Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 5(5(4(x1))) -> 5(1(0(4(2(2(x1))))))
, 5(5(3(x1))) -> 5(1(0(1(2(2(x1))))))
, 4(5(4(x1))) -> 3(2(0(3(2(0(x1))))))
, 4(5(4(x1))) -> 2(2(1(0(4(2(x1))))))
, 4(5(2(x1))) -> 0(5(1(0(0(4(x1))))))
, 4(5(1(x1))) -> 2(1(0(5(3(3(x1))))))
, 3(5(5(x1))) -> 0(5(4(1(0(5(x1))))))
, 3(5(4(x1))) -> 0(5(0(0(1(2(x1))))))
, 3(5(4(x1))) -> 0(2(0(5(0(0(x1))))))
, 3(5(3(x1))) -> 2(3(4(0(4(2(x1))))))
, 3(5(3(x1))) -> 0(5(4(3(3(0(x1))))))
, 3(5(3(x1))) -> 0(2(4(3(3(0(x1))))))
, 3(5(2(x1))) -> 2(3(3(2(1(2(x1))))))
, 3(5(2(x1))) -> 2(0(2(2(3(0(x1))))))
, 3(5(2(x1))) -> 0(4(3(2(2(2(x1))))))
, 3(5(1(x1))) -> 2(1(4(1(0(1(x1))))))
, 3(5(1(x1))) -> 0(4(2(2(3(4(x1))))))
, 3(5(1(x1))) -> 0(4(2(0(0(5(x1))))))
, 3(4(2(x1))) -> 3(4(0(2(2(2(x1))))))
, 3(2(5(x1))) -> 3(2(0(1(0(5(x1))))))
, 2(5(4(x1))) -> 2(0(5(1(0(1(x1))))))
, 2(5(3(x1))) -> 2(0(4(1(3(3(x1))))))
, 2(5(2(x1))) -> 4(0(2(2(3(3(x1))))))
, 2(5(1(x1))) -> 2(2(2(1(2(3(x1))))))
, 1(4(5(x1))) -> 1(2(4(0(2(1(x1))))))
, 1(2(5(x1))) -> 2(0(1(3(1(0(x1))))))
, 1(2(5(x1))) -> 1(2(2(1(0(1(x1))))))
, 1(2(5(x1))) -> 1(0(5(0(5(4(x1))))))
, 4(5(x1)) -> 3(2(0(5(0(0(x1))))))
, 4(5(x1)) -> 2(2(1(3(2(1(x1))))))
, 3(5(x1)) -> 3(2(0(5(3(0(x1))))))
, 3(5(x1)) -> 1(3(2(0(0(1(x1))))))
, 2(5(x1)) -> 2(2(0(5(0(1(x1))))))
, 2(5(x1)) -> 1(3(3(0(1(0(x1))))))}
StartTerms: all
Strategy: none
Certificate: YES(?,O(n^1))
Proof:
The problem is match-bounded by 2.
