Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 5(3(1(5(4(x1))))) -> 5(3(4(1(3(5(x1))))))
, 5(1(4(5(1(x1))))) -> 5(3(4(1(1(5(x1))))))
, 5(1(4(5(1(x1))))) -> 5(0(1(1(5(4(x1))))))
, 5(0(5(0(2(x1))))) -> 2(0(0(0(5(5(x1))))))
, 5(0(1(5(1(x1))))) -> 5(0(3(1(1(5(x1))))))
, 4(3(5(1(1(x1))))) -> 3(4(1(1(1(5(x1))))))
, 4(1(2(4(1(x1))))) -> 4(3(4(1(1(2(x1))))))
, 4(1(2(1(1(x1))))) -> 3(4(1(1(2(1(x1))))))
, 3(5(0(2(1(x1))))) -> 1(2(5(0(3(3(x1))))))
, 3(4(2(1(1(x1))))) -> 3(4(3(1(1(2(x1))))))
, 2(5(5(1(1(x1))))) -> 5(5(2(1(1(3(x1))))))
, 2(0(5(1(1(x1))))) -> 5(0(2(3(1(1(x1))))))
, 2(0(1(2(4(x1))))) -> 2(2(1(3(4(0(x1))))))
, 0(5(5(4(2(x1))))) -> 4(0(3(5(5(2(x1))))))
, 0(5(4(3(2(x1))))) -> 0(0(3(4(2(5(x1))))))
, 0(5(1(3(2(x1))))) -> 0(3(4(1(5(2(x1))))))
, 0(5(0(2(4(x1))))) -> 0(4(0(5(2(4(x1))))))
, 0(4(0(4(2(x1))))) -> 3(0(0(4(4(2(x1))))))
, 0(2(3(5(1(x1))))) -> 5(2(1(0(0(3(x1))))))
, 0(2(1(5(1(x1))))) -> 0(5(2(1(1(0(x1))))))
, 0(2(1(3(2(x1))))) -> 3(0(3(1(2(2(x1))))))
, 0(2(0(5(1(x1))))) -> 5(0(0(0(2(1(x1))))))
, 0(2(0(2(4(x1))))) -> 0(0(2(1(2(4(x1))))))
, 0(1(5(4(1(x1))))) -> 4(0(1(1(3(5(x1))))))
, 0(1(5(1(4(x1))))) -> 0(4(3(1(1(5(x1))))))
, 0(0(2(1(1(x1))))) -> 0(3(0(1(2(1(x1))))))
, 5(4(0(2(x1)))) -> 5(0(3(0(4(2(x1))))))
, 5(3(2(4(x1)))) -> 2(3(4(3(5(x1)))))
, 5(1(0(2(x1)))) -> 2(5(0(3(1(x1)))))
, 2(0(5(4(x1)))) -> 2(4(0(3(5(x1)))))
, 2(0(5(1(x1)))) -> 5(3(0(5(2(1(x1))))))
, 2(0(5(1(x1)))) -> 5(0(3(5(2(1(x1))))))
, 2(0(5(1(x1)))) -> 0(0(0(5(2(1(x1))))))
, 2(0(2(4(x1)))) -> 2(2(4(0(0(x1)))))
, 0(5(4(4(x1)))) -> 4(0(4(3(5(x1)))))
, 0(5(4(1(x1)))) -> 0(0(4(1(1(5(x1))))))
, 0(5(4(1(x1)))) -> 0(3(1(5(4(x1)))))
, 0(5(3(2(x1)))) -> 3(0(3(5(5(2(x1))))))
, 0(5(3(2(x1)))) -> 0(3(0(5(5(2(x1))))))
, 0(5(1(4(x1)))) -> 0(3(3(4(1(5(x1))))))
, 0(5(1(1(x1)))) -> 0(1(3(1(5(x1)))))
, 0(5(1(1(x1)))) -> 0(1(1(3(5(x1)))))
, 0(4(5(1(x1)))) -> 0(0(0(4(1(5(x1))))))
, 0(4(0(2(x1)))) -> 3(0(0(0(4(2(x1))))))
, 0(4(0(2(x1)))) -> 3(0(0(4(2(x1)))))
, 0(2(4(4(x1)))) -> 3(0(4(2(4(x1)))))
, 0(2(3(2(x1)))) -> 0(3(0(3(2(2(x1))))))
, 0(2(1(1(x1)))) -> 0(1(1(1(3(2(x1))))))
, 0(1(2(2(x1)))) -> 0(3(2(2(1(x1)))))
, 0(1(0(2(x1)))) -> 0(0(1(3(2(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:
