Tool Bounds
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ 5(2(0(2(5(3(3(x1))))))) -> 5(2(0(5(1(1(3(2(0(3(x1))))))))))
, 5(1(5(3(3(0(5(x1))))))) -> 4(4(3(2(2(2(5(0(1(1(x1))))))))))
, 5(0(5(3(5(1(5(x1))))))) -> 5(1(1(2(4(0(0(3(2(5(x1))))))))))
, 5(0(5(3(1(0(5(x1))))))) -> 5(2(4(4(2(1(3(5(1(5(x1))))))))))
, 4(5(5(3(1(0(5(x1))))))) -> 1(1(5(2(0(3(3(3(2(1(x1))))))))))
, 4(3(1(2(5(2(4(x1))))))) -> 2(3(1(1(4(3(4(4(2(4(x1))))))))))
, 3(5(0(5(5(5(0(x1))))))) -> 0(0(3(0(3(5(0(3(2(0(x1))))))))))
, 3(3(4(2(5(5(2(x1))))))) -> 1(2(3(3(4(4(1(4(0(1(x1))))))))))
, 3(2(3(5(1(5(2(x1))))))) -> 2(0(3(2(3(2(1(5(5(1(x1))))))))))
, 2(5(4(5(2(5(1(x1))))))) -> 4(3(2(1(4(2(2(4(5(2(x1))))))))))
, 1(5(5(3(3(3(4(x1))))))) -> 1(5(1(0(0(2(2(2(3(5(x1))))))))))
, 1(2(5(5(0(3(3(x1))))))) -> 3(4(1(2(0(3(3(1(0(3(x1))))))))))
, 1(2(0(4(2(5(0(x1))))))) -> 4(2(4(0(3(2(2(4(1(0(x1))))))))))
, 1(0(2(5(2(0(0(x1))))))) -> 3(1(4(4(0(3(0(1(2(2(x1))))))))))
, 0(4(4(2(5(5(5(x1))))))) -> 0(2(4(5(5(4(2(0(1(1(x1))))))))))
, 0(4(4(0(0(5(1(x1))))))) -> 1(3(2(0(4(1(5(1(1(2(x1))))))))))
, 5(5(3(5(0(5(x1)))))) -> 5(4(4(3(5(1(3(3(4(5(x1))))))))))
, 5(5(0(3(4(5(x1)))))) -> 2(0(5(5(2(1(3(2(3(2(x1))))))))))
, 5(5(0(2(5(0(x1)))))) -> 2(0(5(0(2(1(0(0(3(0(x1))))))))))
, 5(2(0(2(5(5(x1)))))) -> 5(5(4(4(4(5(4(4(1(4(x1))))))))))
, 5(1(5(0(2(5(x1)))))) -> 5(0(0(1(4(2(3(2(1(5(x1))))))))))
, 5(0(0(3(5(2(x1)))))) -> 4(4(2(3(0(1(2(0(5(2(x1))))))))))
, 4(5(5(4(2(0(x1)))))) -> 2(4(0(1(3(4(4(4(1(0(x1))))))))))
, 0(5(5(1(5(1(x1)))))) -> 0(5(1(1(3(3(4(2(1(0(x1))))))))))
, 0(5(3(1(2(5(x1)))))) -> 0(2(3(1(1(2(4(4(5(5(x1))))))))))
, 0(2(5(5(1(4(x1)))))) -> 4(0(1(1(1(1(0(4(1(5(x1))))))))))
, 0(2(5(1(5(0(x1)))))) -> 2(1(0(1(5(2(4(0(2(0(x1))))))))))
, 3(5(5(0(0(x1))))) -> 1(4(1(0(0(4(4(0(4(1(x1))))))))))
, 3(0(0(5(3(x1))))) -> 1(3(4(3(5(2(4(1(3(3(x1))))))))))
, 0(5(1(5(0(x1))))) -> 3(4(0(1(4(5(2(2(3(1(x1))))))))))
, 5(5(5(0(x1)))) -> 4(1(2(1(2(3(5(0(1(3(x1))))))))))
, 2(5(5(3(x1)))) -> 4(3(0(2(1(0(1(3(4(3(x1))))))))))
, 0(5(0(5(x1)))) -> 3(2(0(2(0(4(4(1(5(4(x1))))))))))
