(VAR V1 V2 N M X X1 X2 X3)
(RULES 
active(U11(tt,V1,V2)) -> mark(U12(isNat(V1),V2))
active(U12(tt,V2)) -> mark(U13(isNat(V2)))
active(U13(tt)) -> mark(tt)
active(U21(tt,V1)) -> mark(U22(isNat(V1)))
active(U22(tt)) -> mark(tt)
active(U31(tt,V1,V2)) -> mark(U32(isNat(V1),V2))
active(U32(tt,V2)) -> mark(U33(isNat(V2)))
active(U33(tt)) -> mark(tt)
active(U41(tt,N)) -> mark(N)
active(U51(tt,M,N)) -> mark(s(plus(N,M)))
active(U61(tt)) -> mark(0)
active(U71(tt,M,N)) -> mark(plus(x(N,M),N))
active(and(tt,X)) -> mark(X)
active(isNat(0)) -> mark(tt)
active(isNat(plus(V1,V2))) -> mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))
active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
active(isNat(x(V1,V2))) -> mark(U31(and(isNatKind(V1),isNatKind(V2)),V1,V2))
active(isNatKind(0)) -> mark(tt)
active(isNatKind(plus(V1,V2))) -> mark(and(isNatKind(V1),isNatKind(V2)))
active(isNatKind(s(V1))) -> mark(isNatKind(V1))
active(isNatKind(x(V1,V2))) -> mark(and(isNatKind(V1),isNatKind(V2)))
active(plus(N,0)) -> mark(U41(and(isNat(N),isNatKind(N)),N))
active(plus(N,s(M))) -> mark(U51(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))
active(x(N,0)) -> mark(U61(and(isNat(N),isNatKind(N))))
active(x(N,s(M))) -> mark(U71(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))
mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3))
mark(tt) -> active(tt)
mark(U12(X1,X2)) -> active(U12(mark(X1),X2))
mark(isNat(X)) -> active(isNat(X))
mark(U13(X)) -> active(U13(mark(X)))
mark(U21(X1,X2)) -> active(U21(mark(X1),X2))
mark(U22(X)) -> active(U22(mark(X)))
mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3))
mark(U32(X1,X2)) -> active(U32(mark(X1),X2))
mark(U33(X)) -> active(U33(mark(X)))
mark(U41(X1,X2)) -> active(U41(mark(X1),X2))
mark(U51(X1,X2,X3)) -> active(U51(mark(X1),X2,X3))
mark(s(X)) -> active(s(mark(X)))
mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
mark(U61(X)) -> active(U61(mark(X)))
mark(0) -> active(0)
mark(U71(X1,X2,X3)) -> active(U71(mark(X1),X2,X3))
mark(x(X1,X2)) -> active(x(mark(X1),mark(X2)))
mark(and(X1,X2)) -> active(and(mark(X1),X2))
mark(isNatKind(X)) -> active(isNatKind(X))
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) -> U12(X1,X2)
U12(X1,mark(X2)) -> U12(X1,X2)
U12(active(X1),X2) -> U12(X1,X2)
U12(X1,active(X2)) -> U12(X1,X2)
isNat(mark(X)) -> isNat(X)
isNat(active(X)) -> isNat(X)
U13(mark(X)) -> U13(X)
U13(active(X)) -> U13(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(X)) -> U22(X)
U22(active(X)) -> U22(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) -> U32(X1,X2)
U32(X1,mark(X2)) -> U32(X1,X2)
U32(active(X1),X2) -> U32(X1,X2)
U32(X1,active(X2)) -> U32(X1,X2)
U33(mark(X)) -> U33(X)
U33(active(X)) -> U33(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)
U51(mark(X1),X2,X3) -> U51(X1,X2,X3)
U51(X1,mark(X2),X3) -> U51(X1,X2,X3)
U51(X1,X2,mark(X3)) -> U51(X1,X2,X3)
U51(active(X1),X2,X3) -> U51(X1,X2,X3)
U51(X1,active(X2),X3) -> U51(X1,X2,X3)
U51(X1,X2,active(X3)) -> U51(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)
U61(mark(X)) -> U61(X)
U61(active(X)) -> U61(X)
U71(mark(X1),X2,X3) -> U71(X1,X2,X3)
U71(X1,mark(X2),X3) -> U71(X1,X2,X3)
U71(X1,X2,mark(X3)) -> U71(X1,X2,X3)
U71(active(X1),X2,X3) -> U71(X1,X2,X3)
U71(X1,active(X2),X3) -> U71(X1,X2,X3)
U71(X1,X2,active(X3)) -> U71(X1,X2,X3)
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)
and(mark(X1),X2) -> and(X1,X2)
and(X1,mark(X2)) -> and(X1,X2)
and(active(X1),X2) -> and(X1,X2)
and(X1,active(X2)) -> and(X1,X2)
isNatKind(mark(X)) -> isNatKind(X)
isNatKind(active(X)) -> isNatKind(X)
)