YES(?,O(n^1)) 1137.85/298.26 YES(?,O(n^1)) 1137.85/298.26 1137.85/298.26 We are left with following problem, upon which TcT provides the 1137.85/298.26 certificate YES(?,O(n^1)). 1137.85/298.26 1137.85/298.26 Strict Trs: 1137.85/298.26 { 0(0(0(0(0(x1))))) -> 2(0(2(0(x1)))) 1137.85/298.26 , 0(1(2(2(x1)))) -> 0(1(0(1(x1)))) 1137.85/298.26 , 0(5(3(2(4(0(2(1(2(3(3(4(3(3(x1)))))))))))))) -> 1137.85/298.26 0(5(4(4(5(3(4(0(1(0(1(3(1(2(3(x1))))))))))))))) 1137.85/298.26 , 1(0(1(3(5(5(1(2(5(2(3(5(4(x1))))))))))))) -> 1137.85/298.26 1(0(3(4(1(2(3(4(5(3(3(5(4(x1))))))))))))) 1137.85/298.26 , 1(4(1(0(4(1(2(2(5(3(x1)))))))))) -> 1(4(4(2(5(3(1(5(2(x1))))))))) 1137.85/298.26 , 1(4(2(3(1(4(0(2(1(1(x1)))))))))) -> 1137.85/298.26 1(1(4(1(0(4(2(3(2(1(x1)))))))))) 1137.85/298.26 , 1(4(4(2(5(3(1(5(1(2(1(5(0(x1))))))))))))) -> 1137.85/298.26 3(5(2(5(4(1(5(2(4(1(3(2(x1)))))))))))) 1137.85/298.26 , 2(3(2(4(3(2(3(4(4(0(0(0(x1)))))))))))) -> 1137.85/298.26 2(4(2(0(2(2(2(2(4(3(0(x1))))))))))) 1137.85/298.26 , 2(5(1(2(4(5(1(3(1(5(x1)))))))))) -> 2(4(3(0(3(4(2(4(5(x1))))))))) 1137.85/298.26 , 3(1(5(4(1(2(0(0(1(0(0(0(2(0(4(5(x1)))))))))))))))) -> 1137.85/298.26 3(0(2(2(3(3(1(3(2(2(1(2(2(5(5(x1))))))))))))))) 1137.85/298.26 , 3(2(3(4(0(4(1(0(x1)))))))) -> 2(3(2(2(5(3(1(x1))))))) 1137.85/298.26 , 4(0(2(2(4(4(1(1(1(1(0(4(1(5(1(2(0(1(x1)))))))))))))))))) -> 1137.85/298.26 4(5(5(2(5(0(2(1(5(2(4(1(1(1(5(3(2(x1))))))))))))))))) 1137.85/298.26 , 4(1(1(0(5(4(2(0(4(0(5(1(2(0(3(1(x1)))))))))))))))) -> 1137.85/298.26 2(4(3(1(4(1(4(0(1(1(0(5(4(0(5(0(x1)))))))))))))))) 1137.85/298.26 , 4(1(2(5(1(1(0(0(5(4(1(3(1(x1))))))))))))) -> 1137.85/298.26 4(1(1(2(2(3(5(1(4(2(3(1(x1)))))))))))) 1137.85/298.26 , 4(3(0(5(5(2(5(2(3(5(3(0(2(2(4(x1))))))))))))))) -> 1137.85/298.26 4(3(3(4(3(1(4(1(5(0(0(5(1(5(3(4(x1)))))))))))))))) 1137.85/298.26 , 4(4(4(4(3(1(1(3(3(4(2(2(4(0(3(5(4(2(5(2(3(x1))))))))))))))))))))) 1137.85/298.26 -> 2(5(5(4(0(1(5(3(3(5(0(1(5(1(5(4(2(4(2(2(x1)))))))))))))))))))) 1137.85/298.26 , 5(0(2(4(2(4(1(4(4(5(1(4(x1)))))))))))) -> 1137.85/298.26 1(4(5(3(3(2(3(2(3(3(4(x1))))))))))) 1137.85/298.26 , 5(5(3(2(0(3(4(0(0(3(1(4(3(x1))))))))))))) -> 1137.85/298.26 5(5(3(5(0(3(1(5(2(3(1(3(4(x1))))))))))))) } 1137.85/298.26 Obligation: 1137.85/298.26 derivational complexity 1137.85/298.26 Answer: 1137.85/298.26 YES(?,O(n^1)) 1137.85/298.26 1137.85/298.26 The problem is match-bounded by 1. The enriched problem is 1137.85/298.26 compatible with the following automaton. 