Problem ICFP 2010 4036

Tool Bounds

Execution Time	0.63118696ms
Answer	YES(?,O(n^1))
Input	ICFP 2010 4036

stdout:

YES(?,O(n^1))

We consider the following Problem:

  Strict Trs:
    {  5(5(4(5(3(5(5(x1))))))) -> 5(2(4(2(2(2(4(1(5(2(x1))))))))))
     , 5(5(3(3(3(5(4(x1))))))) -> 0(3(5(2(2(1(0(4(2(2(x1))))))))))
     , 5(4(3(4(3(1(5(x1))))))) -> 0(2(0(0(0(0(4(1(5(0(x1))))))))))
     , 5(4(3(2(3(1(3(x1))))))) -> 0(0(0(2(3(0(2(5(4(3(x1))))))))))
     , 5(3(4(4(3(1(2(x1))))))) -> 5(1(0(5(0(3(5(1(1(1(x1))))))))))
     , 5(3(4(3(1(3(3(x1))))))) -> 5(1(1(4(2(4(3(3(4(3(x1))))))))))
     , 5(3(2(1(5(3(4(x1))))))) -> 5(1(2(1(3(3(5(1(2(4(x1))))))))))
     , 4(5(4(3(4(1(0(x1))))))) -> 1(4(1(1(2(4(0(1(2(0(x1))))))))))
     , 4(5(3(4(1(4(5(x1))))))) -> 4(5(4(0(2(0(1(2(1(0(x1))))))))))
     , 4(5(3(1(4(4(3(x1))))))) -> 4(5(5(5(4(2(4(4(2(3(x1))))))))))
     , 4(5(0(5(3(4(5(x1))))))) -> 1(1(1(0(5(4(0(2(4(5(x1))))))))))
     , 4(5(0(5(3(2(1(x1))))))) -> 1(1(4(1(3(0(2(4(2(1(x1))))))))))
     , 4(5(0(4(1(3(1(x1))))))) -> 1(1(1(2(0(0(4(4(5(1(x1))))))))))
     , 4(1(3(4(1(0(2(x1))))))) -> 4(4(1(5(1(2(1(4(2(2(x1))))))))))
     , 3(4(3(4(4(3(2(x1))))))) -> 2(5(4(5(3(4(2(4(4(0(x1))))))))))
     , 3(4(3(3(4(3(5(x1))))))) -> 5(1(1(1(1(1(4(2(3(3(x1))))))))))
     , 3(3(3(5(2(4(5(x1))))))) -> 3(1(0(0(1(4(2(2(0(5(x1))))))))))
     , 3(3(1(5(0(3(4(x1))))))) -> 2(0(0(5(1(2(1(4(1(4(x1))))))))))
     , 3(3(1(3(1(3(3(x1))))))) -> 1(2(1(3(0(5(5(1(2(1(x1))))))))))
     , 3(2(5(2(1(3(4(x1))))))) -> 0(2(1(3(1(2(1(4(2(2(x1))))))))))
     , 3(1(3(1(5(4(1(x1))))))) -> 0(1(2(2(5(5(5(4(2(0(x1))))))))))
     , 3(0(4(4(3(4(5(x1))))))) -> 1(2(2(4(3(2(2(2(0(4(x1))))))))))
     , 3(0(2(1(3(2(1(x1))))))) -> 1(2(0(0(3(3(4(2(2(1(x1))))))))))
     , 2(1(2(3(1(3(3(x1))))))) -> 2(1(4(1(5(1(1(1(1(1(x1))))))))))
     , 1(5(5(5(3(2(1(x1))))))) -> 1(4(1(4(2(1(3(0(1(1(x1))))))))))
     , 1(5(3(2(4(5(4(x1))))))) -> 1(1(0(3(0(0(0(0(3(4(x1))))))))))
     , 1(5(2(5(1(5(2(x1))))))) -> 1(2(3(0(2(3(0(1(0(2(x1))))))))))
     , 1(3(3(4(5(2(5(x1))))))) -> 1(1(1(4(5(1(2(5(2(4(x1))))))))))
     , 0(4(4(3(4(1(3(x1))))))) -> 0(4(2(4(1(3(2(0(2(2(x1))))))))))
     , 0(4(1(5(5(3(5(x1))))))) -> 0(2(2(0(1(2(5(2(5(0(x1))))))))))
     , 5(4(0(1(3(0(x1)))))) -> 0(2(4(2(2(1(2(0(0(0(x1))))))))))
     , 4(3(3(5(1(1(x1)))))) -> 4(4(2(4(4(2(5(0(1(2(x1))))))))))
     , 4(2(1(0(2(5(x1)))))) -> 4(2(5(4(2(2(2(4(2(5(x1))))))))))
