YES(?,O(n^1))
1092.20/297.05	YES(?,O(n^1))
1092.20/297.05	
1092.20/297.05	We are left with following problem, upon which TcT provides the
1092.20/297.05	certificate YES(?,O(n^1)).
1092.20/297.05	
1092.20/297.05	Strict Trs:
1092.20/297.05	  { 2(2(5(0(5(4(x1)))))) -> 2(1(4(1(3(3(2(2(5(4(x1))))))))))
1092.20/297.05	  , 2(5(3(0(x1)))) -> 1(0(0(1(3(0(4(5(1(2(x1))))))))))
1092.20/297.05	  , 5(5(5(5(5(3(x1)))))) -> 5(5(0(1(4(0(0(5(0(1(x1))))))))))
1092.20/297.05	  , 5(1(3(5(0(x1))))) -> 5(1(4(3(0(4(4(5(2(1(x1))))))))))
1092.20/297.05	  , 5(4(5(1(1(2(x1)))))) -> 5(4(0(3(3(3(3(2(5(5(x1))))))))))
1092.20/297.05	  , 5(4(4(2(5(x1))))) -> 4(3(1(1(1(1(5(3(3(5(x1))))))))))
1092.20/297.05	  , 3(5(0(0(5(4(3(x1))))))) -> 0(1(2(1(1(5(5(2(1(0(x1))))))))))
1092.20/297.05	  , 3(5(4(2(5(2(3(x1))))))) -> 4(0(4(0(0(2(2(3(4(4(x1))))))))))
1092.20/297.05	  , 3(5(4(5(1(4(0(x1))))))) -> 1(1(1(0(0(3(3(1(2(5(x1))))))))))
1092.20/297.05	  , 3(5(4(3(5(2(x1)))))) -> 2(0(5(2(0(5(2(2(3(2(x1))))))))))
1092.20/297.05	  , 3(0(5(5(4(3(x1)))))) -> 3(3(0(3(2(3(5(5(1(0(x1))))))))))
1092.20/297.05	  , 1(3(5(4(3(x1))))) -> 2(1(4(1(4(0(3(0(1(1(x1))))))))))
1092.20/297.05	  , 4(5(3(5(5(0(x1)))))) -> 4(2(2(3(0(2(4(1(1(5(x1))))))))))
1092.20/297.05	  , 4(4(2(5(5(0(x1)))))) -> 4(4(0(0(3(3(3(2(2(3(x1)))))))))) }
1092.20/297.05	Obligation:
1092.20/297.05	  derivational complexity
1092.20/297.05	Answer:
1092.20/297.05	  YES(?,O(n^1))
1092.20/297.05	
1092.20/297.05	The problem is match-bounded by 1. The enriched problem is
1092.20/297.05	compatible with the following automaton.