{ 2_0(1) -> 1
, 2_1(1) -> 21
, 2_1(5) -> 8
, 2_1(6) -> 43
, 2_1(7) -> 7
, 2_1(10) -> 48
, 2_1(11) -> 1
, 2_1(11) -> 6
, 2_1(11) -> 14
, 2_1(11) -> 21
, 2_1(11) -> 83
, 2_1(11) -> 154
, 2_1(21) -> 59
, 2_1(22) -> 5
, 2_1(23) -> 21
, 2_1(24) -> 23
, 2_1(29) -> 28
, 2_1(31) -> 7
, 2_1(33) -> 11
, 2_1(52) -> 2
, 2_1(56) -> 55
, 2_1(61) -> 41
, 2_1(188) -> 5
, 2_2(1) -> 154
, 2_2(7) -> 175
, 2_2(9) -> 102
, 2_2(11) -> 84
, 2_2(22) -> 175
, 2_2(23) -> 107
, 2_2(24) -> 151
, 2_2(27) -> 198
, 2_2(31) -> 175
, 2_2(34) -> 107
, 2_2(61) -> 202
, 2_2(72) -> 71
, 2_2(76) -> 206
, 2_2(91) -> 90
, 2_2(121) -> 120
, 2_2(122) -> 121
, 2_2(123) -> 6
, 2_2(123) -> 127
, 2_2(123) -> 187
, 2_2(135) -> 134
, 2_2(177) -> 176
, 2_2(184) -> 14
, 2_2(184) -> 76
, 2_2(184) -> 83
, 2_2(188) -> 7
, 2_2(188) -> 21
, 2_2(188) -> 154
, 2_2(188) -> 175
, 2_2(207) -> 204
, 2_2(208) -> 207
, 0_0(1) -> 1
, 0_1(1) -> 36
, 0_1(3) -> 40
, 0_1(4) -> 44
, 0_1(5) -> 60
, 0_1(7) -> 2
, 0_1(12) -> 11
, 0_1(13) -> 12
, 0_1(14) -> 13
, 0_1(16) -> 1
, 0_1(16) -> 17
, 0_1(16) -> 36
, 0_1(16) -> 60
, 0_1(17) -> 36
, 0_1(20) -> 44
, 0_1(21) -> 60
, 0_1(23) -> 36
, 0_1(26) -> 25
, 0_1(27) -> 54
, 0_1(36) -> 1
, 0_1(36) -> 36
, 0_1(36) -> 77
, 0_1(37) -> 17
, 0_1(38) -> 8
, 0_1(39) -> 3
, 0_1(40) -> 1
, 0_1(40) -> 7
, 0_1(40) -> 21
, 0_1(40) -> 36
, 0_1(40) -> 44
, 0_1(40) -> 60
, 0_1(40) -> 154
, 0_1(41) -> 40
, 0_1(44) -> 15
, 0_1(47) -> 46
, 0_1(49) -> 15
, 0_1(50) -> 49
, 0_1(51) -> 4
, 0_1(54) -> 53
, 0_1(60) -> 1
, 0_1(60) -> 7
, 0_1(60) -> 36
, 0_1(60) -> 60
, 0_1(73) -> 17
, 0_1(75) -> 74
, 0_1(76) -> 3
, 0_2(68) -> 1
, 0_2(68) -> 7
, 0_2(68) -> 36
, 0_2(68) -> 60
, 0_2(68) -> 77
, 0_2(70) -> 69
, 0_2(81) -> 80
, 0_2(82) -> 86
, 0_2(85) -> 3
, 0_2(85) -> 13
, 0_2(86) -> 249
, 0_2(89) -> 88
, 0_2(98) -> 2
, 0_2(103) -> 60
, 0_2(119) -> 44
, 0_2(119) -> 60
, 0_2(124) -> 123
, 0_2(125) -> 124
, 0_2(126) -> 125
, 0_2(137) -> 136
, 0_2(148) -> 147
, 0_2(153) -> 224
, 0_2(168) -> 167
, 0_2(169) -> 168
, 0_2(170) -> 183
, 0_2(172) -> 171
, 0_2(173) -> 172
, 0_2(174) -> 183
, 0_2(179) -> 178
, 0_2(180) -> 179
, 0_2(182) -> 181
, 0_2(183) -> 172
, 0_2(190) -> 189
, 0_2(193) -> 192
