isNat(V1),V2)
            a__U15(X1,X2) -> U15(X1,X2)
            a__U15(tt(),V2) -> a__U16(a__isNat(V2))
            a__U16(X) -> U16(X)
            a__U16(tt()) -> tt()
            a__U21(X1,X2) -> U21(X1,X2)
            a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1)
            a__U22(X1,X2) -> U22(X1,X2)
            a__U22(tt(),V1) -> a__U23(a__isNat(V1))
            a__U23(X) -> U23(X)
            a__U23(tt()) -> tt()
            a__U31(X1,X2) -> U31(X1,X2)
            a__U31(tt(),V2) -> a__U32(a__isNatKind(V2))
            a__U32(X) -> U32(X)
            a__U32(tt()) -> tt()
            a__U41(X) -> U41(X)
            a__U41(tt()) -> tt()
            a__U51(X1,X2) -> U51(X1,X2)
            a__U51(tt(),N) -> a__U52(a__isNatKind(N),N)
            a__U52(X1,X2) -> U52(X1,X2)
            a__U52(tt(),N) -> mark(N)
            a__U61(X1,X2,X3) -> U61(X1,X2,X3)
            a__U61(tt(),M,N) -> a__U62(a__isNatKind(M),M,N)
            a__U62(X1,X2,X3) -> U62(X1,X2,X3)
            a__U62(tt(),M,N) -> a__U63(a__isNat(N),M,N)
            a__U63(X1,X2,X3) -> U63(X1,X2,X3)
            a__U63(tt(),M,N) -> a__U64(a__isNatKind(N),M,N)
            a__U64(X1,X2,X3) -> U64(X1,X2,X3)
            a__U64(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
            a__isNat(X) -> isNat(X)
            a__isNat(0()) -> tt()
            a__isNat(plus(V1,V2)) -> a__U11(a__isNatKind(V1),V1,V2)
            a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1)
            a__isNatKind(X) -> isNatKind(X)
            a__isNatKind(0()) -> tt()
            a__isNatKind(plus(V1,V2)) -> a__U31(a__isNatKind(V1),V2)
            a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1))
            a__plus(N,0()) -> a__U51(a__isNat(N),N)
            a__plus(N,s(M)) -> a__U61(a__isNat(M),M,N)
            a__plus(X1,X2) -> plus(X1,X2)
            mark(0()) -> 0()
            mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
            mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
            mark(U13(X1,X2,X3)) -> a__U13(mark(X1),X2,X3)
            mark(U14(X1,X2,X3)) -> a__U14(mark(X1),X2,X3)
            mark(U15(X1,X2)) -> a__U15(mark(X1),X2)
            mark(U16(X)) -> a__U16(mark(X))
            mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
            mark(U22(X1,X2)) -> a__U22(mark(X1),X2)
            mark(U23(X)) -> a__U23(mark(X))
            mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
            mark(U32(X)) -> a__U32(mark(X))
            mark(U41(X)) -> a__U41(mark(X))
            mark(U51(X1,X2)) -> a__U51(mark(X1),X2)
            mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
            mark(U61(X1,X2,X3)) -> a__U61(mark(X1),X2,X3)
            mark(U62(X1,X2,X3)) -> a__U62(mark(X1),X2,X3)
            mark(U63(X1,X2,X3)) -> a__U63(mark(X1),X2,X3)
            mark(U64(X1,X2,X3)) -> a__U64(mark(X1),X2,X3)
            mark(isNat(X)) -> a__isNat(X)
            mark(isNatKind(X)) -> a__isNatKind(X)
            mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
            mark(s(X)) -> s(mark(X))
            mark(tt()) -> tt()
        - Signature:
            {a__U11/3,a__U12/3,a__U13/3,a__U14/3,a__U15/2,a__U16/1,a__U21/2,a__U22/2,a__U23/1,a__U31/2,a__U32/1,a__U41/1
            ,a__U51/2,a__U52/2,a__U61/3,a__U62/3,a__U63/3,a__U64/3,a__isNat/1,a__isNatKind/1,a__plus/2,mark/1} / {0/0
            ,U11/3,U12/3,U13/3,U14/3,U15/2,U16/1,U21/2,U22/2,U23/1,U31/2,U32/1,U41/1,U51/2,U52/2,U61/3,U62/3,U63/3,U64/3
            ,isNat/1,isNatKind/1,plus/2,s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__U11,a__U12,a__U13,a__U14,a__U15,a__U16,a__U21,a__U22
            ,a__U23,a__U31,a__U32,a__U41,a__U51,a__U52,a__U61,a__U62,a__U63,a__U64,a__isNat,a__isNatKind,a__plus
            ,mark} and constructors {0,U11,U12,U13,U14,U15,U16,U21,U22,U23,U31,U32,U41,U51,U52,U61,U62,U63,U64,isNat
            ,isNatKind,plus,s,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__U11(X1,X2,X3) -> U11(X1,X2,X3)
            a__U11(tt(),V1,V2) -> a__U12(a__isNatKind(V1),V1,V2)
            a__U12(X1,X2,X3) -> U12(X1,X2,X3)
            a__U12(tt(),V1,V2) -> a__U13(a__isNatKind(V2),V1,V2)
            a__U13(X1,X2,X3) -> U13(X1,X2,X3)
            a__U13(tt(),V1,V2) -> a__U14(a__isNatKind(V2),V1,V2)
