* 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__isNat(V1),V2)
            a__U12(X1,X2) -> U12(X1,X2)
            a__U12(tt(),V2) -> a__U13(a__isNat(V2))
            a__U13(X) -> U13(X)
            a__U13(tt()) -> tt()
            a__U21(X1,X2) -> U21(X1,X2)
            a__U21(tt(),V1) -> a__U22(a__isNat(V1))
            a__U22(X) -> U22(X)
            a__U22(tt()) -> tt()
            a__U31(X1,X2,X3) -> U31(X1,X2,X3)
            a__U31(tt(),V1,V2) -> a__U32(a__isNat(V1),V2)
            a__U32(X1,X2) -> U32(X1,X2)
            a__U32(tt(),V2) -> a__U33(a__isNat(V2))
            a__U33(X) -> U33(X)
            a__U33(tt()) -> tt()
            a__U41(X1,X2) -> U41(X1,X2)
            a__U41(tt(),N) -> mark(N)
            a__U51(X1,X2,X3) -> U51(X1,X2,X3)
            a__U51(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
            a__U61(X) -> U61(X)
            a__U61(tt()) -> 0()
            a__U71(X1,X2,X3) -> U71(X1,X2,X3)
            a__U71(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N))
            a__and(X1,X2) -> and(X1,X2)
            a__and(tt(),X) -> mark(X)
            a__isNat(X) -> isNat(X)
            a__isNat(0()) -> tt()
            a__isNat(plus(V1,V2)) -> a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)
            a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1)
            a__isNat(x(V1,V2)) -> a__U31(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)
            a__isNatKind(X) -> isNatKind(X)
            a__isNatKind(0()) -> tt()
            a__isNatKind(plus(V1,V2)) -> a__and(a__isNatKind(V1),isNatKind(V2))
            a__isNatKind(s(V1)) -> a__isNatKind(V1)
            a__isNatKind(x(V1,V2)) -> a__and(a__isNatKind(V1),isNatKind(V2))
            a__plus(N,0()) -> a__U41(a__and(a__isNat(N),isNatKind(N)),N)
            a__plus(N,s(M)) -> a__U51(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
            a__plus(X1,X2) -> plus(X1,X2)
            a__x(N,0()) -> a__U61(a__and(a__isNat(N),isNatKind(N)))
            a__x(N,s(M)) -> a__U71(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
            a__x(X1,X2) -> x(X1,X2)
            mark(0()) -> 0()
            mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
            mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
            mark(U13(X)) -> a__U13(mark(X))
            mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
            mark(U22(X)) -> a__U22(mark(X))
            mark(U31(X1,X2,X3)) -> a__U31(mark(X1),X2,X3)
            mark(U32(X1,X2)) -> a__U32(mark(X1),X2)
            mark(U33(X)) -> a__U33(mark(X))
            mark(U41(X1,X2)) -> a__U41(mark(X1),X2)
            mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
            mark(U61(X)) -> a__U61(mark(X))
            mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3)
            mark(and(X1,X2)) -> a__and(mark(X1),X2)
            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()
            mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
        - Signature:
            {a__U11/3,a__U12/2,a__U13/1,a__U21/2,a__U22/1,a__U31/3,a__U32/2,a__U33/1,a__U41/2,a__U51/3,a__U61/1,a__U71/3
            ,a__and/2,a__isNat/1,a__isNatKind/1,a__plus/2,a__x/2,mark/1} / {0/0,U11/3,U12/2,U13/1,U21/2,U22/1,U31/3
            ,U32/2,U33/1,U41/2,U51/3,U61/1,U71/3,and/2,isNat/1,isNatKind/1,plus/2,s/1,tt/0,x/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__U11,a__U12,a__U13,a__U21,a__U22,a__U31,a__U32,a__U33
            ,a__U41,a__U51,a__U61,a__U71,a__and,a__isNat,a__isNatKind,a__plus,a__x,mark} and constructors {0,U11,U12,U13
            ,U21,U22,U31,U32,U33,U41,U51,U61,U71,and,isNat,isNatKind,plus,s,tt,x}
    + 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__isNat(V1),V2)
