YES(?,O(n^1)) 724.48/237.60 YES(?,O(n^1)) 724.48/237.60 724.48/237.60 We are left with following problem, upon which TcT provides the 724.48/237.60 certificate YES(?,O(n^1)). 724.48/237.60 724.48/237.60 Strict Trs: 724.48/237.60 { active(and(X1, X2)) -> and(active(X1), X2) 724.48/237.60 , active(and(tt(), X)) -> mark(X) 724.48/237.60 , active(plus(X1, X2)) -> plus(X1, active(X2)) 724.48/237.60 , active(plus(X1, X2)) -> plus(active(X1), X2) 724.48/237.60 , active(plus(N, 0())) -> mark(N) 724.48/237.60 , active(plus(N, s(M))) -> mark(s(plus(N, M))) 724.48/237.60 , active(s(X)) -> s(active(X)) 724.48/237.60 , and(mark(X1), X2) -> mark(and(X1, X2)) 724.48/237.60 , and(ok(X1), ok(X2)) -> ok(and(X1, X2)) 724.48/237.60 , plus(X1, mark(X2)) -> mark(plus(X1, X2)) 724.48/237.60 , plus(mark(X1), X2) -> mark(plus(X1, X2)) 724.48/237.60 , plus(ok(X1), ok(X2)) -> ok(plus(X1, X2)) 724.48/237.60 , s(mark(X)) -> mark(s(X)) 724.48/237.60 , s(ok(X)) -> ok(s(X)) 724.48/237.60 , proper(and(X1, X2)) -> and(proper(X1), proper(X2)) 724.48/237.60 , proper(tt()) -> ok(tt()) 724.48/237.60 , proper(plus(X1, X2)) -> plus(proper(X1), proper(X2)) 724.48/237.60 , proper(0()) -> ok(0()) 724.48/237.60 , proper(s(X)) -> s(proper(X)) 724.48/237.60 , top(mark(X)) -> top(proper(X)) 724.48/237.60 , top(ok(X)) -> top(active(X)) } 724.48/237.60 Obligation: 724.48/237.60 innermost runtime complexity 724.48/237.60 Answer: 724.48/237.60 YES(?,O(n^1)) 724.48/237.60 724.48/237.60 The problem is match-bounded by 2. The enriched problem is 724.48/237.60 compatible with the following automaton. 724.48/237.60 { active_0(3) -> 1 724.48/237.60 , active_0(4) -> 1 724.48/237.60 , active_0(6) -> 1 724.48/237.60 , active_0(9) -> 1 724.48/237.60 , active_1(3) -> 15 724.48/237.60 , active_1(4) -> 15 724.48/237.60 , active_1(6) -> 15 724.48/237.60 , active_1(9) -> 15 724.48/237.60 , active_2(14) -> 16 724.48/237.60 , and_0(3, 3) -> 2 724.48/237.60 , and_0(3, 4) -> 2 724.48/237.60 , and_0(3, 6) -> 2 724.48/237.60 , and_0(3, 9) -> 2 724.48/237.60 , and_0(4, 3) -> 2 724.48/237.60 , and_0(4, 4) -> 2 724.48/237.60 , and_0(4, 6) -> 2 724.48/237.60 , and_0(4, 9) -> 2 724.48/237.60 , and_0(6, 3) -> 2 724.48/237.60 , and_0(6, 4) -> 2 724.48/237.60 , and_0(6, 6) -> 2 724.48/237.60 , and_0(6, 9) -> 2 724.48/237.60 , and_0(9, 3) -> 2 724.48/237.60 , and_0(9, 4) -> 2 724.48/237.60 , and_0(9, 6) -> 2 724.48/237.60 , and_0(9, 9) -> 2 724.48/237.60 , and_1(3, 3) -> 11 724.48/237.60 , and_1(3, 4) -> 11 724.48/237.60 , and_1(3, 6) -> 11 724.48/237.60 , and_1(3, 9) -> 11 724.48/237.60 , and_1(4, 3) -> 11 724.48/237.60 , and_1(4, 4) -> 11 724.48/237.60 , and_1(4, 6) -> 11 724.48/237.60 , and_1(4, 9) -> 11 724.48/237.60 , and_1(6, 3) -> 11 724.48/237.60 , and_1(6, 4) -> 11 724.48/237.60 , and_1(6, 6) -> 11 724.48/237.60 , and_1(6, 