(VAR V2 N M V1 X1 X2 X3 X)
(RULES 
active(U11(tt,V2)) -> mark(U12(isNat(V2)))
active(U12(tt)) -> mark(tt)
active(U21(tt)) -> mark(tt)
active(U31(tt,V2)) -> mark(U32(isNat(V2)))
active(U32(tt)) -> mark(tt)
active(U41(tt,N)) -> mark(N)
active(U51(tt,M,N)) -> mark(U52(isNat(N),M,N))
active(U52(tt,M,N)) -> mark(s(plus(N,M)))
active(U61(tt)) -> mark(0)
active(U71(tt,M,N)) -> mark(U72(isNat(N),M,N))
active(U72(tt,M,N)) -> mark(plus(x(N,M),N))
active(isNat(0)) -> mark(tt)
active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2))
active(isNat(s(V1))) -> mark(U21(isNat(V1)))
active(isNat(x(V1,V2))) -> mark(U31(isNat(V1),V2))
active(plus(N,0)) -> mark(U41(isNat(N),N))
active(plus(N,s(M))) -> mark(U51(isNat(M),M,N))
active(x(N,0)) -> mark(U61(isNat(N)))
active(x(N,s(M))) -> mark(U71(isNat(M),M,N))
active(U11(X1,X2)) -> U11(active(X1),X2)
active(U12(X)) -> U12(active(X))
active(U21(X)) -> U21(active(X))
active(U31(X1,X2)) -> U31(active(X1),X2)
active(U32(X)) -> U32(active(X))
active(U41(X1,X2)) -> U41(active(X1),X2)
active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
active(U52(X1,X2,X3)) -> U52(active(X1),X2,X3)
active(s(X)) -> s(active(X))
active(plus(X1,X2)) -> plus(active(X1),X2)
active(plus(X1,X2)) -> plus(X1,active(X2))
active(U61(X)) -> U61(active(X))
active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
active(U72(X1,X2,X3)) -> U72(active(X1),X2,X3)
active(x(X1,X2)) -> x(active(X1),X2)
active(x(X1,X2)) -> x(X1,active(X2))
U11(mark(X1),X2) -> mark(U11(X1,X2))
U12(mark(X)) -> mark(U12(X))
U21(mark(X)) -> mark(U21(X))
U31(mark(X1),X2) -> mark(U31(X1,X2))
U32(mark(X)) -> mark(U32(X))
U41(mark(X1),X2) -> mark(U41(X1,X2))
U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
U52(mark(X1),X2,X3) -> mark(U52(X1,X2,X3))
s(mark(X)) -> mark(s(X))
plus(mark(X1),X2) -> mark(plus(X1,X2))
plus(X1,mark(X2)) -> mark(plus(X1,X2))
U61(mark(X)) -> mark(U61(X))
U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
U72(mark(X1),X2,X3) -> mark(U72(X1,X2,X3))
x(mark(X1),X2) -> mark(x(X1,X2))
x(X1,mark(X2)) -> mark(x(X1,X2))
proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
proper(tt) -> ok(tt)
proper(U12(X)) -> U12(proper(X))
proper(isNat(X)) -> isNat(proper(X))
proper(U21(X)) -> U21(proper(X))
proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
proper(U32(X)) -> U32(proper(X))
proper(U41(X1,X2)) -> U41(proper(X1),proper(X2))
proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
proper(U52(X1,X2,X3)) -> U52(proper(X1),proper(X2),proper(X3))
proper(s(X)) -> s(proper(X))
proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
proper(U61(X)) -> U61(proper(X))
proper(0) -> ok(0)
proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
proper(U72(X1,X2,X3)) -> U72(proper(X1),proper(X2),proper(X3))
proper(x(X1,X2)) -> x(proper(X1),proper(X2))
U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
U12(ok(X)) -> ok(U12(X))
isNat(ok(X)) -> ok(isNat(X))
U21(ok(X)) -> ok(U21(X))
U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
U32(ok(X)) -> ok(U32(X))
U41(ok(X1),ok(X2)) -> ok(U41(X1,X2))
U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
U52(ok(X1),ok(X2),ok(X3)) -> ok(U52(X1,X2,X3))
s(ok(X)) -> ok(s(X))
plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
U61(ok(X)) -> ok(U61(X))
U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
U72(ok(X1),ok(X2),ok(X3)) -> ok(U72(X1,X2,X3))
x(ok(X1),ok(X2)) -> ok(x(X1,X2))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)