Knowledge (XXG)

Encompassment ordering

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31: 491: 532: 106: 561: 47: 525: 551: 51: 30: 131: 518: 556: 205: 94: 388: 127: 227: 123: 502: 498: 428: 453: 449: 55: 17: 545: 433: 416: 216: 460:. Handbook of Theoretical Computer Science. Vol. B. Elsevier. pp. 243–320. 352: 322: 291: 280: 223: 183: 165: 86: 71: 135: 490: 417:"A Complete Proof of Correctness of the Knuth–Bendix Completion Algorithm" 141: 119: 67: 471:
Dershowitz, Jouannaud (1990), sect.5.4, p. 278; somewhat sloppy,
29: 340:
i.e. irreflexive, transitive, and well-founded binary relation
475:
is required to be a "terminating rewrite relation" there.
506: 230:
of (≤). In particular, (<) itself is well-founded.
526: 8: 533: 519: 432: 407: 240: 42:related by the encompassment preorder. 7: 487: 485: 27:Term ordering in abstract rewriting 505:. You can help Knowledge (XXG) by 142:corresponding equivalence relation 25: 107:Knuth–Bendix completion algorithm 489: 215:The union of any well-founded 34:Triangle diagram of two terms 1: 434:10.1016/0022-0000(81)90002-7 48:theoretical computer science 226:, where (<) denotes the 578: 484: 462:Here:sect.2.1, p. 250 52:automated theorem proving 166:equality modulo renaming 105:It is used e.g. in the 562:Computer science stubs 43: 18:Encompassment preorder 206:substitution instance 95:substitution instance 33: 421:J. Comput. Syst. Sci 415:Gerard Huet (1981). 118:Encompassment is a 50:, in particular in 228:irreflexive kernel 70:(≤) on the set of 44: 552:Rewriting systems 514: 513: 16:(Redirected from 569: 535: 528: 521: 499:computer science 493: 486: 476: 469: 463: 461: 445: 439: 438: 436: 412: 395: 338: 332: 323:constant symbols 303: 297: 281:variable symbols 245: 74:, is defined by 21: 577: 576: 572: 571: 570: 568: 567: 566: 542: 541: 540: 539: 482: 480: 479: 470: 466: 458:Rewrite Systems 454:Jan van Leeuwen 450:J.-P. Jouannaud 448:N. Dershowitz, 447: 446: 442: 414: 413: 409: 404: 399: 398: 366: 357: 339: 335: 304: 300: 292:function symbol 246: 242: 237: 222:with (<) is 115: 28: 23: 22: 15: 12: 11: 5: 575: 573: 565: 564: 559: 554: 544: 543: 538: 537: 530: 523: 515: 512: 511: 494: 478: 477: 464: 440: 406: 405: 403: 400: 397: 396: 367:for all terms 362: 353: 333: 305:since neither 298: 271:) ≤  255:) ≤  239: 238: 236: 233: 232: 231: 213: 191: 169: 138: 132:anti-symmetric 114: 111: 103: 102: 56:term rewriting 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 574: 563: 560: 558: 555: 553: 550: 549: 547: 536: 531: 529: 524: 522: 517: 516: 510: 508: 504: 501:article is a 500: 495: 492: 488: 483: 474: 468: 465: 459: 455: 451: 444: 441: 435: 430: 426: 422: 418: 411: 408: 401: 394: 390: 386: 382: 378: 374: 370: 365: 361: 356: 351: 347: 343: 337: 334: 331: 327: 324: 321:for distinct 320: 317: ≤  316: 312: 309: ≤  308: 302: 299: 296: 293: 289: 285: 282: 278: 274: 270: 266: 262: 258: 254: 250: 244: 241: 234: 229: 225: 221: 218: 217:rewrite order 214: 211: 207: 203: 199: 196: ≤  195: 192: 189: 185: 181: 177: 174: ≤  173: 170: 167: 163: 160: ≤  159: 156: ≤  155: 151: 148: ~  147: 144:, defined by 143: 139: 137: 133: 129: 125: 121: 117: 116: 112: 110: 108: 100: 96: 92: 88: 84: 81: ≤  80: 77: 76: 75: 73: 69: 65: 64:encompassment 61: 57: 53: 49: 41: 38: ≤  37: 32: 19: 557:Order theory 507:expanding it 496: 481: 472: 467: 457: 443: 427:(1): 11–21. 424: 420: 410: 392: 389:substitution 384: 380: 379:, each path 376: 372: 368: 363: 359: 354: 349: 345: 341: 336: 329: 325: 318: 314: 310: 306: 301: 294: 287: 283: 276: 272: 268: 264: 260: 256: 252: 248: 243: 224:well-founded 219: 209: 201: 197: 193: 187: 179: 175: 171: 161: 157: 153: 149: 145: 104: 98: 90: 82: 78: 63: 59: 45: 39: 35: 387:, and each 247:since both 60:containment 546:Categories 402:References 344:such that 130:, but not 128:transitive 113:Properties 200:whenever 178:whenever 124:reflexive 452:(1990). 348:implies 120:preorder 68:preorder 456:(ed.). 184:subterm 122:, i.e. 87:subterm 391:  290:and a 279:) for 263:) and 134:, nor 58:, the 497:This 235:Notes 204:is a 182:is a 164:, is 136:total 93:is a 85:if a 72:terms 62:, or 503:stub 313:nor 140:The 126:and 54:and 429:doi 383:of 346:sRt 208:of 186:of 152:if 97:of 89:of 46:In 548:: 425:23 423:. 419:. 375:, 371:, 358:R 328:, 286:, 109:. 66:, 534:e 527:t 520:v 509:. 473:R 437:. 431:: 393:σ 385:u 381:p 377:u 373:t 369:s 364:p 360:u 355:p 350:u 342:R 330:b 326:a 319:a 315:b 311:b 307:a 295:f 288:y 284:x 277:x 275:( 273:f 269:y 267:( 265:f 261:y 259:( 257:f 253:x 251:( 249:f 220:R 212:. 210:s 202:t 198:t 194:s 190:. 188:t 180:s 176:t 172:s 168:. 162:s 158:t 154:s 150:t 146:s 101:. 99:s 91:t 83:t 79:s 40:t 36:s 20:)

Index

Encompassment preorder

theoretical computer science
automated theorem proving
term rewriting
preorder
terms
subterm
substitution instance
Knuth–Bendix completion algorithm
preorder
reflexive
transitive
anti-symmetric
total
corresponding equivalence relation
equality modulo renaming
subterm
substitution instance
rewrite order
well-founded
irreflexive kernel
variable symbols
function symbol
constant symbols
p R up for all terms s, t, u, each path p of u, and each substitution
"A Complete Proof of Correctness of the Knuth–Bendix Completion Algorithm"
doi
10.1016/0022-0000(81)90002-7
J.-P. Jouannaud

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