The rewrite relation of the following TRS is considered.
| 0(0(1(2(x1)))) | → | 2(1(2(x1))) | (1) |
| 0(3(4(2(2(1(x1)))))) | → | 2(2(5(5(3(x1))))) | (2) |
| 2(2(2(5(0(2(1(x1))))))) | → | 4(2(4(5(4(4(5(x1))))))) | (3) |
| 2(2(5(1(1(3(4(x1))))))) | → | 2(5(0(3(3(4(x1)))))) | (4) |
| 3(2(2(4(0(3(4(x1))))))) | → | 3(2(1(0(4(0(x1)))))) | (5) |
| 4(5(1(4(2(4(1(x1))))))) | → | 0(0(4(4(0(1(x1)))))) | (6) |
| 0(3(4(3(0(0(0(3(x1)))))))) | → | 2(2(1(1(4(2(3(x1))))))) | (7) |
| 0(4(4(3(4(1(0(4(x1)))))))) | → | 2(5(2(0(3(1(x1)))))) | (8) |
| 4(4(1(5(1(3(1(1(3(x1))))))))) | → | 3(2(2(1(3(0(0(x1))))))) | (9) |
| 1(4(5(3(3(1(1(1(4(3(x1)))))))))) | → | 3(0(4(0(5(0(0(3(x1)))))))) | (10) |
| 1(0(3(2(4(5(3(3(2(3(5(x1))))))))))) | → | 4(0(3(0(1(2(3(2(3(5(x1)))))))))) | (11) |
| 1(0(3(5(5(2(0(0(4(2(5(x1))))))))))) | → | 3(0(2(0(1(1(1(3(3(3(5(3(x1)))))))))))) | (12) |
| 3(1(5(1(2(4(5(1(4(5(2(x1))))))))))) | → | 3(2(2(2(5(0(0(3(2(x1))))))))) | (13) |
| 3(3(4(4(0(4(0(1(2(0(4(x1))))))))))) | → | 3(0(5(1(5(0(3(1(5(3(1(x1))))))))))) | (14) |
| 1(4(5(0(1(4(1(0(3(3(1(3(x1)))))))))))) | → | 0(2(2(4(5(4(3(5(0(0(x1)))))))))) | (15) |
| 1(5(0(5(4(3(1(3(4(4(1(4(x1)))))))))))) | → | 4(5(0(3(4(5(0(5(3(2(x1)))))))))) | (16) |
| 2(0(5(2(2(4(4(1(5(2(2(4(x1)))))))))))) | → | 2(3(5(3(1(0(1(0(3(4(2(4(1(x1))))))))))))) | (17) |
| 0(3(3(0(5(1(3(0(4(3(3(2(3(x1))))))))))))) | → | 0(5(0(1(2(3(0(2(0(2(3(x1))))))))))) | (18) |
| 3(3(5(4(5(5(4(2(3(1(1(0(1(x1))))))))))))) | → | 4(1(3(3(3(4(5(2(4(3(4(1(5(x1))))))))))))) | (19) |
| 3(5(3(0(0(1(4(5(4(2(5(1(0(x1))))))))))))) | → | 3(0(2(0(0(1(2(5(3(0(0(x1))))))))))) | (20) |
| 3(5(3(0(2(5(0(1(5(2(1(1(3(x1))))))))))))) | → | 3(3(3(3(5(1(3(5(0(4(0(1(5(5(x1)))))))))))))) | (21) |
| 0(4(0(4(1(3(4(0(2(4(0(5(0(3(x1)))))))))))))) | → | 2(3(3(3(1(0(0(2(1(5(5(5(3(x1))))))))))))) | (22) |
| 1(1(0(4(1(3(0(3(2(4(2(3(2(2(x1)))))))))))))) | → | 3(0(1(4(1(5(0(5(2(0(4(4(5(1(x1)))))))))))))) | (23) |
| 5(0(1(4(5(5(2(2(2(0(3(4(4(3(4(x1))))))))))))))) | → | 5(4(1(4(1(1(3(1(2(2(2(1(3(1(2(x1))))))))))))))) | (24) |
| 0(4(4(3(4(2(3(5(0(4(2(4(3(1(1(0(x1)))))))))))))))) | → | 2(5(2(1(0(5(4(0(4(3(3(2(1(3(x1)))))))))))))) | (25) |
| 1(3(3(0(1(2(4(1(1(4(5(5(2(3(0(0(x1)))))))))))))))) | → | 0(3(5(0(5(0(0(4(4(4(2(1(4(0(2(2(x1)))))))))))))))) | (26) |
| 3(1(2(1(1(1(4(4(1(0(2(5(2(1(3(3(x1)))))))))))))))) | → | 1(3(4(2(0(3(0(5(3(1(0(1(4(4(5(3(x1)))))))))))))))) | (27) |