The enriched problem is compatible with the following automaton:
{ 5_0(1) -> 1
, 5_1(1) -> 32
, 5_1(2) -> 1
, 5_1(2) -> 32
, 5_1(3) -> 32
, 5_1(17) -> 16
, 5_1(20) -> 95
, 5_1(23) -> 22
, 5_1(37) -> 36
, 5_1(39) -> 9
, 5_1(45) -> 41
, 5_1(46) -> 130
, 5_1(69) -> 32
, 5_1(78) -> 32
, 5_1(94) -> 93
, 5_1(125) -> 32
, 5_2(3) -> 61
, 5_2(18) -> 177
, 5_2(28) -> 27
, 5_2(69) -> 61
, 5_2(91) -> 131
, 5_2(97) -> 96
, 5_2(99) -> 98
, 5_2(106) -> 105
, 5_2(115) -> 114
, 5_2(119) -> 118
, 5_2(125) -> 61
, 5_2(128) -> 131
, 5_2(143) -> 142
, 5_2(149) -> 148
, 5_2(195) -> 194
, 2_0(1) -> 1
, 2_1(1) -> 6
, 2_1(5) -> 44
, 2_1(6) -> 5
, 2_1(7) -> 6
, 2_1(8) -> 7
, 2_1(11) -> 10
, 2_1(12) -> 1
, 2_1(12) -> 6
, 2_1(12) -> 20
, 2_1(12) -> 24
, 2_1(12) -> 34
, 2_1(12) -> 47
, 2_1(13) -> 12
, 2_1(16) -> 6
, 2_1(17) -> 16
, 2_1(23) -> 71
, 2_1(24) -> 73
, 2_1(34) -> 40
, 2_1(35) -> 16
, 2_1(37) -> 121
, 2_1(39) -> 42
, 2_1(42) -> 41
, 2_1(45) -> 79
, 2_1(47) -> 81
, 2_1(53) -> 43
, 2_1(54) -> 53
, 2_1(69) -> 6
, 2_1(71) -> 70
, 2_1(72) -> 13
, 2_1(73) -> 43
, 2_1(79) -> 78
, 2_1(116) -> 6
, 2_1(151) -> 1
, 2_2(12) -> 67
, 2_2(13) -> 67
, 2_2(20) -> 66
, 2_2(23) -> 146
, 2_2(25) -> 20
, 2_2(29) -> 77
, 2_2(30) -> 146
, 2_2(48) -> 24
, 2_2(53) -> 189
, 2_2(57) -> 56
, 2_2(58) -> 57
, 2_2(66) -> 65
, 2_2(67) -> 66
, 2_2(73) -> 189
, 2_2(74) -> 6
, 2_2(75) -> 74
, 2_2(76) -> 75
, 2_2(79) -> 189
, 2_2(83) -> 34
, 2_2(89) -> 88
, 2_2(90) -> 89
, 2_2(92) -> 109
, 2_2(104) -> 103
, 2_2(107) -> 25
, 2_2(113) -> 112
, 2_2(117) -> 116
, 2_2(124) -> 123
, 2_2(127) -> 126
, 2_2(147) -> 142
, 2_2(151) -> 1
, 2_2(151) -> 20
, 2_2(165) -> 164
, 2_2(166) -> 165
, 2_2(188) -> 187
, 2_2(189) -> 188
, 0_0(1) -> 1
, 0_1(1) -> 11
, 0_1(2) -> 46
, 0_1(4) -> 3
, 0_1(5) -> 62
, 0_1(7) -> 11
, 0_1(9) -> 8
, 0_1(11) -> 37
, 0_1(12) -> 11
, 0_1(15) -> 14
, 0_1(16) -> 1
, 0_1(16) -> 20
, 0_1(16) -> 24
, 0_1(19) -> 18
, 0_1(20) -> 19
, 0_1(22) -> 21
, 0_1(30) -> 8
, 0_1(31) -> 53
, 0_1(32) -> 31
, 0_1(33) -> 17
, 0_1(34) -> 33
, 0_1(36) -> 35
, 0_1(41) -> 12
, 0_1(44) -> 62
, 0_1(45) -> 8
