YES(?,O(n^1)) 703.35/211.59 YES(?,O(n^1)) 703.35/211.59 703.35/211.59 We are left with following problem, upon which TcT provides the 703.35/211.59 certificate YES(?,O(n^1)). 703.35/211.59 703.35/211.59 Strict Trs: 703.35/211.59 { rec(rec(x)) -> sent(rec(x)) 703.35/211.59 , rec(sent(x)) -> sent(rec(x)) 703.35/211.59 , rec(no(x)) -> sent(rec(x)) 703.35/211.59 , rec(bot()) -> up(sent(bot())) 703.35/211.59 , rec(up(x)) -> up(rec(x)) 703.35/211.59 , sent(up(x)) -> up(sent(x)) 703.35/211.59 , no(up(x)) -> up(no(x)) 703.35/211.59 , top(rec(up(x))) -> top(check(rec(x))) 703.35/211.59 , top(sent(up(x))) -> top(check(rec(x))) 703.35/211.59 , top(no(up(x))) -> top(check(rec(x))) 703.35/211.59 , check(rec(x)) -> rec(check(x)) 703.35/211.59 , check(sent(x)) -> sent(check(x)) 703.35/211.59 , check(no(x)) -> no(x) 703.35/211.59 , check(no(x)) -> no(check(x)) 703.35/211.59 , check(up(x)) -> up(check(x)) } 703.35/211.59 Obligation: 703.35/211.59 runtime complexity 703.35/211.59 Answer: 703.35/211.59 YES(?,O(n^1)) 703.35/211.59 703.35/211.59 The problem is match-bounded by 1. The enriched problem is 703.35/211.59 compatible with the following automaton. 703.35/211.59 { rec_0(2) -> 1 703.35/211.59 , rec_1(2) -> 3 703.35/211.59 , sent_0(2) -> 1 703.35/211.59 , sent_1(2) -> 3 703.35/211.59 , sent_1(4) -> 3 703.35/211.59 , no_0(2) -> 1 703.35/211.59 , no_1(2) -> 3 703.35/211.59 , bot_0() -> 2 703.35/211.59 , bot_1() -> 4 703.35/211.59 , up_0(2) -> 2 703.35/211.59 , up_1(3) -> 1 703.35/211.59 , up_1(3) -> 3 703.35/211.59 , top_0(2) -> 1 703.35/211.59 , check_0(2) -> 1 703.35/211.59 , check_1(2) -> 3 } 703.35/211.59 703.35/211.59 Hurray, we answered YES(?,O(n^1)) 703.61/211.73 EOF