, 0_2(194) -> 196
, 0_2(195) -> 13
, 0_2(201) -> 169
, 0_2(205) -> 204
, 0_2(249) -> 170
, 1_0(1) -> 1
, 1_1(1) -> 22
, 1_1(4) -> 16
, 1_1(5) -> 4
, 1_1(6) -> 5
, 1_1(8) -> 7
, 1_1(9) -> 8
, 1_1(11) -> 22
, 1_1(20) -> 19
, 1_1(21) -> 20
, 1_1(22) -> 32
, 1_1(23) -> 1
, 1_1(23) -> 5
, 1_1(23) -> 27
, 1_1(23) -> 138
, 1_1(23) -> 180
, 1_1(23) -> 186
, 1_1(27) -> 30
, 1_1(30) -> 29
, 1_1(33) -> 22
, 1_1(34) -> 33
, 1_1(36) -> 57
, 1_1(39) -> 45
, 1_1(48) -> 61
, 1_1(53) -> 52
, 1_1(57) -> 56
, 1_1(59) -> 58
, 1_1(87) -> 40
, 1_2(11) -> 122
, 1_2(22) -> 208
, 1_2(23) -> 72
, 1_2(24) -> 122
, 1_2(33) -> 122
, 1_2(34) -> 72
, 1_2(70) -> 133
, 1_2(71) -> 70
, 1_2(83) -> 152
, 1_2(99) -> 98
, 1_2(100) -> 99
, 1_2(101) -> 100
, 1_2(102) -> 142
, 1_2(104) -> 103
, 1_2(105) -> 104
, 1_2(106) -> 105
, 1_2(107) -> 146
, 1_2(130) -> 129
, 1_2(131) -> 130
, 1_2(132) -> 131
, 1_2(134) -> 5
, 1_2(134) -> 6
, 1_2(134) -> 27
, 1_2(134) -> 138
, 1_2(134) -> 180
, 1_2(134) -> 186
, 1_2(142) -> 141
, 1_2(146) -> 145
, 1_2(153) -> 152
, 1_2(178) -> 177
, 1_2(188) -> 208
, 1_2(191) -> 209
, 1_2(197) -> 85
, 1_2(198) -> 212
, 1_2(199) -> 198
, 1_2(200) -> 197
, 1_2(209) -> 183
, 1_2(210) -> 209
, 1_2(212) -> 211
, 3_0(1) -> 1
, 3_1(1) -> 27
, 3_1(3) -> 2
, 3_1(4) -> 7
, 3_1(5) -> 87
, 3_1(6) -> 5
, 3_1(8) -> 40
, 3_1(11) -> 40
, 3_1(14) -> 16
, 3_1(15) -> 1
, 3_1(15) -> 3
, 3_1(15) -> 10
, 3_1(15) -> 11
, 3_1(15) -> 27
, 3_1(15) -> 36
, 3_1(15) -> 60
, 3_1(15) -> 73
, 3_1(15) -> 138
, 3_1(17) -> 1
, 3_1(17) -> 36
, 3_1(18) -> 1
, 3_1(18) -> 10
, 3_1(18) -> 17
, 3_1(19) -> 16
, 3_1(21) -> 6
, 3_1(22) -> 75
, 3_1(23) -> 27
, 3_1(27) -> 26
, 3_1(32) -> 31
, 3_1(35) -> 34
, 3_1(38) -> 37
, 3_1(39) -> 7
, 3_1(40) -> 26
, 3_1(42) -> 41
, 3_1(44) -> 1
, 3_1(44) -> 36
, 3_1(44) -> 40
, 3_1(44) -> 60
, 3_1(58) -> 49
, 3_1(59) -> 4
, 3_1(73) -> 11
, 3_1(76) -> 7
, 3_2(1) -> 138
, 3_2(6) -> 180
, 3_2(8) -> 138
, 3_2(11) -> 138
, 3_2(23) -> 180
, 3_2(33) -> 138
, 3_2(69) -> 68
, 3_2(80) -> 3
, 3_2(80) -> 13
, 3_2(82) -> 81
, 3_2(86) -> 85
, 3_2(88) -> 13
, 3_2(88) -> 36
, 3_2(88) -> 60
, 3_2(102) -> 101
, 3_2(107) -> 106
, 3_2(120) -> 119
, 3_2(128) -> 73
, 3_2(134) -> 180
, 3_2(138) -> 137
