MAYBE
0.28/0.38	MAYBE
0.28/0.39	
0.28/0.39	Problem:
0.28/0.39	 active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N))
0.28/0.39	 active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N))
0.28/0.39	 active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N))
0.28/0.39	 active(U104(tt(),M,N)) -> mark(plus(x(N,M),N))
0.28/0.39	 active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
0.28/0.39	 active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
0.28/0.39	 active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
0.28/0.39	 active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
0.28/0.39	 active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
0.28/0.39	 active(U16(tt())) -> mark(tt())
0.28/0.39	 active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
0.28/0.39	 active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
0.28/0.39	 active(U23(tt())) -> mark(tt())
0.28/0.39	 active(U31(tt(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2))
0.28/0.39	 active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2))
0.28/0.39	 active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2))
0.28/0.39	 active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2))
0.28/0.39	 active(U35(tt(),V2)) -> mark(U36(isNat(V2)))
0.28/0.39	 active(U36(tt())) -> mark(tt())
0.28/0.39	 active(U41(tt(),V2)) -> mark(U42(isNatKind(V2)))
0.28/0.39	 active(U42(tt())) -> mark(tt())
0.28/0.39	 active(U51(tt())) -> mark(tt())
0.28/0.39	 active(U61(tt(),V2)) -> mark(U62(isNatKind(V2)))
0.28/0.39	 active(U62(tt())) -> mark(tt())
0.28/0.39	 active(U71(tt(),N)) -> mark(U72(isNatKind(N),N))
0.28/0.39	 active(U72(tt(),N)) -> mark(N)
0.28/0.39	 active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N))
0.28/0.39	 active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N))
0.28/0.39	 active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N))
0.28/0.39	 active(U84(tt(),M,N)) -> mark(s(plus(N,M)))
0.28/0.39	 active(U91(tt(),N)) -> mark(U92(isNatKind(N)))
0.28/0.39	 active(U92(tt())) -> mark(0())
0.28/0.39	 active(isNat(0())) -> mark(tt())
0.28/0.39	 active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
0.28/0.39	 active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
0.28/0.39	 active(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2))
0.28/0.39	 active(isNatKind(0())) -> mark(tt())
0.28/0.39	 active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2))
0.28/0.39	 active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1)))
0.28/0.39	 active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2))
0.28/0.39	 active(plus(N,0())) -> mark(U71(isNat(N),N))
0.28/0.39	 active(plus(N,s(M))) -> mark(U81(isNat(M),M,N))
0.28/0.39	 active(x(N,0())) -> mark(U91(isNat(N),N))
0.28/0.39	 active(x(N,s(M))) -> mark(U101(isNat(M),M,N))
0.28/0.39	 active(U101(X1,X2,X3)) -> U101(active(X1),X2,X3)
0.28/0.39	 active(U102(X1,X2,X3)) -> U102(active(X1),X2,X3)
0.28/0.39	 active(U103(X1,X2,X3)) -> U103(active(X1),X2,X3)
0.28/0.39	 active(U104(X1,X2,X3)) -> U104(active(X1),X2,X3)
0.28/0.39	 active(plus(X1,X2)) -> plus(active(X1),X2)
0.28/0.39	 active(plus(X1,X2)) -> plus(X1,active(X2))
0.28/0.39	 active(x(X1,X2)) -> x(active(X1),X2)
0.28/0.39	 active(x(X1,X2)) -> x(X1,active(X2))
0.28/0.39	 active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
0.28/0.39	 active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
0.28/0.39	 active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
0.28/0.39	 active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
0.28/0.39	 active(U15(X1,X2)) -> U15(active(X1),X2)
0.28/0.39	 active(U16(X)) -> U16(active(X))