9) -> 11 724.48/237.60 , and_1(9, 3) -> 11 724.48/237.60 , and_1(9, 4) -> 11 724.48/237.60 , and_1(9, 6) -> 11 724.48/237.60 , and_1(9, 9) -> 11 724.48/237.60 , tt_0() -> 3 724.48/237.60 , tt_1() -> 14 724.48/237.60 , mark_0(3) -> 4 724.48/237.60 , mark_0(4) -> 4 724.48/237.60 , mark_0(6) -> 4 724.48/237.60 , mark_0(9) -> 4 724.48/237.60 , mark_1(11) -> 2 724.48/237.60 , mark_1(11) -> 11 724.48/237.60 , mark_1(12) -> 5 724.48/237.60 , mark_1(12) -> 12 724.48/237.60 , mark_1(13) -> 7 724.48/237.60 , mark_1(13) -> 13 724.48/237.60 , plus_0(3, 3) -> 5 724.48/237.60 , plus_0(3, 4) -> 5 724.48/237.60 , plus_0(3, 6) -> 5 724.48/237.60 , plus_0(3, 9) -> 5 724.48/237.60 , plus_0(4, 3) -> 5 724.48/237.60 , plus_0(4, 4) -> 5 724.48/237.60 , plus_0(4, 6) -> 5 724.48/237.60 , plus_0(4, 9) -> 5 724.48/237.60 , plus_0(6, 3) -> 5 724.48/237.60 , plus_0(6, 4) -> 5 724.48/237.60 , plus_0(6, 6) -> 5 724.48/237.60 , plus_0(6, 9) -> 5 724.48/237.60 , plus_0(9, 3) -> 5 724.48/237.60 , plus_0(9, 4) -> 5 724.48/237.60 , plus_0(9, 6) -> 5 724.48/237.60 , plus_0(9, 9) -> 5 724.48/237.60 , plus_1(3, 3) -> 12 724.48/237.60 , plus_1(3, 4) -> 12 724.48/237.60 , plus_1(3, 6) -> 12 724.48/237.60 , plus_1(3, 9) -> 12 724.48/237.60 , plus_1(4, 3) -> 12 724.48/237.60 , plus_1(4, 4) -> 12 724.48/237.60 , plus_1(4, 6) -> 12 724.48/237.60 , plus_1(4, 9) -> 12 724.48/237.60 , plus_1(6, 3) -> 12 724.48/237.60 , plus_1(6, 4) -> 12 724.48/237.60 , plus_1(6, 6) -> 12 724.48/237.60 , plus_1(6, 9) -> 12 724.48/237.60 , plus_1(9, 3) -> 12 724.48/237.60 , plus_1(9, 4) -> 12 724.48/237.60 , plus_1(9, 6) -> 12 724.48/237.60 , plus_1(9, 9) -> 12 724.48/237.60 , 0_0() -> 6 724.48/237.60 , 0_1() -> 14 724.48/237.60 , s_0(3) -> 7 724.48/237.60 , s_0(4) -> 7 724.48/237.60 , s_0(6) -> 7 724.48/237.60 , s_0(9) -> 7 724.48/237.60 , s_1(3) -> 13 724.48/237.60 , s_1(4) -> 13 724.48/237.60 , s_1(6) -> 13 724.48/237.60 , s_1(9) -> 13 724.48/237.60 , proper_0(3) -> 8 724.48/237.60 , proper_0(4) -> 8 724.48/237.60 , proper_0(6) -> 8 724.48/237.60 , proper_0(9) -> 8 724.48/237.60 , proper_1(3) -> 15 724.48/237.60 , proper_1(4) -> 15 724.48/237.60 , proper_1(6) -> 15 724.48/237.61 , proper_1(9) -> 15 724.48/237.61 , ok_0(3) -> 9 724.48/237.61 , ok_0(4) -> 9 724.48/237.61 , ok_0(6) -> 9 724.48/237.61 , ok_0(9) -> 9 724.48/237.61 , ok_1(11) -> 2 724.48/237.61 , ok_1(11) -> 11 724.48/237.61 , ok_1(12) -> 5 724.48/237.61 , ok_1(12) -> 12 724.48/237.61 , ok_1(13) -> 7 724.48/237.61 , ok_1(13) -> 13 724.48/237.61 , ok_1(14) -> 8 724.48/237.61 , ok_1(14) -> 15 724.48/237.61 , top_0(3) -> 10 724.48/237.61 , top_0(4) -> 10 724.48/237.61 , top_0(6) -> 10 724.48/237.61 , top_0(9) -> 10 724.48/237.61 , top_1(15) -> 10 724.48/237.61 , top_2(16) -> 10 } 724.48/237.61 724.48/237.61 Hurray, we answered YES(?,O(n^1)) 724.48/237.63 EOF