, 3_2(139) -> 26
, 3_2(141) -> 140
, 3_2(143) -> 11
, 3_2(145) -> 144
, 3_2(149) -> 148
, 3_2(167) -> 40
, 3_2(168) -> 40
, 3_2(171) -> 1
, 3_2(171) -> 4
, 3_2(171) -> 7
, 3_2(171) -> 12
, 3_2(171) -> 17
, 3_2(171) -> 21
, 3_2(171) -> 36
, 3_2(171) -> 44
, 3_2(171) -> 60
, 3_2(171) -> 77
, 3_2(171) -> 154
, 3_2(171) -> 183
, 3_2(172) -> 1
, 3_2(172) -> 17
, 3_2(172) -> 36
, 3_2(172) -> 60
, 3_2(180) -> 137
, 3_2(183) -> 182
, 3_2(185) -> 184
, 3_2(187) -> 186
, 3_2(191) -> 190
, 3_2(192) -> 13
, 3_2(194) -> 193
, 3_2(196) -> 195
, 3_2(198) -> 197
, 3_2(199) -> 200
, 3_2(204) -> 98
, 3_2(206) -> 205
, 4_0(1) -> 1
, 4_1(1) -> 10
, 4_1(2) -> 33
, 4_1(4) -> 3
, 4_1(5) -> 73
, 4_1(7) -> 40
, 4_1(13) -> 16
, 4_1(16) -> 15
, 4_1(17) -> 1
, 4_1(17) -> 10
, 4_1(17) -> 13
, 4_1(17) -> 36
, 4_1(17) -> 60
, 4_1(19) -> 18
, 4_1(21) -> 51
, 4_1(23) -> 2
, 4_1(36) -> 35
, 4_1(40) -> 3
, 4_1(43) -> 42
, 4_1(45) -> 44
, 4_1(46) -> 40
, 4_1(48) -> 4
, 4_1(51) -> 50
, 4_1(60) -> 11
, 4_1(73) -> 3
, 4_1(77) -> 33
, 4_1(189) -> 10
, 4_2(17) -> 91
, 4_2(76) -> 170
, 4_2(84) -> 170
, 4_2(90) -> 89
, 4_2(107) -> 170
, 4_2(129) -> 128
, 4_2(133) -> 80
, 4_2(140) -> 139
, 4_2(144) -> 143
, 4_2(147) -> 3
, 4_2(147) -> 13
, 4_2(147) -> 224
, 4_2(152) -> 86
, 4_2(154) -> 170
, 4_2(170) -> 169
, 4_2(174) -> 173
, 4_2(175) -> 174
, 4_2(186) -> 185
, 4_2(189) -> 188
, 4_2(198) -> 86
, 4_2(202) -> 201
, 4_2(209) -> 86
, 4_2(211) -> 167
, 4_2(224) -> 68
, 5_0(1) -> 1
, 5_1(1) -> 6
, 5_1(2) -> 1
, 5_1(2) -> 6
, 5_1(2) -> 9
, 5_1(2) -> 21
, 5_1(2) -> 36
, 5_1(2) -> 43
, 5_1(2) -> 60
, 5_1(2) -> 154
, 5_1(2) -> 187
, 5_1(5) -> 76
, 5_1(6) -> 14
, 5_1(7) -> 6
, 5_1(10) -> 9
, 5_1(11) -> 6
, 5_1(17) -> 6
, 5_1(21) -> 39
, 5_1(23) -> 6
, 5_1(25) -> 24
, 5_1(28) -> 2
, 5_1(31) -> 6
, 5_1(39) -> 38
, 5_1(48) -> 47
, 5_1(55) -> 40
, 5_1(60) -> 6
, 5_1(74) -> 11
, 5_1(188) -> 6
, 5_2(6) -> 83
, 5_2(7) -> 127
, 5_2(8) -> 210
, 5_2(9) -> 132
, 5_2(17) -> 187
, 5_2(23) -> 191
, 5_2(31) -> 127
, 5_2(60) -> 187
, 5_2(83) -> 82
, 5_2(84) -> 83
, 5_2(107) -> 83
, 5_2(127) -> 126
, 5_2(134) -> 199
, 5_2(136) -> 135
, 5_2(150) -> 149
, 5_2(151) -> 150
, 5_2(153) -> 194
, 5_2(154) -> 153