, 0(2(5(0(x1)))) -> 0(2(1(1(5(2(1(4(1(3(x1))))))))))
, 0(5(0(x1))) -> 3(4(3(3(2(0(4(4(4(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:
{ 0_0(1) -> 1
, 0_1(1) -> 59
, 0_1(4) -> 3
, 0_1(10) -> 9
, 0_1(18) -> 17
, 0_1(19) -> 66
, 0_1(20) -> 59
, 0_1(24) -> 23
, 0_1(25) -> 24
, 0_1(26) -> 193
, 0_1(27) -> 155
, 0_1(34) -> 59
, 0_1(38) -> 37
, 0_1(51) -> 1
, 0_1(51) -> 10
, 0_1(51) -> 59
, 0_1(51) -> 87
, 0_1(51) -> 155
, 0_1(51) -> 193
, 0_1(52) -> 51
, 0_1(54) -> 53
, 0_1(57) -> 56
, 0_1(58) -> 193
, 0_1(67) -> 42
, 0_1(80) -> 155
, 0_1(82) -> 59
, 0_1(83) -> 82
, 0_1(84) -> 83
, 0_1(92) -> 91
, 0_1(97) -> 96
, 0_1(100) -> 199
, 0_1(105) -> 104
, 0_1(107) -> 106
, 0_1(116) -> 115
, 0_1(133) -> 128
, 0_1(136) -> 135
, 0_1(137) -> 136
, 0_1(145) -> 2
, 0_1(146) -> 145
, 0_1(153) -> 152
, 0_1(157) -> 156
, 0_1(182) -> 11
, 0_1(187) -> 186
, 0_1(189) -> 188
, 0_1(196) -> 195
, 0_1(197) -> 196
, 0_1(213) -> 226
, 0_1(215) -> 89
, 0_1(236) -> 74
, 0_1(239) -> 238
, 0_1(243) -> 242
, 0_1(245) -> 244
, 0_1(274) -> 273
, 0_2(18) -> 169
, 0_2(51) -> 284
, 0_2(133) -> 293
, 0_2(145) -> 302
, 0_2(163) -> 162
, 0_2(182) -> 284
, 0_2(203) -> 202
, 0_2(204) -> 203
, 0_2(207) -> 206
, 0_2(215) -> 284
, 0_2(234) -> 233
, 0_2(251) -> 250
, 0_2(253) -> 252
, 0_2(262) -> 193
, 0_2(281) -> 280
, 0_2(290) -> 289
, 0_2(299) -> 298
, 5_0(1) -> 1
, 5_1(1) -> 27
, 5_1(2) -> 1
, 5_1(2) -> 27
, 5_1(2) -> 32
, 5_1(2) -> 73
, 5_1(2) -> 80
, 5_1(2) -> 181
, 5_1(5) -> 4
, 5_1(11) -> 27
, 5_1(17) -> 16
, 5_1(19) -> 73
, 5_1(24) -> 55
, 5_1(26) -> 80
, 5_1(27) -> 181
, 5_1(33) -> 32
, 5_1(36) -> 35
, 5_1(48) -> 248
, 5_1(50) -> 248
, 5_1(56) -> 55
, 5_1(73) -> 72
, 5_1(81) -> 34
, 5_1(89) -> 27
, 5_1(111) -> 110
, 5_1(112) -> 111
, 5_1(119) -> 118
, 5_1(124) -> 123
, 5_1(128) -> 67
, 5_1(129) -> 128
, 5_1(138) -> 2
, 5_1(142) -> 141
, 5_1(170) -> 51
, 5_1(191) -> 190
, 5_1(194) -> 27
, 5_1(211) -> 210
, 5_1(218) -> 217
, 5_1(226) -> 225
, 5_1(260) -> 259
, 5_2(233) -> 232
, 5_2(257) -> 256
