Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs: {a(a(b(b(x1)))) -> b(b(b(a(a(a(a(a(x1))))))))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
The problem is match-bounded by 7.
The enriched problem is compatible with the following automaton:
{ b_0(1) -> 1
, b_1(2) -> 1
, b_1(2) -> 7
, b_1(2) -> 8
, b_1(3) -> 2
, b_1(4) -> 3
, b_2(9) -> 4
, b_2(9) -> 5
, b_2(9) -> 6
, b_2(9) -> 7
, b_2(9) -> 14
, b_2(9) -> 15
, b_2(10) -> 9
, b_2(11) -> 10
, b_3(16) -> 12
, b_3(16) -> 13
, b_3(16) -> 14
, b_3(16) -> 21
, b_3(17) -> 16
, b_3(18) -> 17
, b_3(23) -> 11
, b_3(23) -> 12
, b_3(23) -> 22
, b_3(24) -> 23
, b_3(25) -> 24
, b_4(30) -> 20
, b_4(30) -> 21
, b_4(31) -> 30
, b_4(32) -> 31
, b_4(37) -> 18
, b_4(37) -> 19
, b_4(38) -> 37
, b_4(39) -> 38
, b_4(44) -> 28
, b_4(44) -> 42
, b_4(45) -> 44
, b_4(46) -> 45
, b_4(51) -> 26
, b_4(52) -> 51
, b_4(53) -> 52
, b_4(72) -> 36
, b_4(73) -> 72
, b_4(74) -> 73
, b_5(58) -> 49
, b_5(59) -> 58
, b_5(60) -> 59
, b_5(65) -> 40
, b_5(66) -> 65
, b_5(67) -> 66
, b_5(79) -> 47
, b_5(80) -> 79
, b_5(81) -> 80
, b_5(86) -> 64
, b_5(87) -> 86
, b_5(88) -> 87
, b_5(93) -> 34
, b_5(94) -> 93
, b_5(95) -> 94
, b_5(107) -> 32
, b_5(108) -> 107
, b_5(109) -> 108
, b_5(121) -> 42
, b_5(122) -> 121
, b_5(123) -> 122
, b_6(100) -> 62
, b_6(101) -> 100
, b_6(102) -> 101
, b_6(114) -> 60
, b_6(115) -> 114
, b_6(116) -> 115
, b_6(128) -> 84
, b_6(129) -> 128
, b_6(130) -> 129
, b_6(135) -> 126
, b_6(136) -> 135
, b_6(137) -> 136
, b_6(142) -> 82
, b_6(143) -> 142
, b_6(144) -> 143
, b_6(156) -> 124
, b_6(157) -> 156
, b_6(158) -> 157
, b_7(149) -> 133
, b_7(150) -> 149
, b_7(151) -> 150
, b_7(163) -> 131
, b_7(164) -> 163
, b_7(165) -> 164
, a_0(1) -> 1
, a_1(1) -> 8
, a_1(2) -> 8
, a_1(3) -> 8
, a_1(5) -> 4
, a_1(6) -> 5
, a_1(7) -> 6
, a_1(8) -> 7
, a_2(3) -> 15
, a_2(4) -> 15
, a_2(9) -> 15
, a_2(10) -> 15
, a_2(12) -> 11
, a_2(13) -> 12
, a_2(14) -> 13
, a_2(15) -> 14
, a_3(10) -> 22
, a_3(11) -> 22
, a_3(17) -> 29
, a_3(19) -> 18
, a_3(20) -> 19
, a_3(21) -> 20
, a_3(22) -> 21
, a_3(23) -> 22
, a_3(24) -> 29
, a_3(26) -> 25
, a_3(27) -> 26
, a_3(28) -> 27
, a_3(29) -> 28
, a_4(17) -> 43
, a_4(24) -> 36
, a_4(25) -> 36
, a_4(31) -> 43
, a_4(33) -> 32
, a_4(34) -> 33
, a_4(35) -> 34
, a_4(36) -> 35
, a_4(37) -> 50
, a_4(40) -> 39
, a_4(41) -> 40
, a_4(42) -> 41
, a_4(43) -> 42
, a_4(45) -> 57
, a_4(47) -> 46
, a_4(48) -> 47
, a_4(49) -> 48
, a_4(50) -> 49
, a_4(52) -> 78
, a_4(54) -> 53
, a_4(55) -> 54
, a_4(56) -> 55
, a_4(57) -> 56
, a_4(75) -> 74
, a_4(76) -> 75
, a_4(77) -> 76
, a_4(78) -> 77
, a_5(39) -> 64
, a_5(45) -> 71
, a_5(59) -> 85
, a_5(61) -> 60
, a_5(62) -> 61
, a_5(63) -> 62
, a_5(64) -> 63
, a_5(66) -> 92
, a_5(68) -> 67
, a_5(69) -> 68
, a_5(70) -> 69
, a_5(71) -> 70
, a_5(73) -> 99
, a_5(82) -> 81
, a_5(83) -> 82
, a_5(84) -> 83
, a_5(85) -> 84
, a_5(89) -> 88
, a_5(90) -> 89
, a_5(91) -> 90
, a_5(92) -> 91
, a_5(94) -> 113
, a_5(96) -> 95
, a_5(97) -> 96
, a_5(98) -> 97
, a_5(99) -> 98
, a_5(107) -> 127
, a_5(110) -> 109
, a_5(111) -> 110
, a_5(112) -> 111
, a_5(113) -> 112
, a_5(122) -> 71
, a_5(124) -> 123
, a_5(125) -> 124
, a_5(126) -> 125
, a_5(127) -> 126
, a_6(87) -> 106
, a_6(101) -> 120
, a_6(103) -> 102
, a_6(104) -> 103
, a_6(105) -> 104
, a_6(106) -> 105
, a_6(109) -> 141
, a_6(114) -> 134
, a_6(117) -> 116
, a_6(118) -> 117
, a_6(119) -> 118
, a_6(120) -> 119
, a_6(129) -> 148
, a_6(131) -> 130
, a_6(132) -> 131
, a_6(133) -> 132
, a_6(134) -> 133
, a_6(136) -> 162
, a_6(138) -> 137
, a_6(139) -> 138
, a_6(140) -> 139
, a_6(141) -> 140
, a_6(145) -> 144
, a_6(146) -> 145
, a_6(147) -> 146
, a_6(148) -> 147
, a_6(159) -> 158
, a_6(160) -> 159
, a_6(161) -> 160
, a_6(162) -> 161
, a_7(116) -> 155
, a_7(150) -> 169
, a_7(152) -> 151
, a_7(153) -> 152
, a_7(154) -> 153
, a_7(155) -> 154
, a_7(166) -> 165
, a_7(167) -> 166
, a_7(168) -> 167
, a_7(169) -> 168}
Hurray, we answered YES(?,O(n^1))Tool CDI
stdout:
TIMEOUT
Statistics:
Number of monomials: 0
Last formula building started for bound 0
Last SAT solving started for bound 0Tool EDA
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs: {a(a(b(b(x1)))) -> b(b(b(a(a(a(a(a(x1))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool IDA
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs: {a(a(b(b(x1)))) -> b(b(b(a(a(a(a(a(x1))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool TRI
stdout:
TIMEOUT
We consider the following Problem:
Strict Trs: {a(a(b(b(x1)))) -> b(b(b(a(a(a(a(a(x1))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..Tool TRI2
stdout:
MAYBE
We consider the following Problem:
Strict Trs: {a(a(b(b(x1)))) -> b(b(b(a(a(a(a(a(x1))))))))}
StartTerms: all
Strategy: none
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..