YES(?,O(n^1)) 1093.43/297.08 YES(?,O(n^1)) 1093.43/297.08 1093.43/297.08 We are left with following problem, upon which TcT provides the 1093.43/297.08 certificate YES(?,O(n^1)). 1093.43/297.08 1093.43/297.08 Strict Trs: 1093.43/297.08 { 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1)))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 1093.43/297.08 , 0(1(2(1(x1)))) -> 1093.43/297.08 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) } 1093.43/297.08 Obligation: 1093.43/297.08 derivational complexity 1093.43/297.08 Answer: 1093.43/297.08 YES(?,O(n^1)) 1093.43/297.08 1093.43/297.08 The problem is match-bounded by 3. The enriched problem is 1093.43/297.08 compatible with the following automaton. 1093.43/297.08 { 0_0(1) -> 1 1093.43/297.08 , 0_0(2) -> 1 1093.43/297.08 , 0_0(3) -> 1 1093.43/297.08 , 0_1(8) -> 7 1093.43/297.08 , 0_1(11) -> 10 1093.43/297.08 , 0_2(36) -> 35 1093.43/297.08 , 0_2(39) -> 38 1093.43/297.08 , 0_2(42) -> 41 1093.43/297.08 , 0_2(48) -> 47 1093.43/297.08 , 0_3(60) -> 59 1093.43/297.08 , 0_3(63) -> 62 1093.43/297.08 , 0_3(66) -> 65 1093.43/297.08 , 0_3(69) -> 68 1093.43/297.08 , 0_3(72) -> 71 1093.43/297.08 , 0_3(78) -> 77 1093.43/297.08 , 0_3(81) -> 80 1093.43/297.08 , 0_3(84) -> 83 1093.43/297.08 , 0_3(87) -> 86 1093.43/297.08 , 0_3(90) -> 89 1093.43/297.08 , 0_3(93) -> 92 1093.43/297.08 , 0_3(99) -> 98 1093.43/297.08 , 0_3(102) -> 101 1093.43/297.08 , 0_3(105) -> 104 1093.43/297.08 , 0_3(108) -> 107 1093.43/297.08 , 0_3(111) -> 110 1093.43/297.08 , 0_3(114) -> 113 1093.43/297.08 , 0_3(117) -> 116 1093.43/297.08 , 0_3(123) -> 122 1093.43/297.08 , 0_3(126) -> 125 1093.43/297.08 , 0_3(129) -> 128 1093.43/297.08 , 0_3(132) -> 131 1093.43/297.08 , 0_3(135) -> 134 1093.43/297.08 , 0_3(138) -> 137 1093.43/297.08 , 0_3(141) -> 140 1093.43/297.08 , 0_3(144) -> 143 1093.43/297.08 , 1_0(1) -> 2 1093.43/297.08 , 1_0(2) -> 2 1093.43/297.08 , 1_0(3) -> 2 1093.43/297.08 , 1_1(4) -> 1 1093.43/297.08 , 1_1(4) -> 10 1093.43/297.08 , 1_1(6) -> 5 1093.43/297.08 , 1_1(7) -> 6 1093.43/297.08 , 1_1(9) -> 8 1093.43/297.08 , 1_1(12) -> 11 1093.43/297.08 , 1_2(32) -> 7 1093.43/297.08 , 1_2(32) -> 10 1093.43/297.08 , 1_2(34) -> 33 1093.43/297.08 , 1_2(35) -> 34 1093.43/297.08 , 1_2(37) -> 36 1093.43/297.08 , 1_2(38) -> 46 1093.43/297.08 , 1_2(40) -> 39 1093.43/297.08 , 1_2(43) -> 42 1093.43/297.08 , 1_2(44) -> 7 1093.43/297.08 , 1_2(44) -> 10 1093.43/297.08 , 1_2(46) -> 45 1093.43/297.08 , 1_2(47) -> 46 1093.43/297.08 , 1_2(49) -> 48 1093.43/297.08 , 1_3(56) -> 41 1093.43/297.08 , 1_3(58) -> 57 1093.43/297.08 , 1_3(59) -> 58 1093.43/297.08 , 1_3(61) -> 60 1093.43/297.08 , 1_3(62) -> 58 1093.43/297.08 , 1_3(64) -> 63 1093.43/297.08 , 1_3(65) -> 58 1093.43/297.08 , 1_3(67) -> 66 1093.43/297.08 , 1_3(68) -> 58 1093.43/297.08 , 1_3(70) -> 69 1093.43/297.08 , 1_3(73) -> 72 1093.43/297.08 , 1_3(74) -> 38 1093.43/297.08 , 1_3(76) -> 75 1093.43/297.08 , 1_3(77) -> 76 1093.43/297.08 , 1_3(79) -> 78 1093.43/297.08 , 1_3(80) -> 76 1093.43/297.08 , 1_3(82) -> 81 1093.43/297.08 , 1_3(83) -> 76 1093.43/297.08 , 1_3(85) -> 