, 5_2(266) -> 265
, 4_0(1) -> 1
, 4_1(1) -> 50
, 4_1(2) -> 48
, 4_1(10) -> 241
, 4_1(11) -> 1
, 4_1(11) -> 19
, 4_1(11) -> 26
, 4_1(11) -> 27
, 4_1(11) -> 32
, 4_1(11) -> 59
, 4_1(11) -> 73
, 4_1(11) -> 120
, 4_1(11) -> 181
, 4_1(11) -> 193
, 4_1(12) -> 11
, 4_1(19) -> 100
, 4_1(23) -> 22
, 4_1(26) -> 48
, 4_1(27) -> 127
, 4_1(28) -> 3
, 4_1(29) -> 28
, 4_1(33) -> 187
, 4_1(46) -> 45
, 4_1(47) -> 274
, 4_1(48) -> 47
, 4_1(49) -> 48
, 4_1(51) -> 127
, 4_1(59) -> 276
, 4_1(63) -> 62
, 4_1(64) -> 63
, 4_1(66) -> 65
, 4_1(77) -> 76
, 4_1(80) -> 79
, 4_1(89) -> 88
, 4_1(96) -> 95
, 4_1(100) -> 160
, 4_1(101) -> 100
, 4_1(103) -> 102
, 4_1(104) -> 103
, 4_1(110) -> 109
, 4_1(113) -> 112
, 4_1(117) -> 116
, 4_1(121) -> 2
, 4_1(122) -> 121
, 4_1(138) -> 48
, 4_1(139) -> 138
, 4_1(140) -> 139
, 4_1(141) -> 140
, 4_1(143) -> 142
, 4_1(144) -> 143
, 4_1(148) -> 147
, 4_1(156) -> 42
, 4_1(160) -> 159
, 4_1(170) -> 48
, 4_1(175) -> 174
, 4_1(180) -> 179
, 4_1(181) -> 180
, 4_1(193) -> 192
, 4_1(194) -> 34
, 4_1(198) -> 197
, 4_1(199) -> 198
, 4_1(209) -> 114
, 4_1(213) -> 212
, 4_1(217) -> 216
, 4_1(246) -> 245
, 4_1(247) -> 246
, 4_1(275) -> 274
, 4_1(276) -> 275
, 4_2(162) -> 161
, 4_2(166) -> 165
, 4_2(167) -> 166
, 4_2(168) -> 167
, 4_2(170) -> 257
, 4_2(201) -> 200
, 4_2(205) -> 204
, 4_2(206) -> 205
, 4_2(208) -> 207
, 4_2(227) -> 181
, 4_2(234) -> 268
, 4_2(254) -> 253
, 4_2(255) -> 254
, 4_2(269) -> 268
, 4_2(277) -> 249
, 4_2(282) -> 281
, 4_2(283) -> 282
, 4_2(284) -> 283
, 4_2(286) -> 285
, 4_2(291) -> 290
, 4_2(292) -> 291
, 4_2(293) -> 292
, 4_2(295) -> 294
, 4_2(300) -> 299
, 4_2(301) -> 300
, 4_2(302) -> 301
, 2_0(1) -> 1
, 2_1(1) -> 26
, 2_1(2) -> 26
, 2_1(3) -> 2
, 2_1(9) -> 8
, 2_1(14) -> 13
, 2_1(15) -> 14
, 2_1(16) -> 15
, 2_1(17) -> 113
, 2_1(19) -> 41
, 2_1(20) -> 26
, 2_1(22) -> 21
, 2_1(25) -> 132
, 2_1(26) -> 108
, 2_1(27) -> 26
, 2_1(30) -> 29
, 2_1(33) -> 150
, 2_1(34) -> 26
, 2_1(37) -> 36
, 2_1(42) -> 1
, 2_1(42) -> 10
, 2_1(42) -> 25
, 2_1(42) -> 27
, 2_1(42) -> 50