, 0_1(46) -> 37
, 0_1(47) -> 46
, 0_1(69) -> 11
, 0_1(70) -> 69
, 0_1(81) -> 80
, 0_1(93) -> 78
, 0_1(95) -> 94
, 0_1(116) -> 1
, 0_1(130) -> 13
, 0_1(151) -> 11
, 0_2(2) -> 87
, 0_2(17) -> 120
, 0_2(20) -> 51
, 0_2(23) -> 150
, 0_2(27) -> 26
, 0_2(30) -> 150
, 0_2(52) -> 51
, 0_2(55) -> 24
, 0_2(60) -> 57
, 0_2(61) -> 60
, 0_2(65) -> 64
, 0_2(84) -> 83
, 0_2(86) -> 134
, 0_2(87) -> 106
, 0_2(91) -> 124
, 0_2(92) -> 91
, 0_2(96) -> 88
, 0_2(98) -> 97
, 0_2(105) -> 104
, 0_2(114) -> 113
, 0_2(118) -> 117
, 0_2(128) -> 127
, 0_2(129) -> 128
, 0_2(131) -> 75
, 0_2(142) -> 1
, 0_2(142) -> 20
, 0_2(144) -> 143
, 0_2(145) -> 144
, 0_2(148) -> 147
, 0_2(150) -> 149
, 0_2(155) -> 154
, 0_2(176) -> 165
, 0_2(177) -> 176
, 0_2(187) -> 186
, 0_2(194) -> 74
, 0_2(197) -> 196
, 1_0(1) -> 1
, 1_1(1) -> 47
, 1_1(2) -> 47
, 1_1(3) -> 2
, 1_1(5) -> 4
, 1_1(6) -> 34
, 1_1(11) -> 30
, 1_1(14) -> 13
, 1_1(18) -> 17
, 1_1(21) -> 12
, 1_1(23) -> 68
, 1_1(24) -> 34
, 1_1(31) -> 30
, 1_1(46) -> 45
, 1_1(69) -> 2
, 1_1(73) -> 72
, 1_1(78) -> 1
, 1_1(78) -> 6
, 1_1(78) -> 24
, 1_1(78) -> 34
, 1_1(78) -> 47
, 1_1(82) -> 41
, 1_1(125) -> 2
, 1_2(2) -> 92
, 1_2(3) -> 52
, 1_2(17) -> 129
, 1_2(18) -> 155
, 1_2(23) -> 197
, 1_2(26) -> 25
, 1_2(30) -> 197
, 1_2(49) -> 48
, 1_2(51) -> 50
, 1_2(69) -> 52
, 1_2(77) -> 76
, 1_2(85) -> 84
, 1_2(87) -> 86
, 1_2(88) -> 34
, 1_2(91) -> 90
, 1_2(108) -> 107
, 1_2(120) -> 86
, 1_2(122) -> 24
, 1_2(125) -> 1
, 1_2(125) -> 20
, 1_2(128) -> 90
, 1_2(132) -> 6
, 1_2(146) -> 145
, 1_2(152) -> 151
, 1_2(154) -> 153
, 1_2(196) -> 195
, 3_0(1) -> 1
, 3_1(1) -> 24
, 3_1(3) -> 24
, 3_1(5) -> 43
, 3_1(7) -> 1
, 3_1(7) -> 20
, 3_1(7) -> 24
, 3_1(7) -> 54
, 3_1(8) -> 121
, 3_1(10) -> 9
, 3_1(11) -> 39
, 3_1(12) -> 24
, 3_1(14) -> 12
, 3_1(16) -> 1
, 3_1(16) -> 20
, 3_1(20) -> 54
, 3_1(24) -> 23
, 3_1(30) -> 82
, 3_1(38) -> 12
, 3_1(39) -> 30
, 3_1(40) -> 38
, 3_1(44) -> 43
, 3_1(45) -> 82
, 3_1(46) -> 37
, 3_1(69) -> 24
, 3_1(78) -> 24
, 3_1(81) -> 14
, 3_1(116) -> 1
, 3_1(121) -> 78
, 3_1(125) -> 24
, 3_1(151) -> 24
, 3_2(3) -> 29
, 3_2(18) -> 29
