YES(?,O(n^1)) 1033.53/297.04 YES(?,O(n^1)) 1033.53/297.04 1033.53/297.04 We are left with following problem, upon which TcT provides the 1033.53/297.04 certificate YES(?,O(n^1)). 1033.53/297.04 1033.53/297.04 Strict Trs: 1033.53/297.04 { 0(0(1(2(x1)))) -> 2(3(0(x1))) 1033.53/297.04 , 0(2(3(5(4(2(2(1(0(3(3(5(0(x1))))))))))))) -> 1033.53/297.04 3(3(1(2(3(0(4(0(0(0(2(0(x1)))))))))))) 1033.53/297.04 , 1(3(5(4(1(2(2(x1))))))) -> 3(3(3(4(4(0(x1)))))) 1033.53/297.04 , 1(3(5(5(2(x1))))) -> 1(3(2(3(x1)))) 1033.53/297.04 , 2(0(3(0(2(2(2(0(1(4(2(1(0(4(4(3(3(1(4(4(x1)))))))))))))))))))) -> 1033.53/297.04 5(2(4(1(1(4(5(1(0(1(2(0(3(0(1(2(3(4(3(1(x1)))))))))))))))))))) 1033.53/297.04 , 2(1(0(2(1(4(0(0(2(0(0(0(5(2(x1)))))))))))))) -> 1033.53/297.04 2(2(4(2(1(4(3(0(5(1(3(3(0(x1))))))))))))) 1033.53/297.04 , 2(1(5(2(1(3(4(4(x1)))))))) -> 4(0(3(4(0(1(2(x1))))))) 1033.53/297.04 , 2(2(5(3(2(2(x1)))))) -> 5(1(1(0(3(x1))))) 1033.53/297.04 , 2(4(1(2(5(2(4(1(3(2(0(3(x1)))))))))))) -> 1033.53/297.04 4(3(0(4(2(3(4(3(4(2(0(x1))))))))))) 1033.53/297.04 , 2(5(1(2(1(1(x1)))))) -> 5(2(1(2(4(1(x1)))))) 1033.53/297.04 , 3(4(1(4(2(4(x1)))))) -> 1(3(3(3(x1)))) 1033.53/297.04 , 3(4(2(1(1(2(2(5(4(x1))))))))) -> 3(3(3(1(3(3(4(x1))))))) 1033.53/297.04 , 3(5(2(2(4(5(x1)))))) -> 3(2(4(3(0(x1))))) 1033.53/297.04 , 4(2(5(2(x1)))) -> 1(4(0(x1))) 1033.53/297.04 , 4(5(0(3(1(3(2(2(5(2(2(4(1(3(2(x1))))))))))))))) -> 1033.53/297.04 4(5(3(2(1(4(5(0(0(0(4(5(4(0(0(x1))))))))))))))) 1033.53/297.04 , 4(5(3(4(x1)))) -> 4(4(2(4(x1)))) 1033.53/297.04 , 4(5(4(3(0(5(1(x1))))))) -> 4(3(3(5(4(1(x1)))))) 1033.53/297.04 , 5(2(1(0(1(5(x1)))))) -> 5(4(2(4(5(1(x1)))))) 1033.53/297.04 , 5(2(1(3(1(5(2(5(4(4(x1)))))))))) -> 5(3(4(5(0(1(4(0(3(x1))))))))) 1033.53/297.04 , 5(2(2(1(2(x1))))) -> 0(0(2(3(x1)))) 1033.53/297.04 , 5(2(2(5(2(4(4(1(2(0(1(1(0(1(1(x1))))))))))))))) -> 1033.53/297.04 5(0(5(4(3(2(1(0(3(3(5(0(4(1(x1)))))))))))))) 1033.53/297.04 , 5(4(0(2(2(4(0(4(x1)))))))) -> 3(1(5(1(3(0(4(x1))))))) 1033.53/297.04 , 5(4(1(5(1(5(4(4(2(2(0(4(3(1(5(4(4(3(1(x1))))))))))))))))))) -> 1033.53/297.04 3(0(4(5(1(1(3(5(3(4(4(4(5(1(4(3(3(1(x1)))))))))))))))))) 1033.53/297.04 , 5(4(2(0(3(3(0(0(4(0(3(2(0(5(1(x1))))))))))))))) -> 1033.53/297.04 5(0(1(0(0(2(1(1(0(3(2(2(1(3(x1)))))))))))))) 1033.53/297.04 , 5(4(4(5(0(1(4(5(4(x1))))))))) -> 1(5(5(0(4(1(4(5(4(x1))))))))) } 1033.53/297.04 Obligation: 1033.53/297.04 derivational complexity 1033.53/297.04 Answer: 1033.53/297.04 YES(?,O(n^1)) 1033.53/297.04 1033.53/297.04 The problem is match-bounded by 2. The enriched problem is 1033.53/297.04 compatible with the following automaton. 