            a__U12(X1,X2) -> U12(X1,X2)
            a__U12(tt(),V2) -> a__U13(a__isNat(V2))
            a__U13(X) -> U13(X)
            a__U13(tt()) -> tt()
            a__U21(X1,X2) -> U21(X1,X2)
            a__U21(tt(),V1) -> a__U22(a__isNat(V1))
            a__U22(X) -> U22(X)
            a__U22(tt()) -> tt()
            a__U31(X1,X2,X3) -> U31(X1,X2,X3)
            a__U31(tt(),V1,V2) -> a__U32(a__isNat(V1),V2)
            a__U32(X1,X2) -> U32(X1,X2)
            a__U32(tt(),V2) -> a__U33(a__isNat(V2))
            a__U33(X) -> U33(X)
            a__U33(tt()) -> tt()
            a__U41(X1,X2) -> U41(X1,X2)
            a__U41(tt(),N) -> mark(N)
            a__U51(X1,X2,X3) -> U51(X1,X2,X3)
            a__U51(tt(),M,N) -> s(a__plus(mark(N),mark(M)))
            a__U61(X) -> U61(X)
            a__U61(tt()) -> 0()
            a__U71(X1,X2,X3) -> U71(X1,X2,X3)
            a__U71(tt(),M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N))
            a__and(X1,X2) -> and(X1,X2)
            a__and(tt(),X) -> mark(X)
            a__isNat(X) -> isNat(X)
            a__isNat(0()) -> tt()
            a__isNat(plus(V1,V2)) -> a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)
            a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1)
            a__isNat(x(V1,V2)) -> a__U31(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2)
            a__isNatKind(X) -> isNatKind(X)
            a__isNatKind(0()) -> tt()
            a__isNatKind(plus(V1,V2)) -> a__and(a__isNatKind(V1),isNatKind(V2))
            a__isNatKind(s(V1)) -> a__isNatKind(V1)
            a__isNatKind(x(V1,V2)) -> a__and(a__isNatKind(V1),isNatKind(V2))
            a__plus(N,0()) -> a__U41(a__and(a__isNat(N),isNatKind(N)),N)
            a__plus(N,s(M)) -> a__U51(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
            a__plus(X1,X2) -> plus(X1,X2)
            a__x(N,0()) -> a__U61(a__and(a__isNat(N),isNatKind(N)))
            a__x(N,s(M)) -> a__U71(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)
            a__x(X1,X2) -> x(X1,X2)
            mark(0()) -> 0()
            mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
            mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
            mark(U13(X)) -> a__U13(mark(X))
            mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
            mark(U22(X)) -> a__U22(mark(X))
            mark(U31(X1,X2,X3)) -> a__U31(mark(X1),X2,X3)
            mark(U32(X1,X2)) -> a__U32(mark(X1),X2)
            mark(U33(X)) -> a__U33(mark(X))
            mark(U41(X1,X2)) -> a__U41(mark(X1),X2)
            mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
            mark(U61(X)) -> a__U61(mark(X))
            mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3)
            mark(and(X1,X2)) -> a__and(mark(X1),X2)
            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()
            mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
        - Signature:
            {a__U11/3,a__U12/2,a__U13/1,a__U21/2,a__U22/1,a__U31/3,a__U32/2,a__U33/1,a__U41/2,a__U51/3,a__U61/1,a__U71/3
            ,a__and/2,a__isNat/1,a__isNatKind/1,a__plus/2,a__x/2,mark/1} / {0/0,U11/3,U12/2,U13/1,U21/2,U22/1,U31/3
            ,U32/2,U33/1,U41/2,U51/3,U61/1,U71/3,and/2,isNat/1,isNatKind/1,plus/2,s/1,tt/0,x/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__U11,a__U12,a__U13,a__U21,a__U22,a__U31,a__U32,a__U33
            ,a__U41,a__U51,a__U61,a__U71,a__and,a__isNat,a__isNatKind,a__plus,a__x,mark} and constructors {0,U11,U12,U13
            ,U21,U22,U31,U32,U33,U41,U51,U61,U71,and,isNat,isNatKind,plus,s,tt,x}
    + 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__and(a__isNatKind(x),isNatKind(y))
              = C[a__isNatKind(x) = a__isNatKind(x){}]

WORST_CASE(Omega(n^1),?)