1092.20/297.05	{ 2_0(1) -> 1
1092.20/297.05	, 2_1(1) -> 19
1092.20/297.05	, 2_1(2) -> 1
1092.20/297.05	, 2_1(2) -> 19
1092.20/297.05	, 2_1(2) -> 28
1092.20/297.05	, 2_1(2) -> 51
1092.20/297.05	, 2_1(2) -> 107
1092.20/297.05	, 2_1(8) -> 7
1092.20/297.05	, 2_1(9) -> 8
1092.20/297.05	, 2_1(28) -> 35
1092.20/297.05	, 2_1(42) -> 41
1092.20/297.05	, 2_1(43) -> 74
1092.20/297.05	, 2_1(50) -> 80
1092.20/297.05	, 2_1(52) -> 19
1092.20/297.05	, 2_1(54) -> 53
1092.20/297.05	, 2_1(59) -> 58
1092.20/297.05	, 2_1(65) -> 64
1092.20/297.05	, 2_1(66) -> 65
1092.20/297.05	, 2_1(77) -> 76
1092.20/297.05	, 2_1(80) -> 79
1092.20/297.05	, 2_1(81) -> 80
1092.20/297.05	, 2_1(86) -> 85
1092.20/297.05	, 2_1(93) -> 44
1092.20/297.05	, 2_1(94) -> 93
1092.20/297.05	, 2_1(97) -> 96
1092.20/297.05	, 2_1(106) -> 105
1092.20/297.05	, 2_1(107) -> 106
1092.20/297.05	, 5_0(1) -> 1
1092.20/297.05	, 5_1(1) -> 43
1092.20/297.05	, 5_1(2) -> 43
1092.20/297.05	, 5_1(10) -> 9
1092.20/297.05	, 5_1(18) -> 17
1092.20/297.05	, 5_1(20) -> 1
1092.20/297.05	, 5_1(20) -> 9
1092.20/297.05	, 5_1(20) -> 42
1092.20/297.05	, 5_1(20) -> 43
1092.20/297.05	, 5_1(21) -> 20
1092.20/297.05	, 5_1(22) -> 43
1092.20/297.05	, 5_1(27) -> 26
1092.20/297.05	, 5_1(35) -> 34
1092.20/297.05	, 5_1(43) -> 42
1092.20/297.05	, 5_1(50) -> 49
1092.20/297.05	, 5_1(52) -> 43
1092.20/297.05	, 5_1(57) -> 56
1092.20/297.05	, 5_1(58) -> 57
1092.20/297.05	, 5_1(59) -> 88
1092.20/297.05	, 5_1(61) -> 43
1092.20/297.05	, 5_1(76) -> 75
1092.20/297.05	, 5_1(79) -> 78
1092.20/297.05	, 5_1(88) -> 87
1092.20/297.05	, 3_0(1) -> 1
1092.20/297.05	, 3_1(1) -> 107
1092.20/297.05	, 3_1(6) -> 5
1092.20/297.05	, 3_1(7) -> 6
1092.20/297.05	, 3_1(9) -> 51
1092.20/297.05	, 3_1(15) -> 14
1092.20/297.05	, 3_1(19) -> 81
1092.20/297.05	, 3_1(22) -> 107
1092.20/297.05	, 3_1(31) -> 30
1092.20/297.05	, 3_1(38) -> 37
1092.20/297.05	, 3_1(39) -> 38
1092.20/297.05	, 3_1(40) -> 39
1092.20/297.05	, 3_1(41) -> 40
1092.20/297.05	, 3_1(43) -> 51
1092.20/297.05	, 3_1(45) -> 44
1092.20/297.05	, 3_1(51) -> 50
1092.20/297.05	, 3_1(52) -> 107
1092.20/297.05	, 3_1(67) -> 66
1092.20/297.05	, 3_1(72) -> 71
1092.20/297.05	, 3_1(73) -> 72
1092.20/297.05	, 3_1(82) -> 1
1092.20/297.05	, 3_1(82) -> 107
1092.20/297.05	, 3_1(83) -> 82
1092.20/297.05	, 3_1(85) -> 84
1092.20/297.05	, 3_1(87) -> 86
1092.20/297.05	, 3_1(91) -> 90
1092.20/297.05	, 3_1(95) -> 94
1092.20/297.05	, 3_1(103) -> 102
1092.20/297.05	, 3_1(104) -> 103
1092.20/297.05	, 3_1(105) -> 104
1092.20/297.05	, 0_0(1) -> 1
1092.20/297.05	, 0_1(1) -> 60