     , 4(1(3(4(3(1(x1)))))) -> 4(2(5(0(1(0(0(0(4(4(x1))))))))))
     , 3(5(4(2(1(0(x1)))))) -> 2(5(0(0(0(0(0(4(4(0(x1))))))))))
     , 3(3(5(4(3(4(x1)))))) -> 0(5(1(1(0(4(0(2(4(4(x1))))))))))
     , 3(2(3(3(0(4(x1)))))) -> 5(4(2(2(0(0(4(2(4(4(x1))))))))))
     , 3(0(4(3(3(4(x1)))))) -> 2(3(0(3(5(1(2(4(2(4(x1))))))))))
     , 2(5(0(5(5(1(x1)))))) -> 3(0(1(4(4(0(0(0(0(1(x1))))))))))
     , 2(3(3(4(1(5(x1)))))) -> 0(0(2(4(4(2(0(4(1(3(x1))))))))))
     , 2(3(1(0(3(4(x1)))))) -> 0(0(1(1(5(2(4(1(1(4(x1))))))))))
     , 2(2(4(3(4(5(x1)))))) -> 2(0(1(4(0(0(2(0(0(0(x1))))))))))
     , 2(1(3(1(5(5(x1)))))) -> 1(1(2(2(0(5(0(0(2(2(x1))))))))))
     , 1(5(0(5(5(3(x1)))))) -> 2(1(1(1(1(2(1(3(5(3(x1))))))))))
     , 1(3(1(5(2(3(x1)))))) -> 1(4(3(2(1(0(0(2(4(3(x1))))))))))
     , 1(3(1(1(3(3(x1)))))) -> 1(2(4(2(0(2(1(0(2(5(x1))))))))))
     , 1(1(3(4(1(5(x1)))))) -> 1(1(0(0(2(2(5(2(0(0(x1))))))))))
     , 1(0(1(0(1(4(x1)))))) -> 1(0(2(4(5(4(2(4(2(4(x1))))))))))
     , 5(0(1(0(1(x1))))) -> 5(0(2(0(1(1(4(2(1(2(x1))))))))))
     , 4(3(4(3(4(x1))))) -> 2(1(1(1(4(1(2(4(2(0(x1))))))))))
     , 3(4(5(3(4(x1))))) -> 3(5(0(2(1(1(1(2(1(4(x1))))))))))
     , 1(5(1(5(4(x1))))) -> 1(0(0(2(2(0(5(2(2(4(x1))))))))))
     , 0(3(4(4(x1)))) -> 0(0(0(3(1(1(4(2(2(0(x1))))))))))
     , 0(1(0(1(x1)))) -> 0(1(1(1(0(0(1(2(2(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:
  {  1_0(1) -> 1
   , 1_1(1) -> 42
   , 1_1(9) -> 8
   , 1_1(10) -> 61
   , 1_1(16) -> 15
   , 1_1(17) -> 100
   , 1_1(25) -> 24
   , 1_1(26) -> 70
   , 1_1(34) -> 244
   , 1_1(35) -> 2
   , 1_1(40) -> 157
   , 1_1(41) -> 40
   , 1_1(42) -> 41
   , 1_1(43) -> 35
   , 1_1(49) -> 48
   , 1_1(53) -> 52
   , 1_1(54) -> 128
   , 1_1(55) -> 1
   , 1_1(55) -> 8
   , 1_1(55) -> 10
   , 1_1(55) -> 34
   , 1_1(55) -> 41
   , 1_1(55) -> 42
   , 1_1(55) -> 54
   , 1_1(55) -> 70
   , 1_1(55) -> 83
   , 1_1(55) -> 90
   , 1_1(55) -> 113
   , 1_1(55) -> 244
   , 1_1(57) -> 56
   , 1_1(58) -> 57
   , 1_1(62) -> 61
   , 1_1(69) -> 68
   , 1_1(77) -> 55
   , 1_1(78) -> 77
   , 1_1(86) -> 85
   , 1_1(90) -> 134
   , 1_1(97) -> 96
   , 1_1(99) -> 98
   , 1_1(101) -> 41
   , 1_1(109) -> 43
   , 1_1(110) -> 109
   , 1_1(111) -> 110
   , 1_1(114) -> 42
   , 1_1(115) -> 114
   , 1_1(117) -> 309
   , 1_1(118) -> 117
   , 1_1(125) -> 124
   , 1_1(127) -> 126
   , 1_1(128) -> 249
   , 1_1(129) -> 41
   , 1_1(130) -> 129
   , 1_1(135) -> 19
