Strategy:

innermost rewriting

Signature: {active/1, f/1, 0/0, mark/1, cons/2, s/1, p/1, proper/1, ok/1, top/1}

Rules:

active(f(0))	→	mark(cons(0,f(s(0))))
active(f(s(0)))	→	mark(f(p(s(0))))
active(p(s(X)))	→	mark(X)
active(f(X))	→	f(active(X))
active(cons(X1,X2))	→	cons(active(X1),X2)
active(s(X))	→	s(active(X))
active(p(X))	→	p(active(X))
f(mark(X))	→	mark(f(X))
cons(mark(X1),X2)	→	mark(cons(X1,X2))
s(mark(X))	→	mark(s(X))
p(mark(X))	→	mark(p(X))
proper(f(X))	→	f(proper(X))
proper(0)	→	ok(0)
proper(cons(X1,X2))	→	cons(proper(X1),proper(X2))
proper(s(X))	→	s(proper(X))
proper(p(X))	→	p(proper(X))
f(ok(X))	→	ok(f(X))
cons(ok(X1),ok(X2))	→	ok(cons(X1,X2))
s(ok(X))	→	ok(s(X))
p(ok(X))	→	ok(p(X))
top(mark(X))	→	top(proper(X))
top(ok(X))	→	top(active(X))