, 5_2(176) -> 2
, 5_2(181) -> 6
, 5_2(181) -> 187
, 5_2(188) -> 127
, 5_2(189) -> 187}
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(3(1(5(4(x1))))) -> 5(3(4(1(3(5(x1))))))
, 5(1(4(5(1(x1))))) -> 5(3(4(1(1(5(x1))))))
, 5(1(4(5(1(x1))))) -> 5(0(1(1(5(4(x1))))))
, 5(0(5(0(2(x1))))) -> 2(0(0(0(5(5(x1))))))
, 5(0(1(5(1(x1))))) -> 5(0(3(1(1(5(x1))))))
, 4(3(5(1(1(x1))))) -> 3(4(1(1(1(5(x1))))))
, 4(1(2(4(1(x1))))) -> 4(3(4(1(1(2(x1))))))
, 4(1(2(1(1(x1))))) -> 3(4(1(1(2(1(x1))))))
, 3(5(0(2(1(x1))))) -> 1(2(5(0(3(3(x1))))))
, 3(4(2(1(1(x1))))) -> 3(4(3(1(1(2(x1))))))
, 2(5(5(1(1(x1))))) -> 5(5(2(1(1(3(x1))))))
, 2(0(5(1(1(x1))))) -> 5(0(2(3(1(1(x1))))))
, 2(0(1(2(4(x1))))) -> 2(2(1(3(4(0(x1))))))
, 0(5(5(4(2(x1))))) -> 4(0(3(5(5(2(x1))))))
, 0(5(4(3(2(x1))))) -> 0(0(3(4(2(5(x1))))))
, 0(5(1(3(2(x1))))) -> 0(3(4(1(5(2(x1))))))
, 0(5(0(2(4(x1))))) -> 0(4(0(5(2(4(x1))))))
, 0(4(0(4(2(x1))))) -> 3(0(0(4(4(2(x1))))))
, 0(2(3(5(1(x1))))) -> 5(2(1(0(0(3(x1))))))
, 0(2(1(5(1(x1))))) -> 0(5(2(1(1(0(x1))))))
, 0(2(1(3(2(x1))))) -> 3(0(3(1(2(2(x1))))))
, 0(2(0(5(1(x1))))) -> 5(0(0(0(2(1(x1))))))
, 0(2(0(2(4(x1))))) -> 0(0(2(1(2(4(x1))))))
, 0(1(5(4(1(x1))))) -> 4(0(1(1(3(5(x1))))))
, 0(1(5(1(4(x1))))) -> 0(4(3(1(1(5(x1))))))
, 0(0(2(1(1(x1))))) -> 0(3(0(1(2(1(x1))))))
, 5(4(0(2(x1)))) -> 5(0(3(0(4(2(x1))))))
, 5(3(2(4(x1)))) -> 2(3(4(3(5(x1)))))
, 5(1(0(2(x1)))) -> 2(5(0(3(1(x1)))))
, 2(0(5(4(x1)))) -> 2(4(0(3(5(x1)))))
, 2(0(5(1(x1)))) -> 5(3(0(5(2(1(x1))))))
, 2(0(5(1(x1)))) -> 5(0(3(5(2(1(x1))))))
, 2(0(5(1(x1)))) -> 0(0(0(5(2(1(x1))))))
, 2(0(2(4(x1)))) -> 2(2(4(0(0(x1)))))
, 0(5(4(4(x1)))) -> 4(0(4(3(5(x1)))))
, 0(5(4(1(x1)))) -> 0(0(4(1(1(5(x1))))))
, 0(5(4(1(x1)))) -> 0(3(1(5(4(x1)))))
, 0(5(3(2(x1)))) -> 3(0(3(5(5(2(x1))))))
, 0(5(3(2(x1)))) -> 0(3(0(5(5(2(x1))))))
, 0(5(1(4(x1)))) -> 0(3(3(4(1(5(x1))))))
, 0(5(1(1(x1)))) -> 0(1(3(1(5(x1)))))
, 0(5(1(1(x1)))) -> 0(1(1(3(5(x1)))))
, 0(4(5(1(x1)))) -> 0(0(0(4(1(5(x1))))))
, 0(4(0(2(x1)))) -> 3(0(0(0(4(2(x1))))))
, 0(4(0(2(x1)))) -> 3(0(0(4(2(x1)))))
, 0(2(4(4(x1)))) -> 3(0(4(2(4(x1)))))
, 0(2(3(2(x1)))) -> 0(3(0(3(2(2(x1))))))
, 0(2(1(1(x1)))) -> 0(1(1(1(3(2(x1))))))
, 0(1(2(2(x1)))) -> 0(3(2(2(1(x1)))))