   , 1_1(136) -> 11
   , 1_1(153) -> 101
   , 1_1(155) -> 154
   , 1_1(157) -> 156
   , 1_1(160) -> 159
   , 1_1(173) -> 172
   , 1_1(176) -> 175
   , 1_1(181) -> 180
   , 1_1(186) -> 185
   , 1_1(192) -> 191
   , 1_1(207) -> 206
   , 1_1(216) -> 215
   , 1_1(217) -> 216
   , 1_1(230) -> 229
   , 1_1(233) -> 232
   , 1_1(245) -> 27
   , 1_1(246) -> 245
   , 1_1(250) -> 122
   , 1_1(257) -> 153
   , 1_1(258) -> 257
   , 1_1(259) -> 258
   , 1_1(261) -> 260
   , 1_1(265) -> 264
   , 1_1(272) -> 271
   , 1_1(284) -> 283
   , 1_1(285) -> 284
   , 1_1(297) -> 296
   , 1_1(301) -> 300
   , 1_1(302) -> 301
   , 1_1(303) -> 302
   , 1_1(319) -> 136
   , 1_1(320) -> 319
   , 1_1(323) -> 322
   , 1_2(291) -> 290
   , 1_2(292) -> 291
   , 1_2(295) -> 294
   , 1_2(314) -> 313
   , 1_2(315) -> 314
   , 1_2(325) -> 324
   , 1_2(326) -> 325
   , 1_2(327) -> 326
   , 1_2(330) -> 329
   , 1_2(334) -> 333
   , 1_2(335) -> 334
   , 1_2(336) -> 335
   , 1_2(339) -> 338
   , 1_2(342) -> 341
   , 1_2(343) -> 342
   , 1_2(344) -> 343
   , 1_2(347) -> 346
   , 0_0(1) -> 1
   , 0_1(1) -> 26
   , 0_1(2) -> 26
   , 0_1(10) -> 173
   , 0_1(11) -> 1
   , 0_1(11) -> 10
   , 0_1(11) -> 26
   , 0_1(11) -> 32
   , 0_1(11) -> 34
   , 0_1(11) -> 76
   , 0_1(11) -> 84
   , 0_1(11) -> 112
   , 0_1(11) -> 113
   , 0_1(11) -> 147
   , 0_1(11) -> 166
   , 0_1(11) -> 171
   , 0_1(11) -> 209
   , 0_1(11) -> 238
   , 0_1(17) -> 16
   , 0_1(18) -> 183
   , 0_1(20) -> 19
   , 0_1(21) -> 20
   , 0_1(22) -> 21
   , 0_1(23) -> 22
   , 0_1(26) -> 194
   , 0_1(27) -> 11
   , 0_1(28) -> 27
   , 0_1(31) -> 30
   , 0_1(34) -> 166
   , 0_1(36) -> 35
   , 0_1(38) -> 37
   , 0_1(41) -> 161
   , 0_1(42) -> 238
   , 0_1(53) -> 81
   , 0_1(54) -> 147
   , 0_1(55) -> 26
   , 0_1(61) -> 60
   , 0_1(63) -> 26
   , 0_1(64) -> 26
   , 0_1(66) -> 65
   , 0_1(68) -> 67
   , 0_1(70) -> 171
   , 0_1(79) -> 78
   , 0_1(82) -> 81
   , 0_1(84) -> 121
   , 0_1(88) -> 87
   , 0_1(92) -> 91
   , 0_1(93) -> 92
   , 0_1(96) -> 26
   , 0_1(101) -> 26
   , 0_1(107) -> 214
   , 0_1(114) -> 194
   , 0_1(116) -> 115
   , 0_1(117) -> 116
   , 0_1(122) -> 101
   , 0_1(123) -> 122
   , 0_1(132) -> 131
   , 0_1(148) -> 129
   , 0_1(149) -> 148
   , 0_1(162) -> 77
   , 0_1(164) -> 163
   , 0_1(165) -> 164
   , 0_1(166) -> 165
   , 0_1(167) -> 166
   , 0_1(169) -> 168
   , 0_1(172) -> 171
   , 0_1(183) -> 256
   , 0_1(185) -> 184
