(VAR V1 V2 N M X1 X2 X3 X)
(RULES 
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,V2)) -> mark(U32(isNatKind(V2)))
active(U32(tt)) -> mark(tt)
active(U41(tt)) -> mark(tt)
active(U51(tt,N)) -> mark(U52(isNatKind(N),N))
active(U52(tt,N)) -> mark(N)
active(U61(tt,M,N)) -> mark(U62(isNatKind(M),M,N))
active(U62(tt,M,N)) -> mark(U63(isNat(N),M,N))
active(U63(tt,M,N)) -> mark(U64(isNatKind(N),M,N))
active(U64(tt,M,N)) -> mark(s(plus(N,M)))
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(isNatKind(0)) -> mark(tt)
active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
active(plus(N,0)) -> mark(U51(isNat(N),N))
active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
mark(tt) -> active(tt)
mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3))
mark(isNatKind(X)) -> active(isNatKind(X))
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(isNat(X)) -> active(isNat(X))
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)) -> active(U31(mark(X1),X2))
mark(U32(X)) -> active(U32(mark(X)))
mark(U41(X)) -> active(U41(mark(X)))
mark(U51(X1,X2)) -> active(U51(mark(X1),X2))
mark(U52(X1,X2)) -> active(U52(mark(X1),X2))
mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3))
mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3))
mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3))
mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3))
mark(s(X)) -> active(s(mark(X)))
mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
mark(0) -> active(0)
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)
isNatKind(mark(X)) -> isNatKind(X)
isNatKind(active(X)) -> isNatKind(X)
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)
isNat(mark(X)) -> isNat(X)
isNat(active(X)) -> isNat(X)
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) -> U31(X1,X2)
U31(X1,mark(X2)) -> U31(X1,X2)
U31(active(X1),X2) -> U31(X1,X2)
U31(X1,active(X2)) -> U31(X1,X2)
U32(mark(X)) -> U32(X)
U32(active(X)) -> U32(X)
U41(mark(X)) -> U41(X)
U41(active(X)) -> U41(X)
U51(mark(X1),X2) -> U51(X1,X2)
U51(X1,mark(X2)) -> U51(X1,X2)
U51(active(X1),X2) -> U51(X1,X2)
U51(X1,active(X2)) -> U51(X1,X2)
U52(mark(X1),X2) -> U52(X1,X2)
U52(X1,mark(X2)) -> U52(X1,X2)
U52(active(X1),X2) -> U52(X1,X2)
U52(X1,active(X2)) -> U52(X1,X2)
U61(mark(X1),X2,X3) -> U61(X1,X2,X3)
U61(X1,mark(X2),X3) -> U61(X1,X2,X3)
U61(X1,X2,mark(X3)) -> U61(X1,X2,X3)
U61(active(X1),X2,X3) -> U61(X1,X2,X3)
U61(X1,active(X2),X3) -> U61(X1,X2,X3)
U61(X1,X2,active(X3)) -> U61(X1,X2,X3)
U62(mark(X1),X2,X3) -> U62(X1,X2,X3)
U62(X1,mark(X2),X3) -> U62(X1,X2,X3)
U62(X1,X2,mark(X3)) -> U62(X1,X2,X3)
U62(active(X1),X2,X3) -> U62(X1,X2,X3)
U62(X1,active(X2),X3) -> U62(X1,X2,X3)
U62(X1,X2,active(X3)) -> U62(X1,X2,X3)
U63(mark(X1),X2,X3) -> U63(X1,X2,X3)
U63(X1,mark(X2),X3) -> U63(X1,X2,X3)
U63(X1,X2,mark(X3)) -> U63(X1,X2,X3)
U63(active(X1),X2,X3) -> U63(X1,X2,X3)
U63(X1,active(X2),X3) -> U63(X1,X2,X3)
U63(X1,X2,active(X3)) -> U63(X1,X2,X3)
U64(mark(X1),X2,X3) -> U64(X1,X2,X3)
U64(X1,mark(X2),X3) -> U64(X1,X2,X3)
U64(X1,X2,mark(X3)) -> U64(X1,X2,X3)
U64(active(X1),X2,X3) -> U64(X1,X2,X3)
U64(X1,active(X2),X3) -> U64(X1,X2,X3)
U64(X1,X2,active(X3)) -> U64(X1,X2,X3)
s(mark(X)) -> s(X)
s(active(X)) -> s(X)
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)
)