0.28/0.39	 active(U21(X1,X2)) -> U21(active(X1),X2)
0.28/0.39	 active(U22(X1,X2)) -> U22(active(X1),X2)
0.28/0.39	 active(U23(X)) -> U23(active(X))
0.28/0.39	 active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3)
0.28/0.39	 active(U32(X1,X2,X3)) -> U32(active(X1),X2,X3)
0.28/0.39	 active(U33(X1,X2,X3)) -> U33(active(X1),X2,X3)
0.28/0.39	 active(U34(X1,X2,X3)) -> U34(active(X1),X2,X3)
0.28/0.39	 active(U35(X1,X2)) -> U35(active(X1),X2)
0.28/0.39	 active(U36(X)) -> U36(active(X))
0.28/0.39	 active(U41(X1,X2)) -> U41(active(X1),X2)
0.28/0.39	 active(U42(X)) -> U42(active(X))
0.28/0.39	 active(U51(X)) -> U51(active(X))
0.28/0.39	 active(U61(X1,X2)) -> U61(active(X1),X2)
0.28/0.39	 active(U62(X)) -> U62(active(X))
0.28/0.39	 active(U71(X1,X2)) -> U71(active(X1),X2)
0.28/0.39	 active(U72(X1,X2)) -> U72(active(X1),X2)
0.28/0.39	 active(U81(X1,X2,X3)) -> U81(active(X1),X2,X3)
0.28/0.39	 active(U82(X1,X2,X3)) -> U82(active(X1),X2,X3)
0.28/0.39	 active(U83(X1,X2,X3)) -> U83(active(X1),X2,X3)
0.28/0.39	 active(U84(X1,X2,X3)) -> U84(active(X1),X2,X3)
0.28/0.39	 active(s(X)) -> s(active(X))
0.28/0.39	 active(U91(X1,X2)) -> U91(active(X1),X2)
0.28/0.39	 active(U92(X)) -> U92(active(X))
0.28/0.39	 U101(mark(X1),X2,X3) -> mark(U101(X1,X2,X3))
0.28/0.39	 U102(mark(X1),X2,X3) -> mark(U102(X1,X2,X3))
0.28/0.39	 U103(mark(X1),X2,X3) -> mark(U103(X1,X2,X3))
0.28/0.39	 U104(mark(X1),X2,X3) -> mark(U104(X1,X2,X3))
0.28/0.39	 plus(mark(X1),X2) -> mark(plus(X1,X2))
0.28/0.39	 plus(X1,mark(X2)) -> mark(plus(X1,X2))
0.28/0.39	 x(mark(X1),X2) -> mark(x(X1,X2))
0.28/0.39	 x(X1,mark(X2)) -> mark(x(X1,X2))
0.28/0.39	 U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
0.28/0.39	 U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
0.28/0.39	 U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
0.28/0.39	 U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
0.28/0.39	 U15(mark(X1),X2) -> mark(U15(X1,X2))
0.28/0.39	 U16(mark(X)) -> mark(U16(X))
0.28/0.39	 U21(mark(X1),X2) -> mark(U21(X1,X2))
0.28/0.39	 U22(mark(X1),X2) -> mark(U22(X1,X2))
0.28/0.39	 U23(mark(X)) -> mark(U23(X))
0.28/0.39	 U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3))
0.28/0.39	 U32(mark(X1),X2,X3) -> mark(U32(X1,X2,X3))
0.28/0.39	 U33(mark(X1),X2,X3) -> mark(U33(X1,X2,X3))
0.28/0.39	 U34(mark(X1),X2,X3) -> mark(U34(X1,X2,X3))
0.28/0.39	 U35(mark(X1),X2) -> mark(U35(X1,X2))
0.28/0.39	 U36(mark(X)) -> mark(U36(X))
0.28/0.39	 U41(mark(X1),X2) -> mark(U41(X1,X2))
0.28/0.39	 U42(mark(X)) -> mark(U42(X))
0.28/0.39	 U51(mark(X)) -> mark(U51(X))
0.28/0.39	 U61(mark(X1),X2) -> mark(U61(X1,X2))
0.28/0.39	 U62(mark(X)) -> mark(U62(X))
0.28/0.39	 U71(mark(X1),X2) -> mark(U71(X1,X2))
0.28/0.39	 U72(mark(X1),X2) -> mark(U72(X1,X2))
0.28/0.39	 U81(mark(X1),X2,X3) -> mark(U81(X1,X2,X3))
0.28/0.39	 U82(mark(X1),X2,X3) -> mark(U82(X1,X2,X3))
0.28/0.39	 U83(mark(X1),X2,X3) -> mark(U83(X1,X2,X3))
0.28/0.39	 U84(mark(X1),X2,X3) -> mark(U84(X1,X2,X3))
0.28/0.39	 s(mark(X)) -> mark(s(X))
0.28/0.39	 U91(mark(X1),X2) -> mark(U91(X1,X2))
0.28/0.39	 U92(mark(X)) -> mark(U92(X))
0.28/0.39	 proper(U101(X1,X2,X3)) -> U101(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(tt()) -> ok(tt())
0.28/0.39	 proper(U102(X1,X2,X3)) -> U102(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(isNatKind(X)) -> isNatKind(proper(X))
0.28/0.39	 proper(U103(X1,X2,X3)) -> U103(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(isNat(X)) -> isNat(proper(X))
0.28/0.39	 proper(U104(X1,X2,X3)) -> U104(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
0.28/0.39	 proper(x(X1,X2)) -> x(proper(X1),proper(X2))