1137.85/298.26 { 0_0(1) -> 1 1137.85/298.26 , 0_1(1) -> 4 1137.85/298.26 , 0_1(3) -> 2 1137.85/298.26 , 0_1(5) -> 1 1137.85/298.26 , 0_1(5) -> 4 1137.85/298.26 , 0_1(5) -> 6 1137.85/298.26 , 0_1(7) -> 6 1137.85/298.26 , 0_1(14) -> 13 1137.85/298.26 , 0_1(16) -> 15 1137.85/298.26 , 0_1(21) -> 4 1137.85/298.26 , 0_1(22) -> 21 1137.85/298.26 , 0_1(43) -> 42 1137.85/298.26 , 0_1(59) -> 58 1137.85/298.26 , 0_1(66) -> 65 1137.85/298.26 , 0_1(71) -> 47 1137.85/298.26 , 0_1(92) -> 91 1137.85/298.26 , 0_1(105) -> 104 1137.85/298.26 , 0_1(108) -> 107 1137.85/298.26 , 0_1(111) -> 110 1137.85/298.26 , 0_1(128) -> 127 1137.85/298.26 , 0_1(129) -> 128 1137.85/298.26 , 0_1(136) -> 135 1137.85/298.26 , 0_1(142) -> 141 1137.85/298.26 , 0_1(160) -> 159 1137.85/298.26 , 1_0(1) -> 1 1137.85/298.26 , 1_1(1) -> 7 1137.85/298.26 , 1_1(2) -> 7 1137.85/298.26 , 1_1(5) -> 7 1137.85/298.26 , 1_1(6) -> 5 1137.85/298.26 , 1_1(15) -> 14 1137.85/298.26 , 1_1(17) -> 16 1137.85/298.26 , 1_1(19) -> 18 1137.85/298.26 , 1_1(21) -> 1 1137.85/298.26 , 1_1(21) -> 5 1137.85/298.26 , 1_1(21) -> 7 1137.85/298.26 , 1_1(21) -> 70 1137.85/298.26 , 1_1(21) -> 111 1137.85/298.26 , 1_1(21) -> 117 1137.85/298.26 , 1_1(22) -> 7 1137.85/298.26 , 1_1(25) -> 24 1137.85/298.26 , 1_1(38) -> 37 1137.85/298.26 , 1_1(40) -> 21 1137.85/298.26 , 1_1(42) -> 41 1137.85/298.26 , 1_1(52) -> 51 1137.85/298.26 , 1_1(56) -> 55 1137.85/298.26 , 1_1(76) -> 75 1137.85/298.26 , 1_1(80) -> 79 1137.85/298.26 , 1_1(94) -> 93 1137.85/298.26 , 1_1(98) -> 97 1137.85/298.26 , 1_1(99) -> 98 1137.85/298.26 , 1_1(100) -> 99 1137.85/298.26 , 1_1(101) -> 65 1137.85/298.26 , 1_1(103) -> 102 1137.85/298.26 , 1_1(106) -> 105 1137.85/298.26 , 1_1(107) -> 106 1137.85/298.26 , 1_1(112) -> 87 1137.85/298.26 , 1_1(113) -> 112 1137.85/298.26 , 1_1(118) -> 117 1137.85/298.26 , 1_1(124) -> 123 1137.85/298.26 , 1_1(126) -> 125 1137.85/298.26 , 1_1(131) -> 130 1137.85/298.26 , 1_1(132) -> 165 1137.85/298.26 , 1_1(137) -> 136 1137.85/298.26 , 1_1(143) -> 142 1137.85/298.26 , 1_1(145) -> 144 1137.85/298.26 , 1_1(162) -> 161 1137.85/298.26 , 2_0(1) -> 1 1137.85/298.26 , 2_1(1) -> 39 1137.85/298.26 , 2_1(2) -> 1 1137.85/298.26 , 2_1(2) -> 4 1137.85/298.26 , 2_1(2) -> 19 1137.85/298.26 , 2_1(2) -> 20 1137.85/298.26 , 2_1(2) -> 32 1137.85/298.26 , 2_1(2) -> 39 1137.85/298.26 , 2_1(2) -> 44 