   , 0_1(192) -> 252
   , 0_1(193) -> 235
   , 0_1(194) -> 193
   , 0_1(205) -> 272
   , 0_1(206) -> 200
   , 0_1(207) -> 211
   , 0_1(208) -> 207
   , 0_1(209) -> 208
   , 0_1(210) -> 209
   , 0_1(211) -> 102
   , 0_1(212) -> 211
   , 0_1(213) -> 212
   , 0_1(214) -> 213
   , 0_1(218) -> 217
   , 0_1(220) -> 219
   , 0_1(224) -> 223
   , 0_1(225) -> 224
   , 0_1(227) -> 226
   , 0_1(232) -> 114
   , 0_1(236) -> 235
   , 0_1(237) -> 236
   , 0_1(238) -> 237
   , 0_1(243) -> 242
   , 0_1(252) -> 251
   , 0_1(255) -> 254
   , 0_1(266) -> 265
   , 0_1(267) -> 266
   , 0_1(270) -> 269
   , 0_1(273) -> 162
   , 0_1(277) -> 55
   , 0_1(281) -> 2
   , 0_1(283) -> 282
   , 0_1(298) -> 2
   , 0_1(299) -> 298
   , 0_1(304) -> 277
   , 0_1(307) -> 306
   , 0_1(321) -> 320
   , 0_1(322) -> 321
   , 0_2(56) -> 318
   , 0_2(63) -> 318
   , 0_2(65) -> 318
   , 0_2(96) -> 318
   , 0_2(103) -> 318
   , 0_2(221) -> 318
   , 0_2(288) -> 287
   , 0_2(290) -> 289
   , 0_2(310) -> 166
   , 0_2(311) -> 310
   , 0_2(312) -> 311
   , 0_2(324) -> 171
   , 0_2(328) -> 327
   , 0_2(329) -> 328
   , 0_2(333) -> 60
   , 0_2(333) -> 171
   , 0_2(333) -> 238
   , 0_2(337) -> 336
   , 0_2(338) -> 337
   , 0_2(341) -> 161
   , 0_2(345) -> 344
   , 0_2(346) -> 345
   , 2_0(1) -> 1
   , 2_1(1) -> 10
   , 2_1(2) -> 10
   , 2_1(3) -> 2
   , 2_1(5) -> 4
   , 2_1(6) -> 5
   , 2_1(7) -> 6
   , 2_1(10) -> 18
   , 2_1(11) -> 18
   , 2_1(14) -> 13
   , 2_1(15) -> 14
   , 2_1(18) -> 323
   , 2_1(19) -> 11
   , 2_1(25) -> 188
   , 2_1(26) -> 62
   , 2_1(29) -> 28
   , 2_1(32) -> 31
   , 2_1(33) -> 267
   , 2_1(34) -> 76
   , 2_1(42) -> 90
   , 2_1(43) -> 10
   , 2_1(45) -> 44
   , 2_1(48) -> 35
   , 2_1(53) -> 308
   , 2_1(54) -> 53
   , 2_1(55) -> 10
   , 2_1(59) -> 58
   , 2_1(61) -> 286
   , 2_1(62) -> 119
   , 2_1(63) -> 10
   , 2_1(67) -> 66
   , 2_1(70) -> 69
   , 2_1(74) -> 73
   , 2_1(75) -> 203
   , 2_1(77) -> 10
   , 2_1(83) -> 82
   , 2_1(84) -> 205
   , 2_1(88) -> 202
   , 2_1(89) -> 88
   , 2_1(90) -> 152
   , 2_1(91) -> 78
   , 2_1(100) -> 99
   , 2_1(101) -> 1
   , 2_1(101) -> 10
   , 2_1(101) -> 18
   , 2_1(101) -> 24
   , 2_1(101) -> 33
   , 2_1(101) -> 34
   , 2_1(101) -> 42
   , 2_1(101) -> 47
   , 2_1(101) -> 54
   , 2_1(101) -> 90
   , 2_1(101) -> 113
   , 2_1(101) -> 167
   , 2_1(101) -> 286
   , 2_1(101) -> 308
   , 2_1(107) -> 106
   , 2_1(113) -> 112
   , 2_1(114) -> 10
