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