, 2_1(42) -> 59
, 2_1(42) -> 127
, 2_1(42) -> 180
, 2_1(42) -> 181
, 2_1(42) -> 193
, 2_1(42) -> 241
, 2_1(50) -> 49
, 2_1(51) -> 26
, 2_1(52) -> 26
, 2_1(59) -> 58
, 2_1(60) -> 34
, 2_1(69) -> 68
, 2_1(71) -> 70
, 2_1(75) -> 74
, 2_1(78) -> 77
, 2_1(79) -> 78
, 2_1(85) -> 84
, 2_1(86) -> 85
, 2_1(87) -> 86
, 2_1(91) -> 90
, 2_1(95) -> 11
, 2_1(99) -> 98
, 2_1(100) -> 99
, 2_1(101) -> 175
, 2_1(109) -> 51
, 2_1(115) -> 114
, 2_1(130) -> 129
, 2_1(134) -> 133
, 2_1(149) -> 148
, 2_1(151) -> 12
, 2_1(155) -> 154
, 2_1(171) -> 26
, 2_1(179) -> 178
, 2_1(192) -> 191
, 2_1(212) -> 211
, 2_1(219) -> 218
, 2_1(220) -> 219
, 2_1(222) -> 221
, 2_1(224) -> 223
, 2_1(237) -> 236
, 2_1(242) -> 88
, 2_1(244) -> 243
, 2_1(261) -> 260
, 2_1(273) -> 272
, 2_2(161) -> 109
, 2_2(229) -> 228
, 2_2(231) -> 230
, 2_2(250) -> 249
, 2_2(252) -> 251
, 2_2(263) -> 262
, 2_2(267) -> 266
, 2_2(280) -> 279
, 2_2(289) -> 288
, 2_2(298) -> 297
, 3_0(1) -> 1
, 3_1(1) -> 10
, 3_1(2) -> 137
, 3_1(8) -> 7
, 3_1(10) -> 214
, 3_1(13) -> 12
, 3_1(19) -> 220
, 3_1(26) -> 25
, 3_1(27) -> 87
, 3_1(32) -> 31
, 3_1(39) -> 38
, 3_1(40) -> 39
, 3_1(41) -> 40
, 3_1(43) -> 42
, 3_1(47) -> 46
, 3_1(51) -> 10
, 3_1(53) -> 52
, 3_1(55) -> 54
, 3_1(58) -> 57
, 3_1(59) -> 137
, 3_1(61) -> 60
, 3_1(62) -> 61
, 3_1(68) -> 67
, 3_1(70) -> 69
, 3_1(73) -> 31
, 3_1(74) -> 11
, 3_1(88) -> 1
, 3_1(88) -> 19
, 3_1(88) -> 59
, 3_1(88) -> 101
, 3_1(88) -> 120
, 3_1(88) -> 155
, 3_1(93) -> 92
, 3_1(94) -> 93
, 3_1(98) -> 97
, 3_1(100) -> 240
, 3_1(101) -> 93
, 3_1(106) -> 105
, 3_1(114) -> 34
, 3_1(123) -> 122
, 3_1(126) -> 125
, 3_1(127) -> 126
, 3_1(132) -> 131
, 3_1(145) -> 10
, 3_1(150) -> 149
, 3_1(152) -> 151
, 3_1(159) -> 158
, 3_1(173) -> 172
, 3_1(174) -> 173
, 3_1(176) -> 109
, 3_1(210) -> 209
, 3_1(225) -> 224
, 3_1(241) -> 240
, 3_1(271) -> 89
, 3_1(272) -> 271
, 3_1(275) -> 46
, 3_2(51) -> 270
, 3_2(145) -> 235
, 3_2(165) -> 164
, 3_2(182) -> 235
, 3_2(215) -> 235
, 3_2(232) -> 231
, 3_2(249) -> 155
, 3_2(278) -> 277
, 3_2(279) -> 278
