YES(?,O(n^1)) 1096.14/297.70 YES(?,O(n^1)) 1096.14/297.70 1096.14/297.70 We are left with following problem, upon which TcT provides the 1096.14/297.70 certificate YES(?,O(n^1)). 1096.14/297.70 1096.14/297.70 Strict Trs: 1096.14/297.70 { 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1)))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1096.14/297.70 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1096.14/297.70 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1096.14/297.70 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1096.14/297.70 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))))))))))))))))))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1096.14/297.70 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)))))))))))))))))))))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1096.14/297.70 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))))))))))))))))))))))))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1096.14/297.70 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)))))))))))))))))))))))))))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1096.14/297.70 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))))))))))))))))))))))))))))))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1096.14/297.70 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)))))))))))))))))))))))))))))))))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1096.14/297.70 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))))))))))))))))))))))))))))))))))))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1096.14/297.70 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)))))))))))))))))))))))))))))))))))))))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1096.14/297.70 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))))))))))))))))))))))))))))))))))))))))))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1096.14/297.70 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)))))))))))))))))))))))))))))))))))))))))))))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1096.14/297.70 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))))))))))))))))))))))))))))))))))))))))))))))))))))))) 1096.14/297.70 , 0(1(2(1(x1)))) -> 1096.14/297.70 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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) } 1096.14/297.70 Obligation: 1096.14/297.70 derivational complexity 1096.14/297.70 Answer: 1096.14/297.70 YES(?,O(n^1)) 1096.14/297.70 1096.14/297.70 The problem is match-bounded by 3. The enriched problem is 1096.14/297.70 compatible with the following automaton. 1096.14/297.70 { 0_0(1) -> 1 1096.14/297.70 , 0_1(6) -> 5 1096.14/297.70 , 0_1(9) -> 8 1096.14/297.70 , 0_2(26) -> 25 1096.14/297.70 , 0_2(29) -> 28 1096.14/297.70 , 0_2(32) -> 31 1096.14/297.70 , 0_2(38) -> 37 1096.14/297.70 , 0_3(50) -> 49 1096.14/297.70 , 0_3(53) -> 52 1096.14/297.70 , 0_3(56) -> 55 1096.14/297.70 , 0_3(59) -> 58 1096.14/297.70 , 0_3(62) -> 61 1096.14/297.70 , 0_3(68) -> 67 1096.14/297.70 , 0_3(71) -> 70 1096.14/297.70 , 0_3(74) -> 73 1096.14/297.70 , 0_3(77) -> 76 1096.14/297.70 , 0_3(80) -> 79 1096.14/297.70 , 0_3(83) -> 82 1096.14/297.70 , 0_3(89) -> 88 1096.14/297.70 , 0_3(92) -> 91 1096.14/297.70 , 0_3(95) -> 94 1096.14/297.70 , 0_3(98) -> 97 1096.14/297.70 , 0_3(101) -> 100 1096.14/297.70 , 0_3(104) -> 103 1096.14/297.70 , 0_3(107) -> 106 1096.14/297.70 , 0_3(113) -> 112 1096.14/297.70 , 0_3(116) -> 115 1096.14/297.70 , 0_3(119) -> 118 1096.14/297.70 , 0_3(122) -> 121 1096.14/297.70 , 0_3(125) -> 124 1096.14/297.70 , 0_3(128) -> 127 1096.14/297.70 , 0_3(131) -> 130 1096.14/297.70 , 0_3(134) -> 133 1096.14/297.70 , 1_0(1) -> 1 1096.14/297.70 , 1_1(2) -> 1 1096.14/297.70 , 1_1(2) -> 8 1096.14/297.70 , 1_1(4) -> 3 1096.14/297.70 , 1_1(5) -> 4 1096.14/297.70 , 1_1(7) -> 6 1096.14/297.70 , 1_1(10) -> 9 1096.14/297.70 , 1_2(22) -> 