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