1092.20/297.05	, 0_1(12) -> 11
1092.20/297.05	, 0_1(13) -> 12
1092.20/297.05	, 0_1(16) -> 15
1092.20/297.05	, 0_1(22) -> 21
1092.20/297.05	, 0_1(25) -> 24
1092.20/297.05	, 0_1(26) -> 25
1092.20/297.05	, 0_1(28) -> 27
1092.20/297.05	, 0_1(32) -> 31
1092.20/297.05	, 0_1(37) -> 36
1092.20/297.05	, 0_1(45) -> 60
1092.20/297.05	, 0_1(52) -> 1
1092.20/297.05	, 0_1(52) -> 51
1092.20/297.05	, 0_1(52) -> 107
1092.20/297.05	, 0_1(61) -> 44
1092.20/297.05	, 0_1(63) -> 62
1092.20/297.05	, 0_1(64) -> 63
1092.20/297.05	, 0_1(70) -> 69
1092.20/297.05	, 0_1(71) -> 70
1092.20/297.05	, 0_1(75) -> 2
1092.20/297.05	, 0_1(78) -> 77
1092.20/297.05	, 0_1(82) -> 60
1092.20/297.05	, 0_1(84) -> 83
1092.20/297.05	, 0_1(90) -> 89
1092.20/297.05	, 0_1(92) -> 91
1092.20/297.05	, 0_1(96) -> 95
1092.20/297.05	, 0_1(101) -> 100
1092.20/297.05	, 0_1(102) -> 101
1092.20/297.05	, 1_0(1) -> 1
1092.20/297.05	, 1_1(1) -> 28
1092.20/297.05	, 1_1(3) -> 2
1092.20/297.05	, 1_1(5) -> 4
1092.20/297.05	, 1_1(11) -> 1
1092.20/297.05	, 1_1(11) -> 19
1092.20/297.05	, 1_1(11) -> 51
1092.20/297.05	, 1_1(11) -> 74
1092.20/297.05	, 1_1(11) -> 107
1092.20/297.05	, 1_1(14) -> 13
1092.20/297.05	, 1_1(19) -> 18
1092.20/297.05	, 1_1(23) -> 22
1092.20/297.05	, 1_1(28) -> 92
1092.20/297.05	, 1_1(29) -> 20
1092.20/297.05	, 1_1(43) -> 99
1092.20/297.05	, 1_1(45) -> 28
1092.20/297.05	, 1_1(46) -> 45
1092.20/297.05	, 1_1(47) -> 46
1092.20/297.05	, 1_1(48) -> 47
1092.20/297.05	, 1_1(49) -> 48
1092.20/297.05	, 1_1(52) -> 28
1092.20/297.05	, 1_1(53) -> 52
1092.20/297.05	, 1_1(55) -> 54
1092.20/297.05	, 1_1(56) -> 55
1092.20/297.05	, 1_1(60) -> 59
1092.20/297.05	, 1_1(68) -> 11
1092.20/297.05	, 1_1(69) -> 68
1092.20/297.05	, 1_1(74) -> 73
1092.20/297.05	, 1_1(82) -> 28
1092.20/297.05	, 1_1(99) -> 98
1092.20/297.05	, 4_0(1) -> 1
1092.20/297.05	, 4_1(1) -> 10
1092.20/297.05	, 4_1(4) -> 3
1092.20/297.05	, 4_1(10) -> 67
1092.20/297.05	, 4_1(17) -> 16
1092.20/297.05	, 4_1(24) -> 23
1092.20/297.05	, 4_1(30) -> 29
1092.20/297.05	, 4_1(33) -> 32
1092.20/297.05	, 4_1(34) -> 33
1092.20/297.05	, 4_1(36) -> 20
1092.20/297.05	, 4_1(44) -> 1
1092.20/297.05	, 4_1(44) -> 9
1092.20/297.05	, 4_1(44) -> 10
1092.20/297.05	, 4_1(44) -> 43
1092.20/297.05	, 4_1(44) -> 51
1092.20/297.05	, 4_1(44) -> 67
1092.20/297.05	, 4_1(44) -> 107
1092.20/297.05	, 4_1(62) -> 61
1092.20/297.05	, 4_1(82) -> 10
1092.20/297.05	, 4_1(89) -> 5
1092.20/297.05	, 4_1(98) -> 97
1092.20/297.05	, 4_1(100) -> 44 }
1092.20/297.05	
1092.20/297.05	Hurray, we answered YES(?,O(n^1))
1092.88/297.62	EOF