YES(?,O(n^1)) 792.17/261.05 YES(?,O(n^1)) 792.17/261.05 792.17/261.05 We are left with following problem, upon which TcT provides the 792.17/261.05 certificate YES(?,O(n^1)). 792.17/261.05 792.17/261.05 Strict Trs: 792.17/261.05 { active(__(X1, X2)) -> __(X1, active(X2)) 792.17/261.05 , active(__(X1, X2)) -> __(active(X1), X2) 792.17/261.05 , active(__(X, nil())) -> mark(X) 792.17/261.05 , active(__(__(X, Y), Z)) -> mark(__(X, __(Y, Z))) 792.17/261.05 , active(__(nil(), X)) -> mark(X) 792.17/261.05 , active(and(X1, X2)) -> and(active(X1), X2) 792.17/261.05 , active(and(tt(), X)) -> mark(X) 792.17/261.05 , active(isNePal(X)) -> isNePal(active(X)) 792.17/261.05 , active(isNePal(__(I, __(P, I)))) -> mark(tt()) 792.17/261.05 , __(X1, mark(X2)) -> mark(__(X1, X2)) 792.17/261.05 , __(mark(X1), X2) -> mark(__(X1, X2)) 792.17/261.05 , __(ok(X1), ok(X2)) -> ok(__(X1, X2)) 792.17/261.05 , and(mark(X1), X2) -> mark(and(X1, X2)) 792.17/261.05 , and(ok(X1), ok(X2)) -> ok(and(X1, X2)) 792.17/261.05 , isNePal(mark(X)) -> mark(isNePal(X)) 792.17/261.05 , isNePal(ok(X)) -> ok(isNePal(X)) 792.17/261.05 , proper(__(X1, X2)) -> __(proper(X1), proper(X2)) 792.17/261.05 , proper(nil()) -> ok(nil()) 792.17/261.05 , proper(and(X1, X2)) -> and(proper(X1), proper(X2)) 792.17/261.05 , proper(tt()) -> ok(tt()) 792.17/261.05 , proper(isNePal(X)) -> isNePal(proper(X)) 792.17/261.05 , top(mark(X)) -> top(proper(X)) 792.17/261.05 , top(ok(X)) -> top(active(X)) } 792.17/261.05 Obligation: 792.17/261.05 innermost runtime complexity 792.17/261.05 Answer: 792.17/261.05 YES(?,O(n^1)) 792.17/261.05 792.17/261.05 The problem is match-bounded by 2. The enriched problem is 792.17/261.05 compatible with the following automaton. 792.17/261.05 { active_0(3) -> 1 792.17/261.05 , active_0(4) -> 1 792.17/261.05 , active_0(6) -> 1 792.17/261.05 , active_0(9) -> 1 792.17/261.05 , active_1(3) -> 15 792.17/261.05 , active_1(4) -> 15 792.17/261.05 , active_1(6) -> 15 792.17/261.05 , active_1(9) -> 15 792.17/261.05 , active_2(14) -> 16 792.17/261.05 , ___0(3, 3) -> 2 792.17/261.05 , ___0(3, 4) -> 2 792.17/261.05 , ___0(3, 6) -> 2 792.17/261.05 , ___0(3, 9) -> 2 792.17/261.05 , ___0(4, 3) -> 2 792.17/261.05 , ___0(4, 4) -> 2 792.17/261.05 , ___0(4, 6) -> 2 792.17/261.05 , ___0(4, 9) -> 2 792.17/261.05 , ___0(6, 3) -> 2 792.17/261.05 , ___0(6, 4) -> 2 792.17/261.05 , ___0(6, 6) -> 2 792.17/261.05 , ___0(6, 9) -> 2 792.17/261.05 , ___0(9, 3) -> 2 792.17/261.05 , ___0(9, 4) -> 2 792.17/261.05 , ___0(9, 6) -> 2 792.17/261.05 , ___0(9, 9) -> 2 792.17/261.05 , ___1(3, 3) -> 11 792.17/261.05 , ___1(3, 4) -> 11 792.17/261.05 , ___1(3, 6) -> 11 792.17/261.05 , ___1(3, 9) -> 11 792.17/261.05 , ___1(4, 3) -> 11 792.17/261.05 , ___1(4, 4) -> 11 792.17/261.05 , ___1(4, 6) -> 11 792.17/261.05 , ___1(4, 9) -> 11 792.17/261.05 , ___1(6, 3) -> 11 792.17/261.05 , ___1(6, 4) -> 11 792.17/261.05 , ___1(6, 6) -> 11 792.17/261.05 , ___1(6, 9) -> 11 792.17/261.05 , ___1(9, 3) -> 11 792.17/261.05 , ___1(9, 4) -> 11 792.17/261.05 , ___1(9, 6) -> 11 792.17/261.05 , ___1(9, 9) -> 11 792.17/261.05 , mark_0(3) -> 3 792.17/261.05 , mark_0(4) -> 3 792.17/261.05 , mark_0(6) -> 3 792.17/261.05 , mark_0(9) -> 3 792.17/261.05 , mark_1(11) -> 2 792.17/261.05 , mark_1(11) -> 11 792.17/261.05 , mark_1(12) -> 5 792.17/261.05 , mark_1(12) -> 12 792.17/261.05 , mark_1(13) -> 7 792.17/261.05 , mark_1(13) -> 13 792.17/261.05 , nil_0() -> 4 792.17/261.05 , nil_1() -> 14 792.17/261.05 , and_0(3, 3) -> 5 792.17/261.05 , and_0(3, 4) -> 5 792.17/261.05 , and_0(3, 6) -> 5 792.17/261.05 , and_0(3, 9) -> 5 792.17/261.05 , and_0(4, 3) -> 5 792.17/261.05 , and_0(4, 4) -> 5 792.17/261.05 , and_0(4, 6) -> 5 792.17/261.05 , and_0(4, 9) -> 5 792.17/261.05 , and_0(6, 3) -> 5 792.17/261.05 , and_0(6, 4) -> 5 792.17/261.05 , and_0(6, 6) -> 5 792.17/261.05 , and_0(6, 9) -> 5 792.17/261.05 , and_0(9, 3) -> 5 792.17/261.05 , and_0(9, 4) -> 5 792.17/261.05 , and_0(9, 6) -> 5 792.17/261.05 , and_0(9, 9) -> 5 792.17/261.05 , and_1(3, 3) -> 12 792.17/261.05 , and_1(3, 4) -> 12 792.17/261.05 , and_1(3, 6) -> 12 792.17/261.05 , and_1(3, 9) -> 12 792.17/261.05 , and_1(4, 3) -> 12 792.17/261.05 , and_1(4, 4) -> 12 792.17/261.05 , and_1(4, 6) -> 12 792.17/261.05 , and_1(4, 9) -> 12 792.17/261.05 , and_1(6, 3) -> 12 792.17/261.05 , and_1(6, 4) -> 12 792.17/261.05 , and_1(6, 6) -> 12 792.17/261.05 , and_1(6, 9) -> 12 792.17/261.05 , and_1(9, 3) -> 12 792.17/261.05 , and_1(9, 4) -> 12 792.17/261.05 , and_1(9, 6) -> 12 792.17/261.05 , and_1(9, 9) -> 12 792.17/261.05 , tt_0() -> 6 792.17/261.05 , tt_1() -> 14 792.17/261.05 , isNePal_0(3) -> 7 792.17/261.05 , isNePal_0(4) -> 7 792.17/261.05 , isNePal_0(6) -> 7 792.17/261.05 , isNePal_0(9) -> 7 792.17/261.05 , isNePal_1(3) -> 13 792.17/261.05 , isNePal_1(4) -> 13 792.17/261.05 , isNePal_1(6) -> 13 792.17/261.05 , isNePal_1(9) -> 13 792.17/261.05 , proper_0(3) -> 8 792.17/261.05 , proper_0(4) -> 8 792.17/261.05 , proper_0(6) -> 8 792.17/261.05 , proper_0(9) -> 8 792.17/261.05 , proper_1(3) -> 15 792.17/261.05 , proper_1(4) -> 15 792.17/261.05 , proper_1(6) -> 15 792.17/261.05 , proper_1(9) -> 15 792.17/261.05 , ok_0(3) -> 9 792.17/261.05 , ok_0(4) -> 9 792.17/261.05 , ok_0(6) -> 9 792.17/261.05 , ok_0(9) -> 9 792.17/261.05 , ok_1(11) -> 2 792.17/261.05 , ok_1(11) -> 11 792.17/261.05 , ok_1(12) -> 5 792.17/261.05 , ok_1(12) -> 12 792.17/261.05 , ok_1(13) -> 7 792.17/261.05 , ok_1(13) -> 13 792.17/261.05 , ok_1(14) -> 8 792.17/261.05 , ok_1(14) -> 15 792.17/261.05 , top_0(3) -> 10 792.17/261.05 , top_0(4) -> 10 792.17/261.05 , top_0(6) -> 10 792.17/261.05 , top_0(9) -> 10 792.17/261.05 , top_1(15) -> 10 792.17/261.05 , top_2(16) -> 10 } 792.17/261.05 792.17/261.05 Hurray, we answered YES(?,O(n^1)) 792.17/261.06 EOF