, 3_2(285) -> 42
, 3_2(287) -> 286
, 3_2(288) -> 287
, 3_2(294) -> 59
, 3_2(294) -> 155
, 3_2(296) -> 295
, 3_2(297) -> 296
, 1_0(1) -> 1
, 1_1(1) -> 19
, 1_1(2) -> 19
, 1_1(3) -> 19
, 1_1(6) -> 5
, 1_1(7) -> 6
, 1_1(9) -> 94
, 1_1(10) -> 213
, 1_1(19) -> 18
, 1_1(20) -> 2
, 1_1(21) -> 20
, 1_1(26) -> 120
, 1_1(27) -> 33
, 1_1(31) -> 30
, 1_1(34) -> 1
, 1_1(34) -> 10
, 1_1(34) -> 19
, 1_1(34) -> 33
, 1_1(34) -> 50
, 1_1(34) -> 59
, 1_1(34) -> 87
, 1_1(34) -> 127
, 1_1(34) -> 137
, 1_1(34) -> 180
, 1_1(34) -> 214
, 1_1(35) -> 34
, 1_1(42) -> 19
, 1_1(44) -> 43
, 1_1(45) -> 44
, 1_1(48) -> 144
, 1_1(50) -> 144
, 1_1(51) -> 19
, 1_1(52) -> 19
, 1_1(57) -> 6
, 1_1(59) -> 101
, 1_1(65) -> 64
, 1_1(72) -> 71
, 1_1(76) -> 75
, 1_1(82) -> 81
, 1_1(90) -> 89
, 1_1(102) -> 88
, 1_1(108) -> 107
, 1_1(118) -> 117
, 1_1(120) -> 119
, 1_1(125) -> 124
, 1_1(131) -> 130
, 1_1(135) -> 134
, 1_1(138) -> 19
, 1_1(145) -> 19
, 1_1(146) -> 19
, 1_1(147) -> 146
, 1_1(154) -> 153
, 1_1(158) -> 157
, 1_1(170) -> 19
, 1_1(171) -> 170
, 1_1(172) -> 171
, 1_1(177) -> 176
, 1_1(178) -> 177
, 1_1(183) -> 182
, 1_1(184) -> 183
, 1_1(185) -> 184
, 1_1(186) -> 185
, 1_1(188) -> 42
, 1_1(190) -> 189
, 1_1(195) -> 194
, 1_1(212) -> 261
, 1_1(214) -> 213
, 1_1(216) -> 215
, 1_1(221) -> 11
, 1_1(223) -> 222
, 1_1(238) -> 237
, 1_1(240) -> 239
, 1_1(248) -> 247
, 1_1(258) -> 109
, 1_1(259) -> 258
, 1_2(146) -> 208
, 1_2(164) -> 163
, 1_2(169) -> 168
, 1_2(200) -> 87
, 1_2(202) -> 201
, 1_2(228) -> 227
, 1_2(230) -> 229
, 1_2(235) -> 234
, 1_2(256) -> 255
, 1_2(264) -> 263
, 1_2(265) -> 264
, 1_2(268) -> 267
, 1_2(270) -> 269}
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(2(0(2(5(3(3(x1))))))) -> 5(2(0(5(1(1(3(2(0(3(x1))))))))))
, 5(1(5(3(3(0(5(x1))))))) -> 4(4(3(2(2(2(5(0(1(1(x1))))))))))
, 5(0(5(3(5(1(5(x1))))))) -> 5(1(1(2(4(0(0(3(2(5(x1))))))))))
, 5(0(5(3(1(0(5(x1))))))) -> 5(2(4(4(2(1(3(5(1(5(x1))))))))))
, 4(5(5(3(1(0(5(x1))))))) -> 1(1(5(2(0(3(3(3(2(1(x1))))))))))
, 4(3(1(2(5(2(4(x1))))))) -> 2(3(1(1(4(3(4(4(2(4(x1))))))))))
