(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
active(and(tt, X)) → mark(X)
active(plus(N, 0)) → mark(N)
active(plus(N, s(M))) → mark(s(plus(N, M)))
active(and(X1, X2)) → and(active(X1), X2)
active(plus(X1, X2)) → plus(active(X1), X2)
active(plus(X1, X2)) → plus(X1, active(X2))
active(s(X)) → s(active(X))
and(mark(X1), X2) → mark(and(X1, X2))
plus(mark(X1), X2) → mark(plus(X1, X2))
plus(X1, mark(X2)) → mark(plus(X1, X2))
s(mark(X)) → mark(s(X))
proper(and(X1, X2)) → and(proper(X1), proper(X2))
proper(tt) → ok(tt)
proper(plus(X1, X2)) → plus(proper(X1), proper(X2))
proper(0) → ok(0)
proper(s(X)) → s(proper(X))
and(ok(X1), ok(X2)) → ok(and(X1, X2))
plus(ok(X1), ok(X2)) → ok(plus(X1, X2))
s(ok(X)) → ok(s(X))
top(mark(X)) → top(proper(X))
top(ok(X)) → top(active(X))
Q is empty.