YES(?,O(n^1)) 1113.33/297.06 YES(?,O(n^1)) 1113.33/297.06 1113.33/297.06 We are left with following problem, upon which TcT provides the 1113.33/297.06 certificate YES(?,O(n^1)). 1113.33/297.06 1113.33/297.06 Strict Trs: 1113.33/297.06 { 1(1(3(3(5(3(1(x1))))))) -> 3(5(0(5(3(2(5(0(0(1(x1)))))))))) 1113.33/297.06 , 1(3(3(x1))) -> 3(5(3(2(5(0(2(4(5(4(x1)))))))))) 1113.33/297.06 , 1(2(3(3(3(x1))))) -> 4(1(1(2(3(5(0(4(0(5(x1)))))))))) 1113.33/297.06 , 1(4(4(2(2(x1))))) -> 1(1(2(0(1(1(1(0(2(2(x1)))))))))) 1113.33/297.06 , 3(3(3(3(4(0(x1)))))) -> 3(0(0(2(1(0(5(3(5(4(x1)))))))))) 1113.33/297.06 , 3(5(2(0(1(3(3(x1))))))) -> 3(4(3(2(3(2(4(4(5(5(x1)))))))))) 1113.33/297.06 , 5(1(4(5(3(3(3(x1))))))) -> 5(1(4(5(3(4(4(2(3(2(x1)))))))))) 1113.33/297.06 , 0(1(3(5(2(2(3(x1))))))) -> 0(3(0(0(5(0(0(4(4(3(x1)))))))))) 1113.33/297.06 , 0(3(3(1(4(3(x1)))))) -> 4(4(3(0(2(3(0(3(0(0(x1)))))))))) 1113.33/297.06 , 0(3(3(3(x1)))) -> 5(4(3(5(3(0(5(4(4(0(x1)))))))))) 1113.33/297.06 , 0(3(3(3(1(x1))))) -> 5(4(4(0(3(1(0(5(1(0(x1)))))))))) 1113.33/297.06 , 0(2(3(1(3(2(5(x1))))))) -> 0(4(3(1(2(3(2(3(2(0(x1)))))))))) 1113.33/297.06 , 4(1(4(2(4(0(1(x1))))))) -> 5(2(2(1(0(5(5(4(5(1(x1)))))))))) 1113.33/297.06 , 4(1(4(4(4(1(x1)))))) -> 4(1(0(3(3(5(5(5(4(1(x1)))))))))) 1113.33/297.06 , 4(5(1(2(4(4(4(x1))))))) -> 4(1(1(4(5(3(0(1(0(4(x1)))))))))) 1113.33/297.06 , 4(0(1(3(4(0(x1)))))) -> 2(2(3(0(0(0(5(0(0(0(x1)))))))))) } 1113.33/297.06 Obligation: 1113.33/297.06 derivational complexity 1113.33/297.06 Answer: 1113.33/297.06 YES(?,O(n^1)) 1113.33/297.06 1113.33/297.06 The problem is match-bounded by 1. The enriched problem is 1113.33/297.06 compatible with the following automaton. 1113.33/297.06 { 1_0(1) -> 1 1113.33/297.06 , 1_1(1) -> 10 1113.33/297.06 , 1_1(19) -> 18 1113.33/297.06 , 1_1(20) -> 19 1113.33/297.06 , 1_1(27) -> 1 1113.33/297.06 , 1_1(27) -> 10 1113.33/297.06 , 1_1(28) -> 27 1113.33/297.06 , 1_1(31) -> 30 1113.33/297.06 , 1_1(32) -> 31 1113.33/297.06 , 1_1(33) -> 32 1113.33/297.06 , 1_1(39) -> 38 1113.33/297.06 , 1_1(50) -> 49 1113.33/297.06 , 1_1(73) -> 86 1113.33/297.06 , 1_1(84) -> 83 1113.33/297.06 , 1_1(89) -> 88 1113.33/297.06 , 1_1(96) -> 95 1113.33/297.06 , 1_1(110) -> 31 1113.33/297.06 , 1_1(111) -> 110 1113.33/297.06 , 3_0(1) -> 1 1113.33/297.06 , 3_1(1) -> 65 1113.33/297.06 , 3_1(2) -> 1 1113.33/297.06 , 3_1(2) -> 