, 3(5(0(5(5(5(0(x1))))))) -> 0(0(3(0(3(5(0(3(2(0(x1))))))))))
, 3(3(4(2(5(5(2(x1))))))) -> 1(2(3(3(4(4(1(4(0(1(x1))))))))))
, 3(2(3(5(1(5(2(x1))))))) -> 2(0(3(2(3(2(1(5(5(1(x1))))))))))
, 2(5(4(5(2(5(1(x1))))))) -> 4(3(2(1(4(2(2(4(5(2(x1))))))))))
, 1(5(5(3(3(3(4(x1))))))) -> 1(5(1(0(0(2(2(2(3(5(x1))))))))))
, 1(2(5(5(0(3(3(x1))))))) -> 3(4(1(2(0(3(3(1(0(3(x1))))))))))
, 1(2(0(4(2(5(0(x1))))))) -> 4(2(4(0(3(2(2(4(1(0(x1))))))))))
, 1(0(2(5(2(0(0(x1))))))) -> 3(1(4(4(0(3(0(1(2(2(x1))))))))))
, 0(4(4(2(5(5(5(x1))))))) -> 0(2(4(5(5(4(2(0(1(1(x1))))))))))
, 0(4(4(0(0(5(1(x1))))))) -> 1(3(2(0(4(1(5(1(1(2(x1))))))))))
, 5(5(3(5(0(5(x1)))))) -> 5(4(4(3(5(1(3(3(4(5(x1))))))))))
, 5(5(0(3(4(5(x1)))))) -> 2(0(5(5(2(1(3(2(3(2(x1))))))))))
, 5(5(0(2(5(0(x1)))))) -> 2(0(5(0(2(1(0(0(3(0(x1))))))))))
, 5(2(0(2(5(5(x1)))))) -> 5(5(4(4(4(5(4(4(1(4(x1))))))))))
, 5(1(5(0(2(5(x1)))))) -> 5(0(0(1(4(2(3(2(1(5(x1))))))))))
, 5(0(0(3(5(2(x1)))))) -> 4(4(2(3(0(1(2(0(5(2(x1))))))))))
, 4(5(5(4(2(0(x1)))))) -> 2(4(0(1(3(4(4(4(1(0(x1))))))))))
, 0(5(5(1(5(1(x1)))))) -> 0(5(1(1(3(3(4(2(1(0(x1))))))))))
, 0(5(3(1(2(5(x1)))))) -> 0(2(3(1(1(2(4(4(5(5(x1))))))))))
, 0(2(5(5(1(4(x1)))))) -> 4(0(1(1(1(1(0(4(1(5(x1))))))))))
, 0(2(5(1(5(0(x1)))))) -> 2(1(0(1(5(2(4(0(2(0(x1))))))))))
, 3(5(5(0(0(x1))))) -> 1(4(1(0(0(4(4(0(4(1(x1))))))))))
, 3(0(0(5(3(x1))))) -> 1(3(4(3(5(2(4(1(3(3(x1))))))))))
, 0(5(1(5(0(x1))))) -> 3(4(0(1(4(5(2(2(3(1(x1))))))))))
, 5(5(5(0(x1)))) -> 4(1(2(1(2(3(5(0(1(3(x1))))))))))
, 2(5(5(3(x1)))) -> 4(3(0(2(1(0(1(3(4(3(x1))))))))))
, 0(5(0(5(x1)))) -> 3(2(0(2(0(4(4(1(5(4(x1))))))))))
, 0(2(5(0(x1)))) -> 0(2(1(1(5(2(1(4(1(3(x1))))))))))
, 0(5(0(x1))) -> 3(4(3(3(2(0(4(4(4(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(2(0(2(5(3(3(x1))))))) -> 5(2(0(5(1(1(3(2(0(3(x1))))))))))
, 5(1(5(3(3(0(5(x1))))))) -> 4(4(3(2(2(2(5(0(1(1(x1))))))))))
, 5(0(5(3(5(1(5(x1))))))) -> 5(1(1(2(4(0(0(3(2(5(x1))))))))))
, 5(0(5(3(1(0(5(x1))))))) -> 5(2(4(4(2(1(3(5(1(5(x1))))))))))