, 0(1(0(2(x1)))) -> 0(0(1(3(2(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(3(1(5(4(x1))))) -> 5(3(4(1(3(5(x1))))))
, 5(1(4(5(1(x1))))) -> 5(3(4(1(1(5(x1))))))
, 5(1(4(5(1(x1))))) -> 5(0(1(1(5(4(x1))))))
, 5(0(5(0(2(x1))))) -> 2(0(0(0(5(5(x1))))))
, 5(0(1(5(1(x1))))) -> 5(0(3(1(1(5(x1))))))
, 4(3(5(1(1(x1))))) -> 3(4(1(1(1(5(x1))))))
, 4(1(2(4(1(x1))))) -> 4(3(4(1(1(2(x1))))))
, 4(1(2(1(1(x1))))) -> 3(4(1(1(2(1(x1))))))
, 3(5(0(2(1(x1))))) -> 1(2(5(0(3(3(x1))))))
, 3(4(2(1(1(x1))))) -> 3(4(3(1(1(2(x1))))))
, 2(5(5(1(1(x1))))) -> 5(5(2(1(1(3(x1))))))
, 2(0(5(1(1(x1))))) -> 5(0(2(3(1(1(x1))))))
, 2(0(1(2(4(x1))))) -> 2(2(1(3(4(0(x1))))))
, 0(5(5(4(2(x1))))) -> 4(0(3(5(5(2(x1))))))
, 0(5(4(3(2(x1))))) -> 0(0(3(4(2(5(x1))))))
, 0(5(1(3(2(x1))))) -> 0(3(4(1(5(2(x1))))))
, 0(5(0(2(4(x1))))) -> 0(4(0(5(2(4(x1))))))
, 0(4(0(4(2(x1))))) -> 3(0(0(4(4(2(x1))))))
, 0(2(3(5(1(x1))))) -> 5(2(1(0(0(3(x1))))))
, 0(2(1(5(1(x1))))) -> 0(5(2(1(1(0(x1))))))
, 0(2(1(3(2(x1))))) -> 3(0(3(1(2(2(x1))))))
, 0(2(0(5(1(x1))))) -> 5(0(0(0(2(1(x1))))))
, 0(2(0(2(4(x1))))) -> 0(0(2(1(2(4(x1))))))
, 0(1(5(4(1(x1))))) -> 4(0(1(1(3(5(x1))))))
, 0(1(5(1(4(x1))))) -> 0(4(3(1(1(5(x1))))))
, 0(0(2(1(1(x1))))) -> 0(3(0(1(2(1(x1))))))
, 5(4(0(2(x1)))) -> 5(0(3(0(4(2(x1))))))
, 5(3(2(4(x1)))) -> 2(3(4(3(5(x1)))))
, 5(1(0(2(x1)))) -> 2(5(0(3(1(x1)))))
, 2(0(5(4(x1)))) -> 2(4(0(3(5(x1)))))
, 2(0(5(1(x1)))) -> 5(3(0(5(2(1(x1))))))
, 2(0(5(1(x1)))) -> 5(0(3(5(2(1(x1))))))
, 2(0(5(1(x1)))) -> 0(0(0(5(2(1(x1))))))
, 2(0(2(4(x1)))) -> 2(2(4(0(0(x1)))))
, 0(5(4(4(x1)))) -> 4(0(4(3(5(x1)))))
, 0(5(4(1(x1)))) -> 0(0(4(1(1(5(x1))))))
, 0(5(4(1(x1)))) -> 0(3(1(5(4(x1)))))
, 0(5(3(2(x1)))) -> 3(0(3(5(5(2(x1))))))
, 0(5(3(2(x1)))) -> 0(3(0(5(5(2(x1))))))
, 0(5(1(4(x1)))) -> 0(3(3(4(1(5(x1))))))
, 0(5(1(1(x1)))) -> 0(1(3(1(5(x1)))))
, 0(5(1(1(x1)))) -> 0(1(1(3(5(x1)))))
, 0(4(5(1(x1)))) -> 0(0(0(4(1(5(x1))))))
, 0(4(0(2(x1)))) -> 3(0(0(0(4(2(x1))))))
, 0(4(0(2(x1)))) -> 3(0(0(4(2(x1)))))
, 0(2(4(4(x1)))) -> 3(0(4(2(4(x1)))))
, 0(2(3(2(x1)))) -> 0(3(0(3(2(2(x1))))))
, 0(2(1(1(x1)))) -> 0(1(1(1(3(2(x1))))))
, 0(1(2(2(x1)))) -> 0(3(2(2(1(x1)))))