1033.53/297.04 { 0_0(1) -> 1 1033.53/297.04 , 0_1(1) -> 3 1033.53/297.04 , 0_1(2) -> 3 1033.53/297.04 , 0_1(3) -> 77 1033.53/297.04 , 0_1(4) -> 3 1033.53/297.04 , 0_1(9) -> 8 1033.53/297.04 , 0_1(11) -> 10 1033.53/297.04 , 0_1(12) -> 11 1033.53/297.04 , 0_1(13) -> 12 1033.53/297.04 , 0_1(17) -> 87 1033.53/297.04 , 0_1(18) -> 53 1033.53/297.04 , 0_1(19) -> 3 1033.53/297.04 , 0_1(20) -> 3 1033.53/297.04 , 0_1(27) -> 26 1033.53/297.04 , 0_1(30) -> 29 1033.53/297.04 , 0_1(32) -> 31 1033.53/297.04 , 0_1(38) -> 3 1033.53/297.04 , 0_1(44) -> 43 1033.53/297.04 , 0_1(47) -> 46 1033.53/297.04 , 0_1(50) -> 49 1033.53/297.04 , 0_1(51) -> 12 1033.53/297.04 , 0_1(53) -> 77 1033.53/297.04 , 0_1(55) -> 54 1033.53/297.04 , 0_1(62) -> 97 1033.53/297.04 , 0_1(65) -> 3 1033.53/297.04 , 0_1(66) -> 3 1033.53/297.04 , 0_1(72) -> 71 1033.53/297.04 , 0_1(73) -> 72 1033.53/297.04 , 0_1(74) -> 73 1033.53/297.04 , 0_1(85) -> 84 1033.53/297.04 , 0_1(87) -> 1 1033.53/297.04 , 0_1(88) -> 19 1033.53/297.04 , 0_1(94) -> 93 1033.53/297.04 , 0_1(101) -> 4 1033.53/297.04 , 0_1(116) -> 115 1033.53/297.04 , 0_1(117) -> 116 1033.53/297.04 , 0_1(121) -> 120 1033.53/297.04 , 0_1(126) -> 125 1033.53/297.04 , 0_2(62) -> 135 1033.53/297.04 , 0_2(82) -> 135 1033.53/297.04 , 1_0(1) -> 1 1033.53/297.04 , 1_1(1) -> 37 1033.53/297.04 , 1_1(6) -> 5 1033.53/297.04 , 1_1(15) -> 1 1033.53/297.04 , 1_1(15) -> 62 1033.53/297.04 , 1_1(15) -> 78 1033.53/297.04 , 1_1(16) -> 1 1033.53/297.04 , 1_1(16) -> 18 1033.53/297.04 , 1_1(16) -> 37 1033.53/297.04 , 1_1(16) -> 45 1033.53/297.04 , 1_1(16) -> 64 1033.53/297.04 , 1_1(16) -> 140 1033.53/297.04 , 1_1(17) -> 14 1033.53/297.04 , 1_1(18) -> 45 1033.53/297.04 , 1_1(19) -> 37 1033.53/297.04 , 1_1(22) -> 21 1033.53/297.04 , 1_1(23) -> 22 1033.53/297.04 , 1_1(26) -> 25 1033.53/297.04 , 1_1(28) -> 27 1033.53/297.04 , 1_1(33) -> 32 1033.53/297.04 , 1_1(41) -> 40 1033.53/297.04 , 1_1(46) -> 37 1033.53/297.04 , 1_1(51) -> 50 1033.53/297.04 , 1_1(52) -> 19 1033.53/297.04 , 1_1(53) -> 52 1033.53/297.04 , 1_1(61) -> 20 1033.53/297.04 , 1_1(63) -> 14 1033.53/297.04 , 1_1(69) -> 68 1033.53/297.04 , 1_1(86) -> 85 1033.53/297.04 , 1_1(93) -> 92 1033.53/297.04 , 1_1(98) -> 4 1033.53/297.04 , 1_1(100) -> 99 1033.53/297.04 , 1_1(104) -> 103 1033.53/297.04 , 1_1(105) -> 104 1033.53/297.04 , 1_1(113) -> 112 1033.53/297.04 , 1_1(115) -> 88 1033.53/297.04 , 1_1(119) -> 118 1033.53/297.04 , 1_1(120) -> 119 1033.53/297.04 , 1_1(124) -> 37 1033.53/297.04 , 1_1(128) -> 127 1033.53/297.04 , 1_2(138) -> 64 1033.53/297.04 , 2_0(1) -> 1 1033.53/297.04 , 2_1(1) -> 51 1033.53/297.04 , 2_1(2) -> 1 1033.53/297.04 , 2_1(2) -> 3 1033.53/297.04 , 2_1(2) -> 51 1033.53/297.04 , 2_1(2) -> 77 1033.53/297.04 , 2_1(3) -> 13 1033.53/297.04 , 2_1(7) -> 6 1033.53/297.04 , 2_1(18) -> 17 1033.53/297.04 , 2_1(19) -> 13 1033.53/297.04 , 2_1(20) -> 19 1033.53/297.04 , 2_1(29) -> 28 1033.53/297.04 , 2_1(34) -> 33 1033.53/297.04 , 2_1(38) -> 2 1033.53/297.04 , 2_1(40) -> 39 1033.53/297.04 , 2_1(45) -> 123 1033.53/297.04 , 2_1(46) -> 51 1033.53/297.04 , 2_1(57) -> 56 1033.53/297.04 , 2_1(61) -> 51 1033.53/297.04 , 2_1(62) -> 61 1033.53/297.04 , 2_1(65) -> 4 1033.53/297.04 , 2_1(68) -> 67 1033.53/297.04 , 2_1(80) -> 79 1033.53/297.04 , 2_1(82) -> 61 1033.53/297.04 , 2_1(92) -> 91 1033.53/297.04 , 2_1(118) -> 117 1033.53/297.04 , 2_1(123) -> 122 1033.53/297.04 , 2_2(134) -> 77 1033.53/297.04 , 2_2(143) -> 142 1033.53/297.04 , 3_0(1) -> 1 1033.53/297.04 , 3_1(1) -> 18 1033.53/297.04 , 3_1(2) -> 18 1033.53/297.04 , 3_1(3) -> 2 1033.53/297.04 , 3_1(4) -> 1 1033.53/297.04 , 3_1(4) -> 3 1033.53/297.04 , 3_1(4) -> 12 1033.53/297.04 , 3_1(4) -> 18 1033.53/297.04 , 3_1(4) -> 37 1033.53/297.04 , 3_1(4) -> 45 1033.53/297.04 , 3_1(4) -> 64 1033.53/297.04 , 3_1(4) -> 78 1033.53/297.04 , 3_1(4) -> 87 1033.53/297.04 , 3_1(4) -> 140 1033.53/297.04 , 3_1(5) -> 4 1033.53/297.04 , 3_1(8) -> 7 1033.53/297.04 , 3_1(14) -> 5 1033.53/297.04 , 3_1(15) -> 18 1033.53/297.04 , 3_1(16) -> 18 1033.53/297.04 , 3_1(17) -> 16 1033.53/297.04 , 3_1(18) -> 17 1033.53/297.04 , 3_1(19) -> 18 1033.53/297.04 , 3_1(20) -> 18 1033.53/297.04 , 3_1(31) -> 30 1033.53/297.04 , 3_1(35) -> 34 1033.53/297.04 , 3_1(36) -> 114 1033.53/297.04 , 3_1(37) -> 36 1033.53/297.04 , 3_1(38) -> 18 1033.53/297.04 , 3_1(43) -> 42 1033.53/297.04 , 3_1(46) -> 18 1033.53/297.04 , 3_1(48) -> 47 1033.53/297.04 , 3_1(52) -> 18 1033.53/297.04 , 3_1(54) -> 46 1033.53/297.04 , 3_1(58) -> 57 1033.53/297.04 , 3_1(60) -> 59 1033.53/297.04 , 3_1(61) -> 18 1033.53/297.04 , 3_1(62) -> 64 1033.53/297.04 , 3_1(64) -> 63 1033.53/297.04 , 3_1(67) -> 66 1033.53/297.04 , 3_1(78) -> 54 1033.53/297.04 , 3_1(82) -> 19 1033.53/297.04 , 3_1(91) -> 90 1033.53/297.04 , 3_1(95) -> 94 1033.53/297.04 , 3_1(96) -> 95 1033.53/297.04 , 3_1(97) -> 100 1033.53/297.04 , 3_1(106) -> 105 1033.53/297.04 , 3_1(108) -> 107 1033.53/297.04 , 3_1(122) -> 121 1033.53/297.04 , 3_2(1) -> 140 1033.53/297.04 , 3_2(19) -> 140 1033.53/297.04 , 3_2(37) -> 140 1033.53/297.04 , 3_2(46) -> 140 1033.53/297.04 , 3_2(81) -> 140 1033.53/297.04 , 3_2(83) -> 140 1033.53/297.04 , 3_2(135) -> 134 1033.53/297.04 , 3_2(139) -> 138 1033.53/297.04 , 3_2(140) -> 139 1033.53/297.04 , 3_2(141) -> 140 1033.53/297.04 , 4_0(1) -> 1 1033.53/297.04 , 4_1(1) -> 62 1033.53/297.04 , 4_1(2) -> 65 1033.53/297.04 , 4_1(3) -> 15 1033.53/297.04 , 4_1(10) -> 9 1033.53/297.04 , 4_1(13) -> 60 1033.53/297.04 , 4_1(15) -> 14 1033.53/297.04 , 4_1(17) -> 113 1033.53/297.04 , 4_1(18) -> 35 1033.53/297.04 , 4_1(19) -> 62 1033.53/297.04 , 4_1(21) -> 20 1033.53/297.04 , 4_1(24) -> 23 1033.53/297.04 , 4_1(36) -> 35 1033.53/297.04 , 4_1(37) -> 62 1033.53/297.04 , 4_1(39) -> 38 1033.53/297.04 , 4_1(42) -> 41 1033.53/297.04 , 4_1(46) -> 1 1033.53/297.04 , 4_1(46) -> 51 1033.53/297.04 , 4_1(46) -> 61 1033.53/297.04 , 4_1(46) -> 62 1033.53/297.04 , 4_1(46) -> 128 1033.53/297.04 , 4_1(49) -> 48 1033.53/297.04 , 4_1(53) -> 86 1033.53/297.04 , 4_1(56) -> 55 1033.53/297.04 , 4_1(59) -> 58 1033.53/297.04 , 4_1(61) -> 46 1033.53/297.04 , 4_1(63) -> 113 1033.53/297.04 , 4_1(70) -> 69 1033.53/297.04 , 4_1(75) -> 74 1033.53/297.04 , 4_1(77) -> 76 1033.53/297.04 , 4_1(78) -> 128 1033.53/297.04 , 4_1(79) -> 19 1033.53/297.04 , 4_1(81) -> 80 1033.53/297.04 , 4_1(83) -> 82 1033.53/297.04 , 4_1(90) -> 89 1033.53/297.04 , 4_1(102) -> 101 1033.53/297.04 , 4_1(109) -> 108 1033.53/297.04 , 4_1(110) -> 109 1033.53/297.04 , 4_1(111) -> 110 1033.53/297.04 , 4_1(114) -> 113 1033.53/297.04 , 4_1(127) -> 126 1033.53/297.04 , 4_2(83) -> 143 1033.53/297.04 , 4_2(141) -> 60 1033.53/297.04 , 4_2(141) -> 62 1033.53/297.04 , 4_2(141) -> 128 1033.53/297.04 , 4_2(142) -> 141 1033.53/297.04 , 5_0(1) -> 1 1033.53/297.04 , 5_1(19) -> 1 1033.53/297.04 , 5_1(19) -> 13 1033.53/297.04 , 5_1(19) -> 51 1033.53/297.04 , 5_1(19) -> 78 1033.53/297.04 , 5_1(25) -> 24 1033.53/297.04 , 5_1(37) -> 81 1033.53/297.04 , 5_1(45) -> 44 1033.53/297.04 , 5_1(62) -> 78 1033.53/297.04 , 5_1(66) -> 46 1033.53/297.04 , 5_1(71) -> 70 1033.53/297.04 , 5_1(76) -> 75 1033.53/297.04 , 5_1(84) -> 83 1033.53/297.04 , 5_1(89) -> 88 1033.53/297.04 , 5_1(97) -> 96 1033.53/297.04 , 5_1(99) -> 98 1033.53/297.04 , 5_1(103) -> 102 1033.53/297.04 , 5_1(107) -> 106 1033.53/297.04 , 5_1(112) -> 111 1033.53/297.04 , 5_1(124) -> 15 1033.53/297.04 , 5_1(125) -> 124 } 1033.53/297.04 1033.53/297.04 Hurray, we answered YES(?,O(n^1)) 1034.09/297.55 EOF