, 3_2(29) -> 28
, 3_2(59) -> 58
, 3_2(63) -> 54
, 3_2(69) -> 29
, 3_2(86) -> 85
, 3_2(87) -> 115
, 3_2(103) -> 20
, 3_2(109) -> 108
, 3_2(112) -> 24
, 3_2(116) -> 1
, 3_2(116) -> 20
, 3_2(116) -> 24
, 3_2(116) -> 54
, 3_2(120) -> 119
, 3_2(123) -> 122
, 3_2(125) -> 29
, 3_2(126) -> 125
, 3_2(133) -> 132
, 3_2(134) -> 133
, 3_2(167) -> 166
, 4_0(1) -> 1
, 4_1(1) -> 20
, 4_1(2) -> 20
, 4_1(3) -> 20
, 4_1(5) -> 4
, 4_1(6) -> 15
, 4_1(12) -> 20
, 4_1(14) -> 38
, 4_1(23) -> 17
, 4_1(30) -> 17
, 4_1(34) -> 41
, 4_1(43) -> 16
, 4_1(45) -> 21
, 4_1(62) -> 7
, 4_1(68) -> 41
, 4_1(69) -> 1
, 4_1(69) -> 6
, 4_1(78) -> 7
, 4_1(80) -> 79
, 4_1(125) -> 7
, 4_1(151) -> 20
, 4_2(2) -> 99
, 4_2(3) -> 59
, 4_2(17) -> 99
, 4_2(18) -> 167
, 4_2(50) -> 49
, 4_2(56) -> 55
, 4_2(64) -> 63
, 4_2(69) -> 59
, 4_2(125) -> 59
, 4_2(153) -> 152
, 4_2(164) -> 142
, 4_2(186) -> 116}
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:
{ 5(5(4(x1))) -> 5(1(0(4(2(2(x1))))))
, 5(5(3(x1))) -> 5(1(0(1(2(2(x1))))))
, 4(5(4(x1))) -> 3(2(0(3(2(0(x1))))))
, 4(5(4(x1))) -> 2(2(1(0(4(2(x1))))))
, 4(5(2(x1))) -> 0(5(1(0(0(4(x1))))))
, 4(5(1(x1))) -> 2(1(0(5(3(3(x1))))))
, 3(5(5(x1))) -> 0(5(4(1(0(5(x1))))))
, 3(5(4(x1))) -> 0(5(0(0(1(2(x1))))))
, 3(5(4(x1))) -> 0(2(0(5(0(0(x1))))))
, 3(5(3(x1))) -> 2(3(4(0(4(2(x1))))))
, 3(5(3(x1))) -> 0(5(4(3(3(0(x1))))))
, 3(5(3(x1))) -> 0(2(4(3(3(0(x1))))))
, 3(5(2(x1))) -> 2(3(3(2(1(2(x1))))))
, 3(5(2(x1))) -> 2(0(2(2(3(0(x1))))))
, 3(5(2(x1))) -> 0(4(3(2(2(2(x1))))))
, 3(5(1(x1))) -> 2(1(4(1(0(1(x1))))))
, 3(5(1(x1))) -> 0(4(2(2(3(4(x1))))))
, 3(5(1(x1))) -> 0(4(2(0(0(5(x1))))))
, 3(4(2(x1))) -> 3(4(0(2(2(2(x1))))))
, 3(2(5(x1))) -> 3(2(0(1(0(5(x1))))))
, 2(5(4(x1))) -> 2(0(5(1(0(1(x1))))))
, 2(5(3(x1))) -> 2(0(4(1(3(3(x1))))))
, 2(5(2(x1))) -> 4(0(2(2(3(3(x1))))))
, 2(5(1(x1))) -> 2(2(2(1(2(3(x1))))))
, 1(4(5(x1))) -> 1(2(4(0(2(1(x1))))))
, 1(2(5(x1))) -> 2(0(1(3(1(0(x1))))))
, 1(2(5(x1))) -> 1(2(2(1(0(1(x1))))))
, 1(2(5(x1))) -> 1(0(5(0(5(4(x1))))))
, 4(5(x1)) -> 3(2(0(5(0(0(x1))))))
, 4(5(x1)) -> 2(2(1(3(2(1(x1))))))
, 3(5(x1)) -> 3(2(0(5(3(0(x1))))))