            a__U14(X1,X2,X3) -> U14(X1,X2,X3)
            a__U14(tt(),V1,V2) -> a__U15(a__isNat(V1),V2)
            a__U15(X1,X2) -> U15(X1,X2)
            a__U15(tt(),V2) -> a__U16(a__isNat(V2))
            a__U16(X) -> U16(X)
            a__U16(tt()) -> tt()
            a__U21(X1,X2) -> U21(X1,X2)
            a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1)
            a__U22(X1,X2) -> U22(X1,X2)
            a__U22(tt(),V1) -> a__U23(a__isNat(V1))
            a__U23(X) -> U23(X)
            a__U23(tt()) -> tt()
            a__U31(X1,X2) -> U31(X1,X2)
            a__U31(tt(),V2) -> a__U32(a__isNatKind(V2))
            a__U32(X) -> U32(X)
            a__U32(tt()) -> tt()
            a__U41(X) -> U41(X)
            a__U41(tt()) -> tt()
            a__U51(X1,X2) -> U51(X1,X2)
            a__U51(tt(),N) -> a__U52(a__isNatKind(N),N)
            a__U52(X1,X2) -> U52(X1,X2)
            a__U52(tt(),N) -> mark(N)
            a__U61(X1,X2,X3) -> U61(X1,X2,X3)
            a__U61(tt(),M,N) -> a__U62(a__isNatKind(M),M,N)
            a__U62(X1,X2,X3) -> U62(X1,X2,X3)
            a__U62(tt(),M,N) -> a__U63(a__isNat(N),M,N)
            a__U63(X1,X2,X3) -> U63(X1,X2,X3)
            a__U63(tt(),M,N) -> a__U64(a__isNatKind(N),M,N)
            a__U64(X1,X2,X3) -> U64(X1,X2,X3)
            a__U64(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
            a__isNat(X) -> isNat(X)
            a__isNat(0()) -> tt()
            a__isNat(plus(V1,V2)) -> a__U11(a__isNatKind(V1),V1,V2)
            a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1)
            a__isNatKind(X) -> isNatKind(X)
            a__isNatKind(0()) -> tt()
            a__isNatKind(plus(V1,V2)) -> a__U31(a__isNatKind(V1),V2)
            a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1))
            a__plus(N,0()) -> a__U51(a__isNat(N),N)
            a__plus(N,s(M)) -> a__U61(a__isNat(M),M,N)
            a__plus(X1,X2) -> plus(X1,X2)
            mark(0()) -> 0()
            mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
            mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
            mark(U13(X1,X2,X3)) -> a__U13(mark(X1),X2,X3)
            mark(U14(X1,X2,X3)) -> a__U14(mark(X1),X2,X3)
            mark(U15(X1,X2)) -> a__U15(mark(X1),X2)
            mark(U16(X)) -> a__U16(mark(X))
            mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
            mark(U22(X1,X2)) -> a__U22(mark(X1),X2)
            mark(U23(X)) -> a__U23(mark(X))
            mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
            mark(U32(X)) -> a__U32(mark(X))
            mark(U41(X)) -> a__U41(mark(X))
            mark(U51(X1,X2)) -> a__U51(mark(X1),X2)
            mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
            mark(U61(X1,X2,X3)) -> a__U61(mark(X1),X2,X3)
            mark(U62(X1,X2,X3)) -> a__U62(mark(X1),X2,X3)
            mark(U63(X1,X2,X3)) -> a__U63(mark(X1),X2,X3)
            mark(U64(X1,X2,X3)) -> a__U64(mark(X1),X2,X3)
            mark(isNat(X)) -> a__isNat(X)
            mark(isNatKind(X)) -> a__isNatKind(X)
            mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
            mark(s(X)) -> s(mark(X))
            mark(tt()) -> tt()
        - Signature:
            {a__U11/3,a__U12/3,a__U13/3,a__U14/3,a__U15/2,a__U16/1,a__U21/2,a__U22/2,a__U23/1,a__U31/2,a__U32/1,a__U41/1
            ,a__U51/2,a__U52/2,a__U61/3,a__U62/3,a__U63/3,a__U64/3,a__isNat/1,a__isNatKind/1,a__plus/2,mark/1} / {0/0
            ,U11/3,U12/3,U13/3,U14/3,U15/2,U16/1,U21/2,U22/2,U23/1,U31/2,U32/1,U41/1,U51/2,U52/2,U61/3,U62/3,U63/3,U64/3
            ,isNat/1,isNatKind/1,plus/2,s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__U11,a__U12,a__U13,a__U14,a__U15,a__U16,a__U21,a__U22
            ,a__U23,a__U31,a__U32,a__U41,a__U51,a__U52,a__U61,a__U62,a__U63,a__U64,a__isNat,a__isNatKind,a__plus
            ,mark} and constructors {0,U11,U12,U13,U14,U15,U16,U21,U22,U23,U31,U32,U41,U51,U52,U61,U62,U63,U64,isNat
            ,isNatKind,plus,s,tt}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          a__isNatKind(x){x -> plus(x,y)} =
            a__isNatKind(plus(x,y)) ->^+ a__U31(a__isNatKind(x),y)
              = C[a__isNatKind(x) = a__isNatKind(x){}]

WORST_CASE(Omega(n^1),?)