0.28/0.39	 proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
0.28/0.39	 proper(U16(X)) -> U16(proper(X))
0.28/0.39	 proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
0.28/0.39	 proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
0.28/0.39	 proper(U23(X)) -> U23(proper(X))
0.28/0.39	 proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(U32(X1,X2,X3)) -> U32(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(U33(X1,X2,X3)) -> U33(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(U34(X1,X2,X3)) -> U34(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(U35(X1,X2)) -> U35(proper(X1),proper(X2))
0.28/0.39	 proper(U36(X)) -> U36(proper(X))
0.28/0.39	 proper(U41(X1,X2)) -> U41(proper(X1),proper(X2))
0.28/0.39	 proper(U42(X)) -> U42(proper(X))
0.28/0.39	 proper(U51(X)) -> U51(proper(X))
0.28/0.39	 proper(U61(X1,X2)) -> U61(proper(X1),proper(X2))
0.28/0.39	 proper(U62(X)) -> U62(proper(X))
0.28/0.39	 proper(U71(X1,X2)) -> U71(proper(X1),proper(X2))
0.28/0.39	 proper(U72(X1,X2)) -> U72(proper(X1),proper(X2))
0.28/0.39	 proper(U81(X1,X2,X3)) -> U81(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(U82(X1,X2,X3)) -> U82(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(U83(X1,X2,X3)) -> U83(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(U84(X1,X2,X3)) -> U84(proper(X1),proper(X2),proper(X3))
0.28/0.39	 proper(s(X)) -> s(proper(X))
0.28/0.39	 proper(U91(X1,X2)) -> U91(proper(X1),proper(X2))
0.28/0.39	 proper(U92(X)) -> U92(proper(X))
0.28/0.39	 proper(0()) -> ok(0())
0.28/0.39	 U101(ok(X1),ok(X2),ok(X3)) -> ok(U101(X1,X2,X3))
0.28/0.39	 U102(ok(X1),ok(X2),ok(X3)) -> ok(U102(X1,X2,X3))
0.28/0.39	 isNatKind(ok(X)) -> ok(isNatKind(X))
0.28/0.39	 U103(ok(X1),ok(X2),ok(X3)) -> ok(U103(X1,X2,X3))
0.28/0.39	 isNat(ok(X)) -> ok(isNat(X))
0.28/0.39	 U104(ok(X1),ok(X2),ok(X3)) -> ok(U104(X1,X2,X3))
0.28/0.39	 plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
0.28/0.39	 x(ok(X1),ok(X2)) -> ok(x(X1,X2))
0.28/0.39	 U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
0.28/0.39	 U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
0.28/0.39	 U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
0.28/0.39	 U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
0.28/0.39	 U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
0.28/0.39	 U16(ok(X)) -> ok(U16(X))
0.28/0.39	 U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
0.28/0.39	 U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
0.28/0.39	 U23(ok(X)) -> ok(U23(X))
0.28/0.39	 U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3))
0.28/0.39	 U32(ok(X1),ok(X2),ok(X3)) -> ok(U32(X1,X2,X3))
0.28/0.39	 U33(ok(X1),ok(X2),ok(X3)) -> ok(U33(X1,X2,X3))
0.28/0.39	 U34(ok(X1),ok(X2),ok(X3)) -> ok(U34(X1,X2,X3))
0.28/0.39	 U35(ok(X1),ok(X2)) -> ok(U35(X1,X2))
0.28/0.39	 U36(ok(X)) -> ok(U36(X))
0.28/0.39	 U41(ok(X1),ok(X2)) -> ok(U41(X1,X2))
0.28/0.39	 U42(ok(X)) -> ok(U42(X))
0.28/0.39	 U51(ok(X)) -> ok(U51(X))
0.28/0.39	 U61(ok(X1),ok(X2)) -> ok(U61(X1,X2))
0.28/0.39	 U62(ok(X)) -> ok(U62(X))
0.28/0.39	 U71(ok(X1),ok(X2)) -> ok(U71(X1,X2))
0.28/0.39	 U72(ok(X1),ok(X2)) -> ok(U72(X1,X2))
0.28/0.39	 U81(ok(X1),ok(X2),ok(X3)) -> ok(U81(X1,X2,X3))
0.28/0.39	 U82(ok(X1),ok(X2),ok(X3)) -> ok(U82(X1,X2,X3))
0.28/0.39	 U83(ok(X1),ok(X2),ok(X3)) -> ok(U83(X1,X2,X3))
0.28/0.39	 U84(ok(X1),ok(X2),ok(X3)) -> ok(U84(X1,X2,X3))
0.28/0.39	 s(ok(X)) -> ok(s(X))
0.28/0.39	 U91(ok(X1),ok(X2)) -> ok(U91(X1,X2))
0.28/0.39	 U92(ok(X)) -> ok(U92(X))
0.28/0.39	 top(mark(X)) -> top(proper(X))
0.28/0.39	 top(ok(X)) -> top(active(X))
0.28/0.39	
0.28/0.39	Proof:
0.28/0.39	 Open
0.38/0.40	EOF