YES(?,O(n^1)) 1158.50/299.51 YES(?,O(n^1)) 1158.50/299.51 1158.50/299.51 We are left with following problem, upon which TcT provides the 1158.50/299.51 certificate YES(?,O(n^1)). 1158.50/299.51 1158.50/299.51 Strict Trs: 1158.50/299.51 { 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1)))))))))) 1158.50/299.51 , 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) } 1158.50/299.51 Obligation: 1158.50/299.51 derivational complexity 1158.50/299.51 Answer: 1158.50/299.51 YES(?,O(n^1)) 1158.50/299.51 1158.50/299.51 The problem is match-bounded by 3. The enriched problem is 1158.50/299.51 compatible with the following automaton. 1158.50/299.51 { 0_0(1) -> 1 1158.50/299.51 , 0_1(6) -> 5 1158.50/299.51 , 0_1(9) -> 8 1158.50/299.51 , 0_2(26) -> 25 1158.50/299.51 , 0_2(29) -> 28 1158.50/299.51 , 0_2(32) -> 31 1158.50/299.51 , 0_3(47) -> 46 1158.50/299.51 , 0_3(50) -> 49 1158.50/299.51 , 0_3(53) -> 52 1158.50/299.51 , 0_3(59) -> 58 1158.50/299.51 , 0_3(62) -> 61 1158.50/299.51 , 0_3(68) -> 67 1158.50/299.51 , 0_3(71) -> 70 1158.50/299.51 , 0_3(74) -> 73 1158.50/299.51 , 1_0(1) -> 1 1158.50/299.51 , 1_1(2) -> 1 1158.50/299.51 , 1_1(2) -> 8 1158.50/299.51 , 1_1(4) -> 3 1158.50/299.51 , 1_1(5) -> 4 1158.50/299.51 , 1_1(7) -> 6 1158.50/299.51 , 1_1(10) -> 9 1158.50/299.51 , 1_2(22) -> 5 1158.50/299.51 , 1_2(22) -> 8 1158.50/299.51 , 1_2(24) -> 23 1158.50/299.51 , 1_2(25) -> 24 1158.50/299.51 , 1_2(27) -> 26 1158.50/299.51 , 1_2(28) -> 36 1158.50/299.51 , 1_2(30) -> 29 1158.50/299.51 , 1_2(33) -> 32 1158.50/299.51 , 1_2(34) -> 5 1158.50/299.51 , 1_2(34) -> 8 1158.50/299.51 , 1_2(36) -> 35 1158.50/299.51 , 1_3(43) -> 31 1158.50/299.51 , 1_3(45) -> 44 1158.50/299.51 , 1_3(46) -> 45 1158.50/299.51 , 1_3(48) -> 47 1158.50/299.51 , 1_3(49) -> 45 1158.50/299.51 , 1_3(51) -> 50 1158.50/299.51 , 1_3(54) -> 53 1158.50/299.51 , 1_3(55) -> 28 1158.50/299.51 , 1_3(57) -> 56 1158.50/299.51 , 1_3(58) -> 57 1158.50/299.51 , 1_3(60) -> 59 1158.50/299.51 , 1_3(63) -> 62 1158.50/299.51 , 1_3(64) -> 25 1158.50/299.51 , 1_3(66) -> 65 1158.50/299.51 , 1_3(67) -> 66 1158.50/299.51 , 1_3(69) -> 68 1158.50/299.51 , 1_3(70) -> 66 1158.50/299.51 , 1_3(72) -> 71 1158.50/299.51 , 1_3(75) -> 74 1158.50/299.51 , 2_0(1) -> 1 1158.50/299.51 , 2_1(1) -> 10 1158.50/299.51 , 2_1(2) -> 7 1158.50/299.51 , 2_1(3) -> 2 1158.50/299.51 , 2_1(4) -> 7 1158.50/299.51 , 2_1(5) -> 7 1158.50/299.51 , 2_1(8) -> 7 1158.50/299.51 , 2_2(2) -> 33 1158.50/299.51 , 2_2(5) -> 33 1158.50/299.51 , 2_2(22) -> 33 1158.50/299.51 , 2_2(23) -> 22 1158.50/299.51 , 2_2(28) -> 27 1158.50/299.51 , 2_2(31) -> 30 1158.50/299.51 , 2_2(34) -> 33 1158.50/299.51 , 2_2(35) -> 34 1158.50/299.51 , 2_3(22) -> 51 1158.50/299.51 , 2_3(34) -> 54 1158.50/299.51 , 2_3(43) -> 63 1158.50/299.51 , 2_3(44) -> 43 1158.50/299.51 , 2_3(46) -> 48 1158.50/299.51 , 2_3(49) -> 48 1158.50/299.51 , 2_3(52) -> 51 1158.50/299.51 , 2_3(55) -> 75 1158.50/299.51 , 2_3(56) -> 55 1158.50/299.51 , 2_3(58) -> 60 1158.50/299.51 , 2_3(61) -> 60 1158.50/299.51 , 2_3(65) -> 64 1158.50/299.51 , 2_3(70) -> 69 1158.50/299.51 , 2_3(73) -> 72 } 1158.50/299.51 1158.50/299.51 Hurray, we answered YES(?,O(n^1)) 1159.05/300.07 EOF