MAYBE
0.17/0.22	MAYBE
0.17/0.22	
0.17/0.22	Problem:
0.17/0.22	 active(terms(N)) -> mark(cons(recip(sqr(N)),terms(s(N))))
0.17/0.22	 active(sqr(0())) -> mark(0())
0.17/0.22	 active(sqr(s(X))) -> mark(s(add(sqr(X),dbl(X))))
0.17/0.22	 active(dbl(0())) -> mark(0())
0.17/0.22	 active(dbl(s(X))) -> mark(s(s(dbl(X))))
0.17/0.22	 active(add(0(),X)) -> mark(X)
0.17/0.22	 active(add(s(X),Y)) -> mark(s(add(X,Y)))
0.17/0.22	 active(first(0(),X)) -> mark(nil())
0.17/0.22	 active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
0.17/0.22	 active(half(0())) -> mark(0())
0.17/0.22	 active(half(s(0()))) -> mark(0())
0.17/0.22	 active(half(s(s(X)))) -> mark(s(half(X)))
0.17/0.22	 active(half(dbl(X))) -> mark(X)
0.17/0.22	 active(terms(X)) -> terms(active(X))
0.17/0.22	 active(cons(X1,X2)) -> cons(active(X1),X2)
0.17/0.22	 active(recip(X)) -> recip(active(X))
0.17/0.22	 active(sqr(X)) -> sqr(active(X))
0.17/0.22	 active(s(X)) -> s(active(X))
0.17/0.22	 active(add(X1,X2)) -> add(active(X1),X2)
0.17/0.22	 active(add(X1,X2)) -> add(X1,active(X2))
0.17/0.22	 active(dbl(X)) -> dbl(active(X))
0.17/0.22	 active(first(X1,X2)) -> first(active(X1),X2)
0.17/0.22	 active(first(X1,X2)) -> first(X1,active(X2))
0.17/0.22	 active(half(X)) -> half(active(X))
0.17/0.22	 terms(mark(X)) -> mark(terms(X))
0.17/0.22	 cons(mark(X1),X2) -> mark(cons(X1,X2))
0.17/0.23	 recip(mark(X)) -> mark(recip(X))
0.17/0.23	 sqr(mark(X)) -> mark(sqr(X))
0.17/0.23	 s(mark(X)) -> mark(s(X))
0.17/0.23	 add(mark(X1),X2) -> mark(add(X1,X2))
0.17/0.23	 add(X1,mark(X2)) -> mark(add(X1,X2))
0.17/0.23	 dbl(mark(X)) -> mark(dbl(X))
0.17/0.23	 first(mark(X1),X2) -> mark(first(X1,X2))
0.17/0.23	 first(X1,mark(X2)) -> mark(first(X1,X2))
0.17/0.23	 half(mark(X)) -> mark(half(X))
0.17/0.23	 proper(terms(X)) -> terms(proper(X))
0.17/0.23	 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
0.17/0.23	 proper(recip(X)) -> recip(proper(X))
0.17/0.23	 proper(sqr(X)) -> sqr(proper(X))
0.17/0.23	 proper(s(X)) -> s(proper(X))
0.17/0.23	 proper(0()) -> ok(0())
0.17/0.23	 proper(add(X1,X2)) -> add(proper(X1),proper(X2))
0.17/0.23	 proper(dbl(X)) -> dbl(proper(X))
0.17/0.23	 proper(first(X1,X2)) -> first(proper(X1),proper(X2))
0.17/0.23	 proper(nil()) -> ok(nil())
0.17/0.23	 proper(half(X)) -> half(proper(X))
0.17/0.23	 terms(ok(X)) -> ok(terms(X))
0.17/0.23	 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
0.17/0.23	 recip(ok(X)) -> ok(recip(X))
0.17/0.23	 sqr(ok(X)) -> ok(sqr(X))
0.17/0.23	 s(ok(X)) -> ok(s(X))
0.17/0.23	 add(ok(X1),ok(X2)) -> ok(add(X1,X2))
0.17/0.23	 dbl(ok(X)) -> ok(dbl(X))
0.17/0.23	 first(ok(X1),ok(X2)) -> ok(first(X1,X2))
0.17/0.23	 half(ok(X)) -> ok(half(X))
0.17/0.23	 top(mark(X)) -> top(proper(X))
0.17/0.23	 top(ok(X)) -> top(active(X))
0.17/0.23	
0.17/0.23	Proof:
0.17/0.23	 Open
0.17/0.23	EOF