84 1093.43/297.08 , 1_3(86) -> 76 1093.43/297.08 , 1_3(88) -> 87 1093.43/297.08 , 1_3(89) -> 76 1093.43/297.08 , 1_3(91) -> 90 1093.43/297.08 , 1_3(94) -> 93 1093.43/297.08 , 1_3(95) -> 35 1093.43/297.08 , 1_3(97) -> 96 1093.43/297.08 , 1_3(98) -> 97 1093.43/297.08 , 1_3(100) -> 99 1093.43/297.08 , 1_3(101) -> 97 1093.43/297.08 , 1_3(103) -> 102 1093.43/297.08 , 1_3(104) -> 97 1093.43/297.08 , 1_3(106) -> 105 1093.43/297.08 , 1_3(107) -> 97 1093.43/297.08 , 1_3(109) -> 108 1093.43/297.08 , 1_3(110) -> 97 1093.43/297.08 , 1_3(112) -> 111 1093.43/297.08 , 1_3(113) -> 97 1093.43/297.08 , 1_3(115) -> 114 1093.43/297.08 , 1_3(118) -> 117 1093.43/297.08 , 1_3(119) -> 47 1093.43/297.08 , 1_3(121) -> 120 1093.43/297.08 , 1_3(122) -> 121 1093.43/297.08 , 1_3(124) -> 123 1093.43/297.08 , 1_3(125) -> 121 1093.43/297.08 , 1_3(127) -> 126 1093.43/297.08 , 1_3(128) -> 121 1093.43/297.08 , 1_3(130) -> 129 1093.43/297.08 , 1_3(131) -> 121 1093.43/297.08 , 1_3(133) -> 132 1093.43/297.08 , 1_3(134) -> 121 1093.43/297.08 , 1_3(136) -> 135 1093.43/297.08 , 1_3(137) -> 121 1093.43/297.08 , 1_3(139) -> 138 1093.43/297.08 , 1_3(140) -> 121 1093.43/297.08 , 1_3(142) -> 141 1093.43/297.08 , 1_3(145) -> 144 1093.43/297.08 , 2_0(1) -> 3 1093.43/297.08 , 2_0(2) -> 3 1093.43/297.08 , 2_0(3) -> 3 1093.43/297.08 , 2_1(1) -> 12 1093.43/297.08 , 2_1(2) -> 12 1093.43/297.08 , 2_1(3) -> 12 1093.43/297.08 , 2_1(4) -> 9 1093.43/297.08 , 2_1(5) -> 4 1093.43/297.08 , 2_1(6) -> 9 1093.43/297.08 , 2_1(7) -> 9 1093.43/297.08 , 2_1(10) -> 9 1093.43/297.08 , 2_2(4) -> 43 1093.43/297.08 , 2_2(7) -> 43 1093.43/297.08 , 2_2(32) -> 43 1093.43/297.08 , 2_2(33) -> 32 1093.43/297.08 , 2_2(35) -> 49 1093.43/297.08 , 2_2(38) -> 37 1093.43/297.08 , 2_2(41) -> 40 1093.43/297.08 , 2_2(44) -> 37 1093.43/297.08 , 2_2(45) -> 44 1093.43/297.08 , 2_2(47) -> 49 1093.43/297.08 , 2_3(32) -> 61 1093.43/297.08 , 2_3(44) -> 73 1093.43/297.08 , 2_3(56) -> 94 1093.43/297.08 , 2_3(57) -> 56 1093.43/297.08 , 2_3(59) -> 61 1093.43/297.08 , 2_3(62) -> 61 1093.43/297.08 , 2_3(65) -> 64 1093.43/297.08 , 2_3(68) -> 67 1093.43/297.08 , 2_3(71) -> 70 1093.43/297.08 , 2_3(74) -> 118 1093.43/297.08 , 2_3(75) -> 74 1093.43/297.08 , 2_3(77) -> 79 1093.43/297.08 , 2_3(80) -> 79 1093.43/297.08 , 2_3(83) -> 82 1093.43/297.08 , 2_3(86) -> 85 1093.43/297.08 , 2_3(89) -> 88 1093.43/297.08 , 2_3(92) -> 91 1093.43/297.08 , 2_3(95) -> 145 1093.43/297.08 , 2_3(96) -> 95 1093.43/297.08 , 2_3(98) -> 100 1093.43/297.08 , 2_3(101) -> 100 1093.43/297.08 , 2_3(104) -> 103 1093.43/297.08 , 2_3(107) -> 106 1093.43/297.08 , 2_3(110) -> 109 1093.43/297.08 , 2_3(113) -> 112 1093.43/297.08 , 2_3(116) -> 115 1093.43/297.08 , 2_3(119) -> 124 1093.43/297.08 , 2_3(120) -> 119 1093.43/297.08 , 2_3(122) -> 124 1093.43/297.08 , 2_3(125) -> 124 1093.43/297.08 , 2_3(128) -> 127 1093.43/297.08 , 2_3(131) -> 130 1093.43/297.08 , 2_3(134) -> 133 1093.43/297.08 , 2_3(137) -> 136 1093.43/297.08 , 2_3(140) -> 139 1093.43/297.08 , 2_3(143) -> 142 } 1093.43/297.08 1093.43/297.08 Hurray, we answered YES(?,O(n^1)) 1094.14/297.50 EOF