, 0(1(0(2(x1)))) -> 0(0(1(3(2(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(3(1(5(4(x1))))) -> 5(3(4(1(3(5(x1))))))
, 5(1(4(5(1(x1))))) -> 5(3(4(1(1(5(x1))))))
, 5(1(4(5(1(x1))))) -> 5(0(1(1(5(4(x1))))))
, 5(0(5(0(2(x1))))) -> 2(0(0(0(5(5(x1))))))
, 5(0(1(5(1(x1))))) -> 5(0(3(1(1(5(x1))))))
, 4(3(5(1(1(x1))))) -> 3(4(1(1(1(5(x1))))))
, 4(1(2(4(1(x1))))) -> 4(3(4(1(1(2(x1))))))
, 4(1(2(1(1(x1))))) -> 3(4(1(1(2(1(x1))))))
, 3(5(0(2(1(x1))))) -> 1(2(5(0(3(3(x1))))))
, 3(4(2(1(1(x1))))) -> 3(4(3(1(1(2(x1))))))
, 2(5(5(1(1(x1))))) -> 5(5(2(1(1(3(x1))))))
, 2(0(5(1(1(x1))))) -> 5(0(2(3(1(1(x1))))))
, 2(0(1(2(4(x1))))) -> 2(2(1(3(4(0(x1))))))
, 0(5(5(4(2(x1))))) -> 4(0(3(5(5(2(x1))))))
, 0(5(4(3(2(x1))))) -> 0(0(3(4(2(5(x1))))))
, 0(5(1(3(2(x1))))) -> 0(3(4(1(5(2(x1))))))
, 0(5(0(2(4(x1))))) -> 0(4(0(5(2(4(x1))))))
, 0(4(0(4(2(x1))))) -> 3(0(0(4(4(2(x1))))))
, 0(2(3(5(1(x1))))) -> 5(2(1(0(0(3(x1))))))
, 0(2(1(5(1(x1))))) -> 0(5(2(1(1(0(x1))))))
, 0(2(1(3(2(x1))))) -> 3(0(3(1(2(2(x1))))))
, 0(2(0(5(1(x1))))) -> 5(0(0(0(2(1(x1))))))
, 0(2(0(2(4(x1))))) -> 0(0(2(1(2(4(x1))))))
, 0(1(5(4(1(x1))))) -> 4(0(1(1(3(5(x1))))))
, 0(1(5(1(4(x1))))) -> 0(4(3(1(1(5(x1))))))
, 0(0(2(1(1(x1))))) -> 0(3(0(1(2(1(x1))))))
, 5(4(0(2(x1)))) -> 5(0(3(0(4(2(x1))))))
, 5(3(2(4(x1)))) -> 2(3(4(3(5(x1)))))
, 5(1(0(2(x1)))) -> 2(5(0(3(1(x1)))))
, 2(0(5(4(x1)))) -> 2(4(0(3(5(x1)))))
, 2(0(5(1(x1)))) -> 5(3(0(5(2(1(x1))))))
, 2(0(5(1(x1)))) -> 5(0(3(5(2(1(x1))))))
, 2(0(5(1(x1)))) -> 0(0(0(5(2(1(x1))))))
, 2(0(2(4(x1)))) -> 2(2(4(0(0(x1)))))
, 0(5(4(4(x1)))) -> 4(0(4(3(5(x1)))))
, 0(5(4(1(x1)))) -> 0(0(4(1(1(5(x1))))))
, 0(5(4(1(x1)))) -> 0(3(1(5(4(x1)))))
, 0(5(3(2(x1)))) -> 3(0(3(5(5(2(x1))))))
, 0(5(3(2(x1)))) -> 0(3(0(5(5(2(x1))))))
, 0(5(1(4(x1)))) -> 0(3(3(4(1(5(x1))))))
, 0(5(1(1(x1)))) -> 0(1(3(1(5(x1)))))
, 0(5(1(1(x1)))) -> 0(1(1(3(5(x1)))))
, 0(4(5(1(x1)))) -> 0(0(0(4(1(5(x1))))))
, 0(4(0(2(x1)))) -> 3(0(0(0(4(2(x1))))))
, 0(4(0(2(x1)))) -> 3(0(0(4(2(x1)))))
, 0(2(4(4(x1)))) -> 3(0(4(2(4(x1)))))
, 0(2(3(2(x1)))) -> 0(3(0(3(2(2(x1))))))
, 0(2(1(1(x1)))) -> 0(1(1(1(3(2(x1))))))
, 0(1(2(2(x1)))) -> 0(3(2(2(1(x1)))))
, 0(1(0(2(x1)))) -> 0(0(1(3(2(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(3(1(5(4(x1))))) -> 5(3(4(1(3(5(x1))))))
