(VAR M N V1 V2 X1 X2 X) (RULES U101(tt,M,N) -> U102(isNatKind(activate(M)),activate(M),activate(N)) U102(tt,M,N) -> U103(isNat(activate(N)),activate(M),activate(N)) U103(tt,M,N) -> U104(isNatKind(activate(N)),activate(M),activate(N)) U104(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N)) U11(tt,V1,V2) -> U12(isNatKind(activate(V1)),activate(V1),activate(V2)) U12(tt,V1,V2) -> U13(isNatKind(activate(V2)),activate(V1),activate(V2)) U13(tt,V1,V2) -> U14(isNatKind(activate(V2)),activate(V1),activate(V2)) U14(tt,V1,V2) -> U15(isNat(activate(V1)),activate(V2)) U15(tt,V2) -> U16(isNat(activate(V2))) U16(tt) -> tt U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1)) U22(tt,V1) -> U23(isNat(activate(V1))) U23(tt) -> tt U31(tt,V1,V2) -> U32(isNatKind(activate(V1)),activate(V1),activate(V2)) U32(tt,V1,V2) -> U33(isNatKind(activate(V2)),activate(V1),activate(V2)) U33(tt,V1,V2) -> U34(isNatKind(activate(V2)),activate(V1),activate(V2)) U34(tt,V1,V2) -> U35(isNat(activate(V1)),activate(V2)) U35(tt,V2) -> U36(isNat(activate(V2))) U36(tt) -> tt U41(tt,V2) -> U42(isNatKind(activate(V2))) U42(tt) -> tt U51(tt) -> tt U61(tt,V2) -> U62(isNatKind(activate(V2))) U62(tt) -> tt U71(tt,N) -> U72(isNatKind(activate(N)),activate(N)) U72(tt,N) -> activate(N) U81(tt,M,N) -> U82(isNatKind(activate(M)),activate(M),activate(N)) U82(tt,M,N) -> U83(isNat(activate(N)),activate(M),activate(N)) U83(tt,M,N) -> U84(isNatKind(activate(N)),activate(M),activate(N)) U84(tt,M,N) -> s(plus(activate(N),activate(M))) U91(tt,N) -> U92(isNatKind(activate(N))) U92(tt) -> 0 isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> U11(isNatKind(activate(V1)),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNat(n__x(V1,V2)) -> U31(isNatKind(activate(V1)),activate(V1),activate(V2)) isNatKind(n__0) -> tt isNatKind(n__plus(V1,V2)) -> U41(isNatKind(activate(V1)),activate(V2)) isNatKind(n__s(V1)) -> U51(isNatKind(activate(V1))) isNatKind(n__x(V1,V2)) -> U61(isNatKind(activate(V1)),activate(V2)) plus(N,0) -> U71(isNat(N),N) plus(N,s(M)) -> U81(isNat(M),M,N) x(N,0) -> U91(isNat(N),N) x(N,s(M)) -> U101(isNat(M),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) x(X1,X2) -> n__x(X1,X2) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__s(X)) -> s(X) activate(n__x(X1,X2)) -> x(X1,X2) activate(X) -> X )