(VAR N M X V1 V2 X1 X2 X3)
(RULES 
active(U11(tt,N)) -> mark(N)
active(U21(tt,M,N)) -> mark(s(plus(N,M)))
active(and(tt,X)) -> mark(X)
active(isNat(0)) -> mark(tt)
active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2)))
active(isNat(s(V1))) -> mark(isNat(V1))
active(plus(N,0)) -> mark(U11(isNat(N),N))
active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N))
active(U11(X1,X2)) -> U11(active(X1),X2)
active(U21(X1,X2,X3)) -> U21(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(and(X1,X2)) -> and(active(X1),X2)
U11(mark(X1),X2) -> mark(U11(X1,X2))
U21(mark(X1),X2,X3) -> mark(U21(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))
and(mark(X1),X2) -> mark(and(X1,X2))
proper(U11(X1,X2)) -> U11(proper(X1),proper(X2))
proper(tt) -> ok(tt)
proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
proper(s(X)) -> s(proper(X))
proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
proper(and(X1,X2)) -> and(proper(X1),proper(X2))
proper(isNat(X)) -> isNat(proper(X))
proper(0) -> ok(0)
U11(ok(X1),ok(X2)) -> ok(U11(X1,X2))
U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
s(ok(X)) -> ok(s(X))
plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
and(ok(X1),ok(X2)) -> ok(and(X1,X2))
isNat(ok(X)) -> ok(isNat(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
)