, 3(5(x1)) -> 1(3(2(0(0(1(x1))))))
, 2(5(x1)) -> 2(2(0(5(0(1(x1))))))
, 2(5(x1)) -> 1(3(3(0(1(0(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:
{ 5(5(4(x1))) -> 5(1(0(4(2(2(x1))))))
, 5(5(3(x1))) -> 5(1(0(1(2(2(x1))))))
, 4(5(4(x1))) -> 3(2(0(3(2(0(x1))))))
, 4(5(4(x1))) -> 2(2(1(0(4(2(x1))))))
, 4(5(2(x1))) -> 0(5(1(0(0(4(x1))))))
, 4(5(1(x1))) -> 2(1(0(5(3(3(x1))))))
, 3(5(5(x1))) -> 0(5(4(1(0(5(x1))))))
, 3(5(4(x1))) -> 0(5(0(0(1(2(x1))))))
, 3(5(4(x1))) -> 0(2(0(5(0(0(x1))))))
, 3(5(3(x1))) -> 2(3(4(0(4(2(x1))))))
, 3(5(3(x1))) -> 0(5(4(3(3(0(x1))))))
, 3(5(3(x1))) -> 0(2(4(3(3(0(x1))))))
, 3(5(2(x1))) -> 2(3(3(2(1(2(x1))))))
, 3(5(2(x1))) -> 2(0(2(2(3(0(x1))))))
, 3(5(2(x1))) -> 0(4(3(2(2(2(x1))))))
, 3(5(1(x1))) -> 2(1(4(1(0(1(x1))))))
, 3(5(1(x1))) -> 0(4(2(2(3(4(x1))))))
, 3(5(1(x1))) -> 0(4(2(0(0(5(x1))))))
, 3(4(2(x1))) -> 3(4(0(2(2(2(x1))))))
, 3(2(5(x1))) -> 3(2(0(1(0(5(x1))))))
, 2(5(4(x1))) -> 2(0(5(1(0(1(x1))))))
, 2(5(3(x1))) -> 2(0(4(1(3(3(x1))))))
, 2(5(2(x1))) -> 4(0(2(2(3(3(x1))))))
, 2(5(1(x1))) -> 2(2(2(1(2(3(x1))))))
, 1(4(5(x1))) -> 1(2(4(0(2(1(x1))))))
, 1(2(5(x1))) -> 2(0(1(3(1(0(x1))))))
, 1(2(5(x1))) -> 1(2(2(1(0(1(x1))))))
, 1(2(5(x1))) -> 1(0(5(0(5(4(x1))))))
, 4(5(x1)) -> 3(2(0(5(0(0(x1))))))
, 4(5(x1)) -> 2(2(1(3(2(1(x1))))))
, 3(5(x1)) -> 3(2(0(5(3(0(x1))))))
, 3(5(x1)) -> 1(3(2(0(0(1(x1))))))
, 2(5(x1)) -> 2(2(0(5(0(1(x1))))))
, 2(5(x1)) -> 1(3(3(0(1(0(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:
{ 5(5(4(x1))) -> 5(1(0(4(2(2(x1))))))
, 5(5(3(x1))) -> 5(1(0(1(2(2(x1))))))
, 4(5(4(x1))) -> 3(2(0(3(2(0(x1))))))
, 4(5(4(x1))) -> 2(2(1(0(4(2(x1))))))
, 4(5(2(x1))) -> 0(5(1(0(0(4(x1))))))
, 4(5(1(x1))) -> 2(1(0(5(3(3(x1))))))
, 3(5(5(x1))) -> 0(5(4(1(0(5(x1))))))
, 3(5(4(x1))) -> 0(5(0(0(1(2(x1))))))
, 3(5(4(x1))) -> 0(2(0(5(0(0(x1))))))
, 3(5(3(x1))) -> 2(3(4(0(4(2(x1))))))
, 3(5(3(x1))) -> 0(5(4(3(3(0(x1))))))
, 3(5(3(x1))) -> 0(2(4(3(3(0(x1))))))
, 3(5(2(x1))) -> 2(3(3(2(1(2(x1))))))
, 3(5(2(x1))) -> 2(0(2(2(3(0(x1))))))
, 3(5(2(x1))) -> 0(4(3(2(2(2(x1))))))
, 3(5(1(x1))) -> 2(1(4(1(0(1(x1))))))