1137.85/298.26 , 2_1(2) -> 56 1137.85/298.26 , 2_1(4) -> 3 1137.85/298.26 , 2_1(5) -> 39 1137.85/298.26 , 2_1(6) -> 39 1137.85/298.26 , 2_1(7) -> 46 1137.85/298.26 , 2_1(20) -> 19 1137.85/298.26 , 2_1(21) -> 39 1137.85/298.26 , 2_1(26) -> 25 1137.85/298.26 , 2_1(35) -> 34 1137.85/298.26 , 2_1(39) -> 149 1137.85/298.26 , 2_1(45) -> 44 1137.85/298.26 , 2_1(47) -> 39 1137.85/298.26 , 2_1(49) -> 48 1137.85/298.26 , 2_1(54) -> 53 1137.85/298.26 , 2_1(56) -> 44 1137.85/298.26 , 2_1(58) -> 57 1137.85/298.26 , 2_1(60) -> 59 1137.85/298.26 , 2_1(61) -> 60 1137.85/298.26 , 2_1(62) -> 61 1137.85/298.26 , 2_1(63) -> 62 1137.85/298.26 , 2_1(69) -> 68 1137.85/298.26 , 2_1(72) -> 71 1137.85/298.26 , 2_1(73) -> 72 1137.85/298.26 , 2_1(78) -> 77 1137.85/298.26 , 2_1(79) -> 78 1137.85/298.26 , 2_1(81) -> 80 1137.85/298.26 , 2_1(82) -> 81 1137.85/298.26 , 2_1(83) -> 39 1137.85/298.26 , 2_1(84) -> 83 1137.85/298.26 , 2_1(85) -> 84 1137.85/298.26 , 2_1(86) -> 119 1137.85/298.26 , 2_1(90) -> 89 1137.85/298.26 , 2_1(93) -> 92 1137.85/298.26 , 2_1(96) -> 95 1137.85/298.26 , 2_1(114) -> 113 1137.85/298.26 , 2_1(115) -> 114 1137.85/298.26 , 2_1(120) -> 19 1137.85/298.26 , 2_1(148) -> 147 1137.85/298.26 , 2_1(153) -> 152 1137.85/298.26 , 2_1(155) -> 154 1137.85/298.26 , 2_1(164) -> 163 1137.85/298.26 , 3_0(1) -> 1 1137.85/298.26 , 3_1(1) -> 20 1137.85/298.26 , 3_1(2) -> 132 1137.85/298.26 , 3_1(4) -> 64 1137.85/298.26 , 3_1(7) -> 86 1137.85/298.26 , 3_1(12) -> 11 1137.85/298.26 , 3_1(18) -> 17 1137.85/298.26 , 3_1(21) -> 132 1137.85/298.26 , 3_1(23) -> 22 1137.85/298.26 , 3_1(27) -> 26 1137.85/298.26 , 3_1(30) -> 29 1137.85/298.26 , 3_1(31) -> 30 1137.85/298.26 , 3_1(32) -> 132 1137.85/298.26 , 3_1(37) -> 36 1137.85/298.26 , 3_1(39) -> 56 1137.85/298.26 , 3_1(46) -> 45 1137.85/298.26 , 3_1(47) -> 1 1137.85/298.26 , 3_1(47) -> 7 1137.85/298.26 , 3_1(47) -> 20 1137.85/298.26 , 3_1(47) -> 86 1137.85/298.26 , 3_1(65) -> 57 1137.85/298.26 , 3_1(67) -> 66 1137.85/298.26 , 3_1(74) -> 73 1137.85/298.26 , 3_1(75) -> 74 1137.85/298.26 , 3_1(77) -> 76 1137.85/298.26 , 3_1(83) -> 2 1137.85/298.26 , 3_1(116) -> 115 1137.85/298.26 , 3_1(120) -> 87 1137.85/298.26 , 3_1(121) -> 120 1137.85/298.26 , 3_1(123) -> 122 1137.85/298.26 , 3_1(132) -> 155 1137.85/298.26 , 3_1(139) -> 138 1137.85/298.26 , 3_1(140) -> 139 1137.85/298.26 , 3_1(151) -> 150 1137.85/298.26 , 3_1(152) -> 151 1137.85/298.26 , 3_1(154) -> 