10 1113.33/297.06 , 3_1(2) -> 65 1113.33/297.06 , 3_1(6) -> 5 1113.33/297.06 , 3_1(11) -> 3 1113.33/297.06 , 3_1(16) -> 41 1113.33/297.06 , 3_1(22) -> 21 1113.33/297.06 , 3_1(35) -> 56 1113.33/297.06 , 3_1(43) -> 42 1113.33/297.06 , 3_1(45) -> 44 1113.33/297.06 , 3_1(53) -> 52 1113.33/297.06 , 3_1(58) -> 57 1113.33/297.06 , 3_1(67) -> 66 1113.33/297.06 , 3_1(70) -> 69 1113.33/297.06 , 3_1(72) -> 71 1113.33/297.06 , 3_1(75) -> 74 1113.33/297.06 , 3_1(77) -> 76 1113.33/297.06 , 3_1(83) -> 82 1113.33/297.06 , 3_1(88) -> 87 1113.33/297.06 , 3_1(91) -> 90 1113.33/297.06 , 3_1(93) -> 92 1113.33/297.06 , 3_1(102) -> 101 1113.33/297.06 , 3_1(103) -> 102 1113.33/297.06 , 3_1(109) -> 108 1113.33/297.06 , 3_1(114) -> 113 1113.33/297.06 , 5_0(1) -> 1 1113.33/297.06 , 5_1(1) -> 26 1113.33/297.06 , 5_1(2) -> 26 1113.33/297.06 , 5_1(3) -> 2 1113.33/297.06 , 5_1(5) -> 4 1113.33/297.06 , 5_1(8) -> 7 1113.33/297.06 , 5_1(10) -> 100 1113.33/297.06 , 5_1(13) -> 12 1113.33/297.06 , 5_1(17) -> 16 1113.33/297.06 , 5_1(23) -> 22 1113.33/297.06 , 5_1(26) -> 48 1113.33/297.06 , 5_1(41) -> 40 1113.33/297.06 , 5_1(48) -> 103 1113.33/297.06 , 5_1(49) -> 1 1113.33/297.06 , 5_1(49) -> 17 1113.33/297.06 , 5_1(49) -> 26 1113.33/297.06 , 5_1(49) -> 73 1113.33/297.06 , 5_1(49) -> 100 1113.33/297.06 , 5_1(49) -> 106 1113.33/297.06 , 5_1(52) -> 51 1113.33/297.06 , 5_1(61) -> 60 1113.33/297.06 , 5_1(76) -> 75 1113.33/297.06 , 5_1(79) -> 78 1113.33/297.06 , 5_1(86) -> 85 1113.33/297.06 , 5_1(98) -> 97 1113.33/297.06 , 5_1(99) -> 98 1113.33/297.06 , 5_1(104) -> 103 1113.33/297.06 , 5_1(105) -> 104 1113.33/297.06 , 5_1(106) -> 105 1113.33/297.06 , 5_1(108) -> 107 1113.33/297.06 , 5_1(118) -> 117 1113.33/297.06 , 2_0(1) -> 1 1113.33/297.06 , 2_1(1) -> 35 1113.33/297.06 , 2_1(2) -> 35 1113.33/297.06 , 2_1(7) -> 6 1113.33/297.06 , 2_1(12) -> 11 1113.33/297.06 , 2_1(15) -> 14 1113.33/297.06 , 2_1(21) -> 20 1113.33/297.06 , 2_1(29) -> 28 1113.33/297.06 , 2_1(35) -> 34 1113.33/297.06 , 2_1(38) -> 37 1113.33/297.06 , 2_1(44) -> 43 1113.33/297.06 , 2_1(46) -> 45 1113.33/297.06 , 2_1(56) -> 55 1113.33/297.06 , 2_1(69) -> 68 1113.33/297.06 , 2_1(73) -> 93 1113.33/297.06 , 2_1(90) -> 89 1113.33/297.06 , 2_1(92) -> 91 1113.33/297.06 , 2_1(94) -> 49 1113.33/297.06 , 2_1(95) -> 94 1113.33/297.06 , 2_1(112) -> 1 1113.33/297.06 , 2_1(112) -> 17 1113.33/297.06 , 2_1(112) -> 80 1113.33/297.06 , 2_1(113) -> 112 1113.33/297.06 , 0_0(1) -> 1 1113.33/297.06 , 0_1(1) -> 73 1113.33/297.06 , 0_1(2) -> 73 1113.33/297.06 , 0_1(4) -> 3 1113.33/297.06 , 0_1(9) -> 8 1113.33/297.06 , 0_1(10) -> 9 1113.33/297.06 , 0_1(14) -> 13 1113.33/297.06 , 0_1(17) -> 111 1113.33/297.06 , 0_1(18) -> 111 1113.33/297.06 , 0_1(24) -> 23 1113.33/297.06 , 0_1(26) -> 25 1113.33/297.06 , 0_1(27) -> 73 1113.33/297.06 , 0_1(30) -> 29 1113.33/297.06 , 0_1(34) -> 33 1113.33/297.06 , 0_1(35) -> 33 1113.33/297.06 , 0_1(36) -> 2 1113.33/297.06 , 0_1(37) -> 36 1113.33/297.06 , 0_1(40) -> 39 1113.33/297.06 , 0_1(49) -> 73 1113.33/297.06 , 0_1(57) -> 1 1113.33/297.06 , 0_1(57) -> 9 1113.33/297.06 , 0_1(57) -> 33 1113.33/297.06 , 0_1(57) -> 73 1113.33/297.06 , 0_1(59) -> 58 1113.33/297.06 , 0_1(60) -> 59 1113.33/297.06 , 0_1(62) -> 61 1113.33/297.06 , 0_1(63) -> 62 1113.33/297.06 , 0_1(68) -> 67 1113.33/297.06 , 0_1(71) -> 70 1113.33/297.06 , 0_1(72) -> 118 1113.33/297.06 , 0_1(73) -> 72 1113.33/297.06 , 0_1(78) -> 77 1113.33/297.06 , 0_1(82) -> 81 1113.33/297.06 , 0_1(85) -> 84 1113.33/297.06 , 0_1(97) -> 96 1113.33/297.06 , 0_1(101) -> 19 1113.33/297.06 , 0_1(110) -> 109 1113.33/297.06 , 0_1(115) -> 114 1113.33/297.06 , 0_1(116) -> 115 1113.33/297.06 , 0_1(117) -> 116 1113.33/297.06 , 4_0(1) -> 1 1113.33/297.06 , 4_1(1) -> 17 1113.33/297.06 , 4_1(2) -> 17 1113.33/297.06 , 4_1(10) -> 106 1113.33/297.06 , 4_1(16) -> 15 1113.33/297.06 , 4_1(17) -> 63 1113.33/297.06 , 4_1(18) -> 1 1113.33/297.06 , 4_1(18) -> 10 1113.33/297.06 , 4_1(18) -> 17 1113.33/297.06 , 4_1(18) -> 73 1113.33/297.06 , 4_1(18) -> 99 1113.33/297.06 , 4_1(18) -> 106 1113.33/297.06 , 4_1(25) -> 24 1113.33/297.06 , 4_1(42) -> 2 1113.33/297.06 , 4_1(47) -> 46 1113.33/297.06 , 4_1(48) -> 47 1113.33/297.06 , 4_1(51) -> 50 1113.33/297.06 , 4_1(54) -> 53 1113.33/297.06 , 4_1(55) -> 54 1113.33/297.06 , 4_1(57) -> 17 1113.33/297.06 , 4_1(64) -> 63 1113.33/297.06 , 4_1(65) -> 64 1113.33/297.06 , 4_1(66) -> 18 1113.33/297.06 , 4_1(73) -> 80 1113.33/297.06 , 4_1(74) -> 49 1113.33/297.06 , 4_1(80) -> 79 1113.33/297.06 , 4_1(81) -> 74 1113.33/297.06 , 4_1(87) -> 57 1113.33/297.06 , 4_1(100) -> 99 1113.33/297.06 , 4_1(107) -> 20 1113.33/297.06 , 4_1(113) -> 17 } 1113.33/297.06 1113.33/297.06 Hurray, we answered YES(?,O(n^1)) 1113.92/297.54 EOF