5 1096.14/297.70 , 1_2(22) -> 8 1096.14/297.70 , 1_2(24) -> 23 1096.14/297.70 , 1_2(25) -> 24 1096.14/297.70 , 1_2(27) -> 26 1096.14/297.70 , 1_2(28) -> 36 1096.14/297.70 , 1_2(30) -> 29 1096.14/297.70 , 1_2(33) -> 32 1096.14/297.70 , 1_2(34) -> 5 1096.14/297.70 , 1_2(34) -> 8 1096.14/297.70 , 1_2(36) -> 35 1096.14/297.70 , 1_2(37) -> 36 1096.14/297.70 , 1_2(39) -> 38 1096.14/297.70 , 1_3(46) -> 31 1096.14/297.70 , 1_3(48) -> 47 1096.14/297.70 , 1_3(49) -> 48 1096.14/297.70 , 1_3(51) -> 50 1096.14/297.70 , 1_3(52) -> 48 1096.14/297.70 , 1_3(54) -> 53 1096.14/297.70 , 1_3(55) -> 48 1096.14/297.70 , 1_3(57) -> 56 1096.14/297.70 , 1_3(58) -> 48 1096.14/297.70 , 1_3(60) -> 59 1096.14/297.70 , 1_3(63) -> 62 1096.14/297.70 , 1_3(64) -> 28 1096.14/297.70 , 1_3(66) -> 65 1096.14/297.70 , 1_3(67) -> 66 1096.14/297.70 , 1_3(69) -> 68 1096.14/297.70 , 1_3(70) -> 66 1096.14/297.70 , 1_3(72) -> 71 1096.14/297.70 , 1_3(73) -> 66 1096.14/297.70 , 1_3(75) -> 74 1096.14/297.70 , 1_3(76) -> 66 1096.14/297.70 , 1_3(78) -> 77 1096.14/297.70 , 1_3(79) -> 66 1096.14/297.70 , 1_3(81) -> 80 1096.14/297.70 , 1_3(84) -> 83 1096.14/297.70 , 1_3(85) -> 25 1096.14/297.70 , 1_3(87) -> 86 1096.14/297.70 , 1_3(88) -> 87 1096.14/297.70 , 1_3(90) -> 89 1096.14/297.70 , 1_3(91) -> 87 1096.14/297.70 , 1_3(93) -> 92 1096.14/297.70 , 1_3(94) -> 87 1096.14/297.70 , 1_3(96) -> 95 1096.14/297.70 , 1_3(97) -> 87 1096.14/297.70 , 1_3(99) -> 98 1096.14/297.70 , 1_3(100) -> 87 1096.14/297.70 , 1_3(102) -> 101 1096.14/297.70 , 1_3(103) -> 87 1096.14/297.70 , 1_3(105) -> 104 1096.14/297.70 , 1_3(108) -> 107 1096.14/297.70 , 1_3(109) -> 37 1096.14/297.70 , 1_3(111) -> 110 1096.14/297.70 , 1_3(112) -> 111 1096.14/297.70 , 1_3(114) -> 113 1096.14/297.70 , 1_3(115) -> 111 1096.14/297.70 , 1_3(117) -> 116 1096.14/297.70 , 1_3(118) -> 111 1096.14/297.70 , 1_3(120) -> 119 1096.14/297.70 , 1_3(121) -> 111 1096.14/297.70 , 1_3(123) -> 122 1096.14/297.70 , 1_3(124) -> 111 1096.14/297.70 , 1_3(126) -> 125 1096.14/297.70 , 1_3(127) -> 111 1096.14/297.70 , 1_3(129) -> 128 1096.14/297.70 , 1_3(130) -> 111 1096.14/297.70 , 1_3(132) -> 131 1096.14/297.70 , 1_3(135) -> 134 1096.14/297.70 , 2_0(1) -> 1 1096.14/297.70 , 2_1(1) -> 10 1096.14/297.70 , 2_1(2) -> 7 1096.14/297.70 , 2_1(3) -> 2 1096.14/297.70 , 2_1(4) -> 7 1096.14/297.70 , 2_1(5) -> 7 1096.14/297.70 , 2_1(8) -> 7 1096.14/297.70 , 2_2(2) -> 33 1096.14/297.70 , 2_2(5) -> 33 1096.14/297.70 , 2_2(22) -> 33 1096.14/297.70 , 2_2(23) -> 22 1096.14/297.70 , 2_2(25) -> 39 1096.14/297.70 , 2_2(28) -> 27 1096.14/297.70 , 2_2(31) -> 30 1096.14/297.70 , 2_2(34) -> 27 1096.14/297.70 , 2_2(35) -> 34 1096.14/297.70 , 2_2(37) -> 39 1096.14/297.70 , 2_3(22) -> 51 1096.14/297.70 , 2_3(34) -> 63 1096.14/297.70 , 2_3(46) -> 84 1096.14/297.70 , 2_3(47) -> 46 1096.14/297.70 , 2_3(49) -> 51 1096.14/297.70 , 2_3(52) -> 51 1096.14/297.70 , 2_3(55) -> 54 1096.14/297.70 , 2_3(58) -> 57 1096.14/297.70 , 2_3(61) -> 60 1096.14/297.70 , 2_3(64) -> 108 1096.14/297.70 , 2_3(65) -> 64 1096.14/297.70 , 2_3(67) -> 69 1096.14/297.70 , 2_3(70) -> 69 1096.14/297.70 , 2_3(73) -> 72 1096.14/297.70 , 2_3(76) -> 75 1096.14/297.70 , 2_3(79) -> 78 1096.14/297.70 , 2_3(82) -> 81 1096.14/297.70 , 2_3(85) -> 135 1096.14/297.70 , 2_3(86) -> 85 1096.14/297.70 , 2_3(88) -> 90 1096.14/297.70 , 2_3(91) -> 90 1096.14/297.70 , 2_3(94) -> 93 1096.14/297.70 , 2_3(97) -> 96 1096.14/297.70 , 2_3(100) -> 99 1096.14/297.70 , 2_3(103) -> 102 1096.14/297.70 , 2_3(106) -> 105 1096.14/297.70 , 2_3(109) -> 114 1096.14/297.70 , 2_3(110) -> 109 1096.14/297.70 , 2_3(112) -> 114 1096.14/297.70 , 2_3(115) -> 114 1096.14/297.70 , 2_3(118) -> 117 1096.14/297.70 , 2_3(121) -> 120 1096.14/297.70 , 2_3(124) -> 123 1096.14/297.70 , 2_3(127) -> 126 1096.14/297.70 , 2_3(130) -> 129 1096.14/297.70 , 2_3(133) -> 132 } 1096.14/297.70 1096.14/297.70 Hurray, we answered YES(?,O(n^1)) 1096.56/298.11 EOF