   , 2_1(120) -> 119
   , 2_1(121) -> 120
   , 2_1(126) -> 125
   , 2_1(128) -> 303
   , 2_1(129) -> 55
   , 2_1(136) -> 10
   , 2_1(137) -> 136
   , 2_1(138) -> 137
   , 2_1(141) -> 297
   , 2_1(142) -> 129
   , 2_1(145) -> 144
   , 2_1(146) -> 145
   , 2_1(147) -> 146
   , 2_1(159) -> 158
   , 2_1(170) -> 169
   , 2_1(177) -> 176
   , 2_1(179) -> 178
   , 2_1(183) -> 182
   , 2_1(184) -> 19
   , 2_1(187) -> 186
   , 2_1(190) -> 189
   , 2_1(191) -> 190
   , 2_1(193) -> 192
   , 2_1(194) -> 276
   , 2_1(195) -> 96
   , 2_1(198) -> 197
   , 2_1(199) -> 63
   , 2_1(202) -> 201
   , 2_1(203) -> 202
   , 2_1(204) -> 203
   , 2_1(210) -> 220
   , 2_1(221) -> 10
   , 2_1(222) -> 221
   , 2_1(223) -> 222
   , 2_1(231) -> 230
   , 2_1(239) -> 27
   , 2_1(242) -> 241
   , 2_1(248) -> 247
   , 2_1(253) -> 77
   , 2_1(254) -> 253
   , 2_1(260) -> 259
   , 2_1(264) -> 263
   , 2_1(269) -> 268
   , 2_1(271) -> 270
   , 2_1(274) -> 273
   , 2_1(275) -> 274
   , 2_1(277) -> 18
   , 2_1(278) -> 277
   , 2_1(282) -> 281
   , 2_1(300) -> 299
   , 2_1(305) -> 304
   , 2_1(306) -> 305
   , 2_2(35) -> 332
   , 2_2(55) -> 332
   , 2_2(77) -> 332
   , 2_2(97) -> 332
   , 2_2(136) -> 295
   , 2_2(153) -> 295
   , 2_2(233) -> 295
   , 2_2(250) -> 349
   , 2_2(289) -> 288
   , 2_2(294) -> 293
   , 2_2(295) -> 340
   , 2_2(317) -> 316
   , 2_2(318) -> 317
   , 2_2(331) -> 330
   , 2_2(332) -> 331
   , 2_2(340) -> 339
   , 2_2(348) -> 347
   , 2_2(349) -> 348
   , 4_0(1) -> 1
   , 4_1(1) -> 54
   , 4_1(2) -> 54
   , 4_1(4) -> 3
   , 4_1(8) -> 7
   , 4_1(10) -> 231
   , 4_1(11) -> 210
   , 4_1(18) -> 17
   , 4_1(24) -> 23
   , 4_1(26) -> 108
   , 4_1(34) -> 33
   , 4_1(44) -> 43
   , 4_1(46) -> 45
   , 4_1(53) -> 231
   , 4_1(54) -> 210
   , 4_1(55) -> 54
   , 4_1(56) -> 55
   , 4_1(60) -> 59
   , 4_1(62) -> 141
   , 4_1(63) -> 1
   , 4_1(63) -> 33
   , 4_1(63) -> 54
   , 4_1(63) -> 83
   , 4_1(63) -> 89
   , 4_1(63) -> 231
   , 4_1(63) -> 243
   , 4_1(64) -> 54
   , 4_1(65) -> 64
   , 4_1(73) -> 72
   , 4_1(75) -> 74
   , 4_1(76) -> 75
   , 4_1(81) -> 80
   , 4_1(82) -> 89
   , 4_1(83) -> 93
   , 4_1(84) -> 83
   , 4_1(85) -> 77
   , 4_1(90) -> 89
   , 4_1(94) -> 93
   , 4_1(95) -> 94
   , 4_1(96) -> 63
   , 4_1(101) -> 33
   , 4_1(102) -> 54
   , 4_1(103) -> 102
   , 4_1(106) -> 105
   , 4_1(108) -> 107
   , 4_1(112) -> 111
   , 4_1(115) -> 54
   , 4_1(119) -> 118