| 3(3(2(5(2(3(0(5(3(1(0(2(0(1(0(4(x1)))))))))))))))) | → | 0(2(0(3(5(1(2(1(5(2(4(2(3(0(4(5(x1)))))))))))))))) | (28) |
| 3(3(3(5(5(4(0(2(1(0(1(0(4(3(4(3(x1)))))))))))))))) | → | 3(2(4(4(3(5(4(0(4(4(0(4(1(4(3(3(x1)))))))))))))))) | (29) |
| 0(5(0(2(3(3(5(1(4(5(2(5(2(0(3(4(1(2(x1)))))))))))))))))) | → | 0(3(0(2(1(4(5(3(0(5(1(1(3(5(2(0(4(2(x1)))))))))))))))))) | (30) |
| 1(5(5(2(3(3(1(3(4(0(4(5(1(0(2(5(2(0(x1)))))))))))))))))) | → | 2(0(3(5(3(1(0(4(5(1(1(2(1(3(4(4(1(2(5(x1))))))))))))))))))) | (31) |
| 3(0(3(5(1(3(4(0(1(2(3(4(5(4(4(1(1(0(x1)))))))))))))))))) | → | 0(2(0(1(1(5(0(0(4(2(3(4(5(3(3(0(x1)))))))))))))))) | (32) |
| 5(1(1(0(0(2(4(2(1(5(0(5(4(1(3(5(4(0(x1)))))))))))))))))) | → | 5(0(3(1(4(5(5(2(5(1(5(1(4(3(5(5(4(x1))))))))))))))))) | (33) |
| 1(0(1(0(4(4(1(1(2(1(2(1(4(0(4(2(1(2(5(x1))))))))))))))))))) | → | 0(2(4(4(5(4(1(1(1(3(5(4(0(4(5(2(1(3(3(3(x1)))))))))))))))))))) | (34) |
| 1(5(5(4(1(5(2(3(0(3(3(2(4(5(3(4(1(1(4(x1))))))))))))))))))) | → | 4(4(0(4(4(0(0(5(5(0(5(4(0(3(3(0(1(1(4(x1))))))))))))))))))) | (35) |
| 2(2(3(5(1(5(4(0(0(1(4(0(1(3(5(0(3(5(1(x1))))))))))))))))))) | → | 2(1(5(0(2(1(4(4(3(1(3(5(0(4(3(1(2(x1))))))))))))))))) | (36) |
| 3(5(4(3(1(5(0(1(4(5(0(5(2(1(5(2(3(2(2(x1))))))))))))))))))) | → | 3(4(2(4(1(4(3(4(0(1(2(2(0(0(2(2(5(2(x1)))))))))))))))))) | (37) |
| 4(2(2(4(0(5(5(0(5(3(2(5(3(1(3(2(3(4(4(x1))))))))))))))))))) | → | 2(4(5(1(4(2(1(3(2(0(1(5(4(4(4(5(2(4(x1)))))))))))))))))) | (38) |
| 1(4(1(1(5(0(1(4(4(1(2(0(5(1(0(0(4(5(1(0(1(x1))))))))))))))))))))) | → | 0(4(3(5(3(4(2(4(2(4(1(0(2(4(4(1(3(4(4(4(1(x1))))))))))))))))))))) | (39) |
| 4(0(3(0(3(4(2(2(1(3(5(4(4(5(3(1(2(0(1(4(1(x1))))))))))))))))))))) | → | 2(1(0(2(5(0(0(2(0(3(3(0(5(0(2(1(3(1(x1)))))))))))))))))) | (40) |
{5(☐), 4(☐), 3(☐), 2(☐), 1(☐), 0(☐)}
We obtain the transformed TRSThere are 240 ruless (increase limit for explicit display).
{5(☐), 4(☐), 3(☐), 2(☐), 1(☐), 0(☐)}
We obtain the transformed TRSThere are 1440 ruless (increase limit for explicit display).
As carrier we take the set {0,...,35}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 36):
| [5(x1)] | = | 6x1 + 0 |
| [4(x1)] | = | 6x1 + 1 |
| [3(x1)] | = | 6x1 + 2 |
| [2(x1)] | = | 6x1 + 3 |
| [1(x1)] | = | 6x1 + 4 |
| [0(x1)] | = | 6x1 + 5 |
There are 51840 ruless (increase limit for explicit display).