, 4(5(5(3(1(0(5(x1))))))) -> 1(1(5(2(0(3(3(3(2(1(x1))))))))))
, 4(3(1(2(5(2(4(x1))))))) -> 2(3(1(1(4(3(4(4(2(4(x1))))))))))
, 3(5(0(5(5(5(0(x1))))))) -> 0(0(3(0(3(5(0(3(2(0(x1))))))))))
, 3(3(4(2(5(5(2(x1))))))) -> 1(2(3(3(4(4(1(4(0(1(x1))))))))))
, 3(2(3(5(1(5(2(x1))))))) -> 2(0(3(2(3(2(1(5(5(1(x1))))))))))
, 2(5(4(5(2(5(1(x1))))))) -> 4(3(2(1(4(2(2(4(5(2(x1))))))))))
, 1(5(5(3(3(3(4(x1))))))) -> 1(5(1(0(0(2(2(2(3(5(x1))))))))))
, 1(2(5(5(0(3(3(x1))))))) -> 3(4(1(2(0(3(3(1(0(3(x1))))))))))
, 1(2(0(4(2(5(0(x1))))))) -> 4(2(4(0(3(2(2(4(1(0(x1))))))))))
, 1(0(2(5(2(0(0(x1))))))) -> 3(1(4(4(0(3(0(1(2(2(x1))))))))))
, 0(4(4(2(5(5(5(x1))))))) -> 0(2(4(5(5(4(2(0(1(1(x1))))))))))
, 0(4(4(0(0(5(1(x1))))))) -> 1(3(2(0(4(1(5(1(1(2(x1))))))))))
, 5(5(3(5(0(5(x1)))))) -> 5(4(4(3(5(1(3(3(4(5(x1))))))))))
, 5(5(0(3(4(5(x1)))))) -> 2(0(5(5(2(1(3(2(3(2(x1))))))))))
, 5(5(0(2(5(0(x1)))))) -> 2(0(5(0(2(1(0(0(3(0(x1))))))))))
, 5(2(0(2(5(5(x1)))))) -> 5(5(4(4(4(5(4(4(1(4(x1))))))))))
, 5(1(5(0(2(5(x1)))))) -> 5(0(0(1(4(2(3(2(1(5(x1))))))))))
, 5(0(0(3(5(2(x1)))))) -> 4(4(2(3(0(1(2(0(5(2(x1))))))))))
, 4(5(5(4(2(0(x1)))))) -> 2(4(0(1(3(4(4(4(1(0(x1))))))))))
, 0(5(5(1(5(1(x1)))))) -> 0(5(1(1(3(3(4(2(1(0(x1))))))))))
, 0(5(3(1(2(5(x1)))))) -> 0(2(3(1(1(2(4(4(5(5(x1))))))))))
, 0(2(5(5(1(4(x1)))))) -> 4(0(1(1(1(1(0(4(1(5(x1))))))))))
, 0(2(5(1(5(0(x1)))))) -> 2(1(0(1(5(2(4(0(2(0(x1))))))))))
, 3(5(5(0(0(x1))))) -> 1(4(1(0(0(4(4(0(4(1(x1))))))))))
, 3(0(0(5(3(x1))))) -> 1(3(4(3(5(2(4(1(3(3(x1))))))))))
, 0(5(1(5(0(x1))))) -> 3(4(0(1(4(5(2(2(3(1(x1))))))))))
, 5(5(5(0(x1)))) -> 4(1(2(1(2(3(5(0(1(3(x1))))))))))
, 2(5(5(3(x1)))) -> 4(3(0(2(1(0(1(3(4(3(x1))))))))))
, 0(5(0(5(x1)))) -> 3(2(0(2(0(4(4(1(5(4(x1))))))))))
, 0(2(5(0(x1)))) -> 0(2(1(1(5(2(1(4(1(3(x1))))))))))
, 0(5(0(x1))) -> 3(4(3(3(2(0(4(4(4(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(2(0(2(5(3(3(x1))))))) -> 5(2(0(5(1(1(3(2(0(3(x1))))))))))
, 5(1(5(3(3(0(5(x1))))))) -> 4(4(3(2(2(2(5(0(1(1(x1))))))))))
, 5(0(5(3(5(1(5(x1))))))) -> 5(1(1(2(4(0(0(3(2(5(x1))))))))))