   , 4_1(128) -> 127
   , 4_1(143) -> 142
   , 4_1(152) -> 151
   , 4_1(154) -> 153
   , 4_1(158) -> 57
   , 4_1(174) -> 78
   , 4_1(178) -> 11
   , 4_1(180) -> 179
   , 4_1(189) -> 19
   , 4_1(196) -> 195
   , 4_1(197) -> 196
   , 4_1(201) -> 200
   , 4_1(205) -> 204
   , 4_1(219) -> 218
   , 4_1(220) -> 225
   , 4_1(221) -> 2
   , 4_1(230) -> 280
   , 4_1(234) -> 233
   , 4_1(235) -> 234
   , 4_1(240) -> 239
   , 4_1(241) -> 240
   , 4_1(244) -> 243
   , 4_1(249) -> 248
   , 4_1(251) -> 250
   , 4_1(268) -> 129
   , 4_1(279) -> 278
   , 4_1(286) -> 285
   , 4_1(296) -> 258
   , 4_2(293) -> 292
   , 4_2(316) -> 315
   , 3_0(1) -> 1
   , 3_1(1) -> 34
   , 3_1(2) -> 34
   , 3_1(12) -> 11
   , 3_1(17) -> 150
   , 3_1(30) -> 29
   , 3_1(33) -> 47
   , 3_1(34) -> 113
   , 3_1(39) -> 38
   , 3_1(47) -> 46
   , 3_1(50) -> 49
   , 3_1(51) -> 50
   , 3_1(54) -> 167
   , 3_1(64) -> 167
   , 3_1(87) -> 86
   , 3_1(98) -> 135
   , 3_1(105) -> 104
   , 3_1(114) -> 1
   , 3_1(114) -> 10
   , 3_1(114) -> 34
   , 3_1(114) -> 113
   , 3_1(114) -> 167
   , 3_1(114) -> 188
   , 3_1(114) -> 205
   , 3_1(131) -> 130
   , 3_1(144) -> 143
   , 3_1(150) -> 149
   , 3_1(151) -> 150
   , 3_1(161) -> 160
   , 3_1(163) -> 162
   , 3_1(168) -> 129
   , 3_1(171) -> 170
   , 3_1(182) -> 181
   , 3_1(226) -> 101
   , 3_1(228) -> 227
   , 3_1(262) -> 261
   , 3_1(263) -> 56
   , 3_1(298) -> 34
   , 3_1(309) -> 28
   , 3_2(313) -> 312
   , 5_0(1) -> 1
   , 5_1(1) -> 84
   , 5_1(2) -> 1
   , 5_1(2) -> 25
   , 5_1(2) -> 34
   , 5_1(2) -> 47
   , 5_1(2) -> 84
   , 5_1(2) -> 167
   , 5_1(2) -> 262
   , 5_1(10) -> 9
   , 5_1(13) -> 12
   , 5_1(18) -> 307
   , 5_1(26) -> 25
   , 5_1(33) -> 32
   , 5_1(34) -> 262
   , 5_1(37) -> 36
   , 5_1(40) -> 39
   , 5_1(42) -> 95
   , 5_1(52) -> 51
   , 5_1(53) -> 177
   , 5_1(60) -> 198
   , 5_1(64) -> 63
   , 5_1(71) -> 64
   , 5_1(72) -> 71
   , 5_1(80) -> 79
   , 5_1(98) -> 97
   , 5_1(102) -> 101
   , 5_1(104) -> 103
   , 5_1(114) -> 84
   , 5_1(124) -> 123
   , 5_1(133) -> 132
   , 5_1(134) -> 133
   , 5_1(139) -> 138
   , 5_1(140) -> 139
   , 5_1(141) -> 140
   , 5_1(156) -> 155
   , 5_1(157) -> 39
   , 5_1(175) -> 174
   , 5_1(188) -> 187
   , 5_1(200) -> 199
   , 5_1(215) -> 11
   , 5_1(229) -> 228
   , 5_1(247) -> 246
   , 5_1(256) -> 255
   , 5_1(276) -> 275
   , 5_1(280) -> 279
   , 5_1(298) -> 114
   , 5_1(308) -> 307
   , 5_2(287) -> 198}