153 1137.85/298.26 , 3_1(158) -> 157 1137.85/298.26 , 3_1(161) -> 160 1137.85/298.26 , 3_1(165) -> 164 1137.85/298.26 , 4_0(1) -> 1 1137.85/298.26 , 4_1(1) -> 32 1137.85/298.26 , 4_1(9) -> 8 1137.85/298.26 , 4_1(10) -> 9 1137.85/298.26 , 4_1(13) -> 12 1137.85/298.26 , 4_1(24) -> 23 1137.85/298.26 , 4_1(28) -> 27 1137.85/298.26 , 4_1(33) -> 21 1137.85/298.26 , 4_1(34) -> 33 1137.85/298.26 , 4_1(41) -> 40 1137.85/298.26 , 4_1(44) -> 43 1137.85/298.26 , 4_1(47) -> 2 1137.85/298.26 , 4_1(51) -> 50 1137.85/298.26 , 4_1(55) -> 54 1137.85/298.26 , 4_1(57) -> 2 1137.85/298.26 , 4_1(64) -> 63 1137.85/298.26 , 4_1(68) -> 67 1137.85/298.26 , 4_1(70) -> 69 1137.85/298.26 , 4_1(87) -> 1 1137.85/298.26 , 4_1(87) -> 32 1137.85/298.26 , 4_1(87) -> 63 1137.85/298.26 , 4_1(97) -> 96 1137.85/298.26 , 4_1(102) -> 101 1137.85/298.26 , 4_1(104) -> 103 1137.85/298.26 , 4_1(110) -> 109 1137.85/298.26 , 4_1(119) -> 118 1137.85/298.26 , 4_1(120) -> 2 1137.85/298.26 , 4_1(122) -> 121 1137.85/298.26 , 4_1(125) -> 124 1137.85/298.26 , 4_1(135) -> 134 1137.85/298.26 , 4_1(147) -> 146 1137.85/298.26 , 4_1(149) -> 148 1137.85/298.26 , 5_0(1) -> 1 1137.85/298.26 , 5_1(1) -> 70 1137.85/298.26 , 5_1(4) -> 111 1137.85/298.26 , 5_1(8) -> 5 1137.85/298.26 , 5_1(11) -> 10 1137.85/298.26 , 5_1(29) -> 28 1137.85/298.26 , 5_1(32) -> 31 1137.85/298.26 , 5_1(36) -> 35 1137.85/298.26 , 5_1(39) -> 38 1137.85/298.26 , 5_1(48) -> 47 1137.85/298.26 , 5_1(50) -> 49 1137.85/298.26 , 5_1(53) -> 52 1137.85/298.26 , 5_1(56) -> 100 1137.85/298.26 , 5_1(70) -> 82 1137.85/298.26 , 5_1(86) -> 85 1137.85/298.26 , 5_1(87) -> 82 1137.85/298.26 , 5_1(88) -> 87 1137.85/298.26 , 5_1(89) -> 88 1137.85/298.26 , 5_1(91) -> 90 1137.85/298.26 , 5_1(95) -> 94 1137.85/298.26 , 5_1(109) -> 108 1137.85/298.26 , 5_1(117) -> 116 1137.85/298.26 , 5_1(127) -> 126 1137.85/298.26 , 5_1(130) -> 129 1137.85/298.26 , 5_1(132) -> 131 1137.85/298.26 , 5_1(133) -> 2 1137.85/298.26 , 5_1(134) -> 133 1137.85/298.26 , 5_1(138) -> 137 1137.85/298.26 , 5_1(141) -> 140 1137.85/298.26 , 5_1(144) -> 143 1137.85/298.26 , 5_1(146) -> 145 1137.85/298.26 , 5_1(150) -> 33 1137.85/298.26 , 5_1(156) -> 1 1137.85/298.26 , 5_1(156) -> 70 1137.85/298.26 , 5_1(156) -> 82 1137.85/298.26 , 5_1(157) -> 156 1137.85/298.26 , 5_1(159) -> 158 1137.85/298.26 , 5_1(163) -> 162 } 1137.85/298.26 1137.85/298.26 Hurray, we answered YES(?,O(n^1)) 1138.53/298.74 EOF