, 5(1(4(5(1(x1))))) -> 5(3(4(1(1(5(x1))))))
, 5(1(4(5(1(x1))))) -> 5(0(1(1(5(4(x1))))))
, 5(0(5(0(2(x1))))) -> 2(0(0(0(5(5(x1))))))
, 5(0(1(5(1(x1))))) -> 5(0(3(1(1(5(x1))))))
, 4(3(5(1(1(x1))))) -> 3(4(1(1(1(5(x1))))))
, 4(1(2(4(1(x1))))) -> 4(3(4(1(1(2(x1))))))
, 4(1(2(1(1(x1))))) -> 3(4(1(1(2(1(x1))))))
, 3(5(0(2(1(x1))))) -> 1(2(5(0(3(3(x1))))))
, 3(4(2(1(1(x1))))) -> 3(4(3(1(1(2(x1))))))
, 2(5(5(1(1(x1))))) -> 5(5(2(1(1(3(x1))))))
, 2(0(5(1(1(x1))))) -> 5(0(2(3(1(1(x1))))))
, 2(0(1(2(4(x1))))) -> 2(2(1(3(4(0(x1))))))
, 0(5(5(4(2(x1))))) -> 4(0(3(5(5(2(x1))))))
, 0(5(4(3(2(x1))))) -> 0(0(3(4(2(5(x1))))))
, 0(5(1(3(2(x1))))) -> 0(3(4(1(5(2(x1))))))
, 0(5(0(2(4(x1))))) -> 0(4(0(5(2(4(x1))))))
, 0(4(0(4(2(x1))))) -> 3(0(0(4(4(2(x1))))))
, 0(2(3(5(1(x1))))) -> 5(2(1(0(0(3(x1))))))
, 0(2(1(5(1(x1))))) -> 0(5(2(1(1(0(x1))))))
, 0(2(1(3(2(x1))))) -> 3(0(3(1(2(2(x1))))))
, 0(2(0(5(1(x1))))) -> 5(0(0(0(2(1(x1))))))
, 0(2(0(2(4(x1))))) -> 0(0(2(1(2(4(x1))))))
, 0(1(5(4(1(x1))))) -> 4(0(1(1(3(5(x1))))))
, 0(1(5(1(4(x1))))) -> 0(4(3(1(1(5(x1))))))
, 0(0(2(1(1(x1))))) -> 0(3(0(1(2(1(x1))))))
, 5(4(0(2(x1)))) -> 5(0(3(0(4(2(x1))))))
, 5(3(2(4(x1)))) -> 2(3(4(3(5(x1)))))
, 5(1(0(2(x1)))) -> 2(5(0(3(1(x1)))))
, 2(0(5(4(x1)))) -> 2(4(0(3(5(x1)))))
, 2(0(5(1(x1)))) -> 5(3(0(5(2(1(x1))))))
, 2(0(5(1(x1)))) -> 5(0(3(5(2(1(x1))))))
, 2(0(5(1(x1)))) -> 0(0(0(5(2(1(x1))))))
, 2(0(2(4(x1)))) -> 2(2(4(0(0(x1)))))
, 0(5(4(4(x1)))) -> 4(0(4(3(5(x1)))))
, 0(5(4(1(x1)))) -> 0(0(4(1(1(5(x1))))))
, 0(5(4(1(x1)))) -> 0(3(1(5(4(x1)))))
, 0(5(3(2(x1)))) -> 3(0(3(5(5(2(x1))))))
, 0(5(3(2(x1)))) -> 0(3(0(5(5(2(x1))))))
, 0(5(1(4(x1)))) -> 0(3(3(4(1(5(x1))))))
, 0(5(1(1(x1)))) -> 0(1(3(1(5(x1)))))
, 0(5(1(1(x1)))) -> 0(1(1(3(5(x1)))))
, 0(4(5(1(x1)))) -> 0(0(0(4(1(5(x1))))))
, 0(4(0(2(x1)))) -> 3(0(0(0(4(2(x1))))))
, 0(4(0(2(x1)))) -> 3(0(0(4(2(x1)))))
, 0(2(4(4(x1)))) -> 3(0(4(2(4(x1)))))
, 0(2(3(2(x1)))) -> 0(3(0(3(2(2(x1))))))
, 0(2(1(1(x1)))) -> 0(1(1(1(3(2(x1))))))
, 0(1(2(2(x1)))) -> 0(3(2(2(1(x1)))))
, 0(1(0(2(x1)))) -> 0(0(1(3(2(x1)))))}
StartTerms: all
Strategy: none
Certificate: MAYBE
Proof:
The input cannot be shown compatible
Arrrr..