, 5(0(5(3(1(0(5(x1))))))) -> 5(2(4(4(2(1(3(5(1(5(x1))))))))))
, 4(5(5(3(1(0(5(x1))))))) -> 1(1(5(2(0(3(3(3(2(1(x1))))))))))
, 4(3(1(2(5(2(4(x1))))))) -> 2(3(1(1(4(3(4(4(2(4(x1))))))))))
, 3(5(0(5(5(5(0(x1))))))) -> 0(0(3(0(3(5(0(3(2(0(x1))))))))))
, 3(3(4(2(5(5(2(x1))))))) -> 1(2(3(3(4(4(1(4(0(1(x1))))))))))
, 3(2(3(5(1(5(2(x1))))))) -> 2(0(3(2(3(2(1(5(5(1(x1))))))))))
, 2(5(4(5(2(5(1(x1))))))) -> 4(3(2(1(4(2(2(4(5(2(x1))))))))))
, 1(5(5(3(3(3(4(x1))))))) -> 1(5(1(0(0(2(2(2(3(5(x1))))))))))
, 1(2(5(5(0(3(3(x1))))))) -> 3(4(1(2(0(3(3(1(0(3(x1))))))))))
, 1(2(0(4(2(5(0(x1))))))) -> 4(2(4(0(3(2(2(4(1(0(x1))))))))))
, 1(0(2(5(2(0(0(x1))))))) -> 3(1(4(4(0(3(0(1(2(2(x1))))))))))
, 0(4(4(2(5(5(5(x1))))))) -> 0(2(4(5(5(4(2(0(1(1(x1))))))))))
, 0(4(4(0(0(5(1(x1))))))) -> 1(3(2(0(4(1(5(1(1(2(x1))))))))))
, 5(5(3(5(0(5(x1)))))) -> 5(4(4(3(5(1(3(3(4(5(x1))))))))))
, 5(5(0(3(4(5(x1)))))) -> 2(0(5(5(2(1(3(2(3(2(x1))))))))))
, 5(5(0(2(5(0(x1)))))) -> 2(0(5(0(2(1(0(0(3(0(x1))))))))))
, 5(2(0(2(5(5(x1)))))) -> 5(5(4(4(4(5(4(4(1(4(x1))))))))))
, 5(1(5(0(2(5(x1)))))) -> 5(0(0(1(4(2(3(2(1(5(x1))))))))))
, 5(0(0(3(5(2(x1)))))) -> 4(4(2(3(0(1(2(0(5(2(x1))))))))))
, 4(5(5(4(2(0(x1)))))) -> 2(4(0(1(3(4(4(4(1(0(x1))))))))))
, 0(5(5(1(5(1(x1)))))) -> 0(5(1(1(3(3(4(2(1(0(x1))))))))))
, 0(5(3(1(2(5(x1)))))) -> 0(2(3(1(1(2(4(4(5(5(x1))))))))))
, 0(2(5(5(1(4(x1)))))) -> 4(0(1(1(1(1(0(4(1(5(x1))))))))))
, 0(2(5(1(5(0(x1)))))) -> 2(1(0(1(5(2(4(0(2(0(x1))))))))))
, 3(5(5(0(0(x1))))) -> 1(4(1(0(0(4(4(0(4(1(x1))))))))))
, 3(0(0(5(3(x1))))) -> 1(3(4(3(5(2(4(1(3(3(x1))))))))))
, 0(5(1(5(0(x1))))) -> 3(4(0(1(4(5(2(2(3(1(x1))))))))))
, 5(5(5(0(x1)))) -> 4(1(2(1(2(3(5(0(1(3(x1))))))))))
, 2(5(5(3(x1)))) -> 4(3(0(2(1(0(1(3(4(3(x1))))))))))
, 0(5(0(5(x1)))) -> 3(2(0(2(0(4(4(1(5(4(x1))))))))))
, 0(2(5(0(x1)))) -> 0(2(1(1(5(2(1(4(1(3(x1))))))))))
, 0(5(0(x1))) -> 3(4(3(3(2(0(4(4(4(0(x1))))))))))}
StartTerms: all
Strategy: none
Certificate: TIMEOUT
Proof:
Computation stopped due to timeout after 60.0 seconds.
Arrrr..