Hurray, we answered YES(?,O(n^1))

Tool CDI

Execution Time	60.05339ms
Answer	TIMEOUT
Input	ICFP 2010 4036

stdout:

TIMEOUT

Statistics:
Number of monomials: 0
Last formula building started for bound 0
Last SAT solving started for bound 0

Tool EDA

Execution Time	60.149178ms
Answer	TIMEOUT
Input	ICFP 2010 4036

stdout:

TIMEOUT

We consider the following Problem:

  Strict Trs:
    {  5(5(4(5(3(5(5(x1))))))) -> 5(2(4(2(2(2(4(1(5(2(x1))))))))))
     , 5(5(3(3(3(5(4(x1))))))) -> 0(3(5(2(2(1(0(4(2(2(x1))))))))))
     , 5(4(3(4(3(1(5(x1))))))) -> 0(2(0(0(0(0(4(1(5(0(x1))))))))))
     , 5(4(3(2(3(1(3(x1))))))) -> 0(0(0(2(3(0(2(5(4(3(x1))))))))))
     , 5(3(4(4(3(1(2(x1))))))) -> 5(1(0(5(0(3(5(1(1(1(x1))))))))))
     , 5(3(4(3(1(3(3(x1))))))) -> 5(1(1(4(2(4(3(3(4(3(x1))))))))))
     , 5(3(2(1(5(3(4(x1))))))) -> 5(1(2(1(3(3(5(1(2(4(x1))))))))))
     , 4(5(4(3(4(1(0(x1))))))) -> 1(4(1(1(2(4(0(1(2(0(x1))))))))))
     , 4(5(3(4(1(4(5(x1))))))) -> 4(5(4(0(2(0(1(2(1(0(x1))))))))))
     , 4(5(3(1(4(4(3(x1))))))) -> 4(5(5(5(4(2(4(4(2(3(x1))))))))))
     , 4(5(0(5(3(4(5(x1))))))) -> 1(1(1(0(5(4(0(2(4(5(x1))))))))))
     , 4(5(0(5(3(2(1(x1))))))) -> 1(1(4(1(3(0(2(4(2(1(x1))))))))))
     , 4(5(0(4(1(3(1(x1))))))) -> 1(1(1(2(0(0(4(4(5(1(x1))))))))))
     , 4(1(3(4(1(0(2(x1))))))) -> 4(4(1(5(1(2(1(4(2(2(x1))))))))))
     , 3(4(3(4(4(3(2(x1))))))) -> 2(5(4(5(3(4(2(4(4(0(x1))))))))))
     , 3(4(3(3(4(3(5(x1))))))) -> 5(1(1(1(1(1(4(2(3(3(x1))))))))))
     , 3(3(3(5(2(4(5(x1))))))) -> 3(1(0(0(1(4(2(2(0(5(x1))))))))))
     , 3(3(1(5(0(3(4(x1))))))) -> 2(0(0(5(1(2(1(4(1(4(x1))))))))))
     , 3(3(1(3(1(3(3(x1))))))) -> 1(2(1(3(0(5(5(1(2(1(x1))))))))))
     , 3(2(5(2(1(3(4(x1))))))) -> 0(2(1(3(1(2(1(4(2(2(x1))))))))))
     , 3(1(3(1(5(4(1(x1))))))) -> 0(1(2(2(5(5(5(4(2(0(x1))))))))))
     , 3(0(4(4(3(4(5(x1))))))) -> 1(2(2(4(3(2(2(2(0(4(x1))))))))))
     , 3(0(2(1(3(2(1(x1))))))) -> 1(2(0(0(3(3(4(2(2(1(x1))))))))))
     , 2(1(2(3(1(3(3(x1))))))) -> 2(1(4(1(5(1(1(1(1(1(x1))))))))))
     , 1(5(5(5(3(2(1(x1))))))) -> 1(4(1(4(2(1(3(0(1(1(x1))))))))))
     , 1(5(3(2(4(5(4(x1))))))) -> 1(1(0(3(0(0(0(0(3(4(x1))))))))))