, 3(5(1(x1))) -> 0(4(2(2(3(4(x1))))))
, 3(5(1(x1))) -> 0(4(2(0(0(5(x1))))))
, 3(4(2(x1))) -> 3(4(0(2(2(2(x1))))))
, 3(2(5(x1))) -> 3(2(0(1(0(5(x1))))))
, 2(5(4(x1))) -> 2(0(5(1(0(1(x1))))))
, 2(5(3(x1))) -> 2(0(4(1(3(3(x1))))))
, 2(5(2(x1))) -> 4(0(2(2(3(3(x1))))))
, 2(5(1(x1))) -> 2(2(2(1(2(3(x1))))))
, 1(4(5(x1))) -> 1(2(4(0(2(1(x1))))))
, 1(2(5(x1))) -> 2(0(1(3(1(0(x1))))))
, 1(2(5(x1))) -> 1(2(2(1(0(1(x1))))))
, 1(2(5(x1))) -> 1(0(5(0(5(4(x1))))))
, 4(5(x1)) -> 3(2(0(5(0(0(x1))))))
, 4(5(x1)) -> 2(2(1(3(2(1(x1))))))
, 3(5(x1)) -> 3(2(0(5(3(0(x1))))))
, 3(5(x1)) -> 1(3(2(0(0(1(x1))))))
, 2(5(x1)) -> 2(2(0(5(0(1(x1))))))
, 2(5(x1)) -> 1(3(3(0(1(0(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:
{ 5(5(4(x1))) -> 5(1(0(4(2(2(x1))))))
, 5(5(3(x1))) -> 5(1(0(1(2(2(x1))))))
, 4(5(4(x1))) -> 3(2(0(3(2(0(x1))))))
, 4(5(4(x1))) -> 2(2(1(0(4(2(x1))))))
, 4(5(2(x1))) -> 0(5(1(0(0(4(x1))))))
, 4(5(1(x1))) -> 2(1(0(5(3(3(x1))))))
, 3(5(5(x1))) -> 0(5(4(1(0(5(x1))))))
, 3(5(4(x1))) -> 0(5(0(0(1(2(x1))))))
, 3(5(4(x1))) -> 0(2(0(5(0(0(x1))))))
, 3(5(3(x1))) -> 2(3(4(0(4(2(x1))))))
, 3(5(3(x1))) -> 0(5(4(3(3(0(x1))))))
, 3(5(3(x1))) -> 0(2(4(3(3(0(x1))))))
, 3(5(2(x1))) -> 2(3(3(2(1(2(x1))))))
, 3(5(2(x1))) -> 2(0(2(2(3(0(x1))))))
, 3(5(2(x1))) -> 0(4(3(2(2(2(x1))))))
, 3(5(1(x1))) -> 2(1(4(1(0(1(x1))))))
, 3(5(1(x1))) -> 0(4(2(2(3(4(x1))))))
, 3(5(1(x1))) -> 0(4(2(0(0(5(x1))))))
, 3(4(2(x1))) -> 3(4(0(2(2(2(x1))))))
, 3(2(5(x1))) -> 3(2(0(1(0(5(x1))))))
, 2(5(4(x1))) -> 2(0(5(1(0(1(x1))))))
, 2(5(3(x1))) -> 2(0(4(1(3(3(x1))))))
, 2(5(2(x1))) -> 4(0(2(2(3(3(x1))))))
, 2(5(1(x1))) -> 2(2(2(1(2(3(x1))))))
, 1(4(5(x1))) -> 1(2(4(0(2(1(x1))))))
, 1(2(5(x1))) -> 2(0(1(3(1(0(x1))))))
, 1(2(5(x1))) -> 1(2(2(1(0(1(x1))))))
, 1(2(5(x1))) -> 1(0(5(0(5(4(x1))))))
, 4(5(x1)) -> 3(2(0(5(0(0(x1))))))
, 4(5(x1)) -> 2(2(1(3(2(1(x1))))))
, 3(5(x1)) -> 3(2(0(5(3(0(x1))))))
, 3(5(x1)) -> 1(3(2(0(0(1(x1))))))
, 2(5(x1)) -> 2(2(0(5(0(1(x1))))))
, 2(5(x1)) -> 1(3(3(0(1(0(x1))))))}
StartTerms: all
Strategy: none
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..