* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
            U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
            U12(mark(X1),X2) -> mark(U12(X1,X2))
            U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
            U13(mark(X)) -> mark(U13(X))
            U13(ok(X)) -> ok(U13(X))
            U21(mark(X1),X2) -> mark(U21(X1,X2))
            U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
            U22(mark(X)) -> mark(U22(X))
            U22(ok(X)) -> ok(U22(X))
            U31(mark(X1),X2) -> mark(U31(X1,X2))
            U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
            U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
            U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
            active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
            active(U11(tt(),V1,V2)) -> mark(U12(isNat(V1),V2))
            active(U12(X1,X2)) -> U12(active(X1),X2)
            active(U12(tt(),V2)) -> mark(U13(isNat(V2)))
            active(U13(X)) -> U13(active(X))
            active(U13(tt())) -> mark(tt())
            active(U21(X1,X2)) -> U21(active(X1),X2)
            active(U21(tt(),V1)) -> mark(U22(isNat(V1)))
            active(U22(X)) -> U22(active(X))
            active(U22(tt())) -> mark(tt())
            active(U31(X1,X2)) -> U31(active(X1),X2)
            active(U31(tt(),N)) -> mark(N)
            active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
            active(U41(tt(),M,N)) -> mark(s(plus(N,M)))
            active(and(X1,X2)) -> and(active(X1),X2)
            active(and(tt(),X)) -> mark(X)
            active(isNat(0())) -> mark(tt())
            active(isNat(plus(V1,V2))) -> mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))
            active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
            active(isNatKind(0())) -> mark(tt())
            active(isNatKind(plus(V1,V2))) -> mark(and(isNatKind(V1),isNatKind(V2)))
            active(isNatKind(s(V1))) -> mark(isNatKind(V1))
            active(plus(N,0())) -> mark(U31(and(isNat(N),isNatKind(N)),N))
            active(plus(N,s(M))) -> mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))
            active(plus(X1,X2)) -> plus(X1,active(X2))
            active(plus(X1,X2)) -> plus(active(X1),X2)
            active(s(X)) -> s(active(X))
            and(mark(X1),X2) -> mark(and(X1,X2))
            and(ok(X1),ok(X2)) -> ok(and(X1,X2))
            isNat(ok(X)) -> ok(isNat(X))
            isNatKind(ok(X)) -> ok(isNatKind(X))
            plus(X1,mark(X2)) -> mark(plus(X1,X2))
            plus(mark(X1),X2) -> mark(plus(X1,X2))
            plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
            proper(0()) -> ok(0())
            proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
            proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
            proper(U13(X)) -> U13(proper(X))
            proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
            proper(U22(X)) -> U22(proper(X))
            proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
            proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
            proper(and(X1,X2)) -> and(proper(X1),proper(X2))
            proper(isNat(X)) -> isNat(proper(X))
            proper(isNatKind(X)) -> isNatKind(proper(X))
            proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
            proper(s(X)) -> s(proper(X))
            proper(tt()) -> ok(tt())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {U11/3,U12/2,U13/1,U21/2,U22/1,U31/2,U41/3,active/1,and/2,isNat/1,isNatKind/1,plus/2,proper/1,s/1
            ,top/1} / {0/0,mark/1,ok/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11,U12,U13,U21,U22,U31,U41,active,and,isNat,isNatKind
            ,plus,proper,s,top} and constructors {0,mark,ok,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
            U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
            U12(mark(X1),X2) -> mark(U12(X1,X2))
            U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
            U13(mark(X)) -> mark(U13(X))
            U13(ok(X)) -> ok(U13(X))
            U21(mark(X1),X2) -> mark(U21(X1,X2))
            U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
            U22(mark(X)) -> mark(U22(X))
            U22(ok(X)) -> ok(U22(X))
            U31(mark(X1),X2) -> mark(U31(X1,X2))
            U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
            U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3))
            U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3))
            active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
            active(U11(tt(),V1,V2)) -> mark(U12(isNat(V1),V2))
            active(U12(X1,X2)) -> U12(active(X1),X2)
            active(U12(tt(),V2)) -> mark(U13(isNat(V2)))
            active(U13(X)) -> U13(active(X))
            active(U13(tt())) -> mark(tt())
            active(U21(X1,X2)) -> U21(active(X1),X2)
            active(U21(tt(),V1)) -> mark(U22(isNat(V1)))
            active(U22(X)) -> U22(active(X))
            active(U22(tt())) -> mark(tt())
            active(U31(X1,X2)) -> U31(active(X1),X2)
            active(U31(tt(),N)) -> mark(N)
            active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3)
            active(U41(tt(),M,N)) -> mark(s(plus(N,M)))
            active(and(X1,X2)) -> and(active(X1),X2)
            active(and(tt(),X)) -> mark(X)
            active(isNat(0())) -> mark(tt())
            active(isNat(plus(V1,V2))) -> mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))
            active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
            active(isNatKind(0())) -> mark(tt())
            active(isNatKind(plus(V1,V2))) -> mark(and(isNatKind(V1),isNatKind(V2)))
            active(isNatKind(s(V1))) -> mark(isNatKind(V1))
            active(plus(N,0())) -> mark(U31(and(isNat(N),isNatKind(N)),N))
            active(plus(N,s(M))) -> mark(U41(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))
            active(plus(X1,X2)) -> plus(X1,active(X2))
            active(plus(X1,X2)) -> plus(active(X1),X2)
            active(s(X)) -> s(active(X))
            and(mark(X1),X2) -> mark(and(X1,X2))
            and(ok(X1),ok(X2)) -> ok(and(X1,X2))
            isNat(ok(X)) -> ok(isNat(X))
            isNatKind(ok(X)) -> ok(isNatKind(X))
            plus(X1,mark(X2)) -> mark(plus(X1,X2))
            plus(mark(X1),X2) -> mark(plus(X1,X2))
            plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
            proper(0()) -> ok(0())
            proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
            proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
            proper(U13(X)) -> U13(proper(X))
            proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
            proper(U22(X)) -> U22(proper(X))
            proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
            proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3))
            proper(and(X1,X2)) -> and(proper(X1),proper(X2))
            proper(isNat(X)) -> isNat(proper(X))
            proper(isNatKind(X)) -> isNatKind(proper(X))
            proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
            proper(s(X)) -> s(proper(X))
            proper(tt()) -> ok(tt())
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {U11/3,U12/2,U13/1,U21/2,U22/1,U31/2,U41/3,active/1,and/2,isNat/1,isNatKind/1,plus/2,proper/1,s/1
            ,top/1} / {0/0,mark/1,ok/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {U11,U12,U13,U21,U22,U31,U41,active,and,isNat,isNatKind
            ,plus,proper,s,top} and constructors {0,mark,ok,tt}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          U11(x,y,z){x -> mark(x)} =
            U11(mark(x),y,z) ->^+ mark(U11(x,y,z))
              = C[U11(x,y,z) = U11(x,y,z){}]

WORST_CASE(Omega(n^1),?)