     , 1(5(2(5(1(5(2(x1))))))) -> 1(2(3(0(2(3(0(1(0(2(x1))))))))))
     , 1(3(3(4(5(2(5(x1))))))) -> 1(1(1(4(5(1(2(5(2(4(x1))))))))))
     , 0(4(4(3(4(1(3(x1))))))) -> 0(4(2(4(1(3(2(0(2(2(x1))))))))))
     , 0(4(1(5(5(3(5(x1))))))) -> 0(2(2(0(1(2(5(2(5(0(x1))))))))))
     , 5(4(0(1(3(0(x1)))))) -> 0(2(4(2(2(1(2(0(0(0(x1))))))))))
     , 4(3(3(5(1(1(x1)))))) -> 4(4(2(4(4(2(5(0(1(2(x1))))))))))
     , 4(2(1(0(2(5(x1)))))) -> 4(2(5(4(2(2(2(4(2(5(x1))))))))))
     , 4(1(3(4(3(1(x1)))))) -> 4(2(5(0(1(0(0(0(4(4(x1))))))))))
     , 3(5(4(2(1(0(x1)))))) -> 2(5(0(0(0(0(0(4(4(0(x1))))))))))
     , 3(3(5(4(3(4(x1)))))) -> 0(5(1(1(0(4(0(2(4(4(x1))))))))))
     , 3(2(3(3(0(4(x1)))))) -> 5(4(2(2(0(0(4(2(4(4(x1))))))))))
     , 3(0(4(3(3(4(x1)))))) -> 2(3(0(3(5(1(2(4(2(4(x1))))))))))
     , 2(5(0(5(5(1(x1)))))) -> 3(0(1(4(4(0(0(0(0(1(x1))))))))))
     , 2(3(3(4(1(5(x1)))))) -> 0(0(2(4(4(2(0(4(1(3(x1))))))))))
     , 2(3(1(0(3(4(x1)))))) -> 0(0(1(1(5(2(4(1(1(4(x1))))))))))
     , 2(2(4(3(4(5(x1)))))) -> 2(0(1(4(0(0(2(0(0(0(x1))))))))))
     , 2(1(3(1(5(5(x1)))))) -> 1(1(2(2(0(5(0(0(2(2(x1))))))))))
     , 1(5(0(5(5(3(x1)))))) -> 2(1(1(1(1(2(1(3(5(3(x1))))))))))
     , 1(3(1(5(2(3(x1)))))) -> 1(4(3(2(1(0(0(2(4(3(x1))))))))))
     , 1(3(1(1(3(3(x1)))))) -> 1(2(4(2(0(2(1(0(2(5(x1))))))))))
     , 1(1(3(4(1(5(x1)))))) -> 1(1(0(0(2(2(5(2(0(0(x1))))))))))
     , 1(0(1(0(1(4(x1)))))) -> 1(0(2(4(5(4(2(4(2(4(x1))))))))))
     , 5(0(1(0(1(x1))))) -> 5(0(2(0(1(1(4(2(1(2(x1))))))))))
     , 4(3(4(3(4(x1))))) -> 2(1(1(1(4(1(2(4(2(0(x1))))))))))
     , 3(4(5(3(4(x1))))) -> 3(5(0(2(1(1(1(2(1(4(x1))))))))))
     , 1(5(1(5(4(x1))))) -> 1(0(0(2(2(0(5(2(2(4(x1))))))))))
     , 0(3(4(4(x1)))) -> 0(0(0(3(1(1(4(2(2(0(x1))))))))))
     , 0(1(0(1(x1)))) -> 0(1(1(1(0(0(1(2(2(2(x1))))))))))}
  StartTerms: all
  Strategy: none

Certificate: TIMEOUT

Proof:
  Computation stopped due to timeout after 60.0 seconds.

Arrrr..

Tool IDA

Execution Time	60.166355ms
Answer	TIMEOUT
Input	ICFP 2010 4036

stdout:

Tool TRI

Execution Time	60.13663ms
Answer	TIMEOUT
Input	ICFP 2010 4036

stdout:

Tool TRI2

Execution Time	60.139767ms
Answer	TIMEOUT
Input	ICFP 2010 4036