| [50(x1)] | = |
x1 +
|
||||
| [56(x1)] | = |
x1 +
|
||||
| [512(x1)] | = |
x1 +
|
||||
| [518(x1)] | = |
x1 +
|
||||
| [524(x1)] | = |
x1 +
|
||||
| [530(x1)] | = |
x1 +
|
||||
| [51(x1)] | = |
x1 +
|
||||
| [57(x1)] | = |
x1 +
|
||||
| [513(x1)] | = |
x1 +
|
||||
| [519(x1)] | = |
x1 +
|
||||
| [525(x1)] | = |
x1 +
|
||||
| [531(x1)] | = |
x1 +
|
||||
| [52(x1)] | = |
x1 +
|
||||
| [58(x1)] | = |
x1 +
|
||||
| [514(x1)] | = |
x1 +
|
||||
| [520(x1)] | = |
x1 +
|
||||
| [526(x1)] | = |
x1 +
|
||||
| [532(x1)] | = |
x1 +
|
||||
| [53(x1)] | = |
x1 +
|
||||
| [59(x1)] | = |
x1 +
|
||||
| [515(x1)] | = |
x1 +
|
||||
| [521(x1)] | = |
x1 +
|
||||
| [527(x1)] | = |
x1 +
|
||||
| [533(x1)] | = |
x1 +
|
||||
| [54(x1)] | = |
x1 +
|
||||
| [510(x1)] | = |
x1 +
|
||||
| [516(x1)] | = |
x1 +
|
||||
| [522(x1)] | = |
x1 +
|
||||
| [528(x1)] | = |
x1 +
|
||||
| [534(x1)] | = |
x1 +
|
||||
| [55(x1)] | = |
x1 +
|
||||
| [511(x1)] | = |
x1 +
|
||||
| [517(x1)] | = |
x1 +
|
||||
| [523(x1)] | = |
x1 +
|
||||
| [529(x1)] | = |
x1 +
|
||||
| [535(x1)] | = |
x1 +
|
||||
| [40(x1)] | = |
x1 +
|
||||
| [46(x1)] | = |
x1 +
|
||||
| [412(x1)] | = |
x1 +
|
||||
| [418(x1)] | = |
x1 +
|
||||
| [424(x1)] | = |
x1 +
|
||||
| [430(x1)] | = |
x1 +
|
||||
| [41(x1)] | = |
x1 +
|
||||
| [47(x1)] | = |
x1 +
|
||||
| [413(x1)] | = |
x1 +
|
||||
| [419(x1)] | = |
x1 +
|
||||
| [425(x1)] | = |
x1 +
|
||||
| [431(x1)] | = |
x1 +
|
||||
| [42(x1)] | = |
x1 +
|
||||
| [48(x1)] | = |
x1 +
|
||||
| [414(x1)] | = |
x1 +
|
||||
| [420(x1)] | = |
x1 +
|
||||
| [426(x1)] | = |
x1 +
|
||||
| [432(x1)] | = |
x1 +
|
||||
| [43(x1)] | = |
x1 +
|
||||
| [49(x1)] | = |
x1 +
|
||||
| [415(x1)] | = |
x1 +
|
||||
| [421(x1)] | = |
x1 +
|
||||
| [427(x1)] | = |
x1 +
|
||||
| [433(x1)] | = |
x1 +
|
||||
| [44(x1)] | = |
x1 +
|
||||
| [410(x1)] | = |
x1 +
|
||||
| [416(x1)] | = |
x1 +
|
||||
| [422(x1)] | = |
x1 +
|
||||
| [428(x1)] | = |
x1 +
|
||||
| [434(x1)] | = |
x1 +
|
||||
| [45(x1)] | = |
x1 +
|
||||
| [411(x1)] | = |
x1 +
|
||||
| [417(x1)] | = |
x1 +
|
||||
| [423(x1)] | = |
x1 +
|
||||
| [429(x1)] | = |
x1 +
|
||||
| [435(x1)] | = |
x1 +
|
||||
| [30(x1)] | = |
x1 +
|
||||
| [36(x1)] | = |
x1 +
|
||||
| [312(x1)] | = |
x1 +
|
||||
| [318(x1)] | = |
x1 +
|
||||
| [324(x1)] | = |
x1 +
|
||||
| [330(x1)] | = |
x1 +
|
||||
| [31(x1)] | = |
x1 +
|
||||
| [37(x1)] | = |
x1 +
|
||||
| [313(x1)] | = |
x1 +
|
||||
| [319(x1)] | = |
x1 +
|
||||
| [325(x1)] | = |
x1 +
|
||||
| [331(x1)] | = |
x1 +
|
||||
| [32(x1)] | = |
x1 +
|
||||
| [38(x1)] | = |
x1 +
|
||||
| [314(x1)] | = |
x1 +
|
||||
| [320(x1)] | = |
x1 +
|
||||
| [326(x1)] | = |
x1 +
|
||||
| [332(x1)] | = |
x1 +
|
||||
| [33(x1)] | = |
x1 +
|
||||
| [39(x1)] | = |
x1 +
|
||||
| [315(x1)] | = |
x1 +
|
||||
| [321(x1)] | = |
x1 +
|
||||
| [327(x1)] | = |
x1 +
|
||||
| [333(x1)] | = |
x1 +
|
||||
| [34(x1)] | = |
x1 +
|
||||
| [310(x1)] | = |
x1 +
|
||||
| [316(x1)] | = |
x1 +
|
||||
| [322(x1)] | = |
x1 +
|
||||
| [328(x1)] | = |
x1 +
|
||||
| [334(x1)] | = |
x1 +
|
||||
| [35(x1)] | = |
x1 +
|
||||
| [311(x1)] | = |
x1 +
|
||||
| [317(x1)] | = |
x1 +
|
||||
| [323(x1)] | = |
x1 +
|
||||
| [329(x1)] | = |
x1 +
|
||||
| [335(x1)] | = |
x1 +
|
||||
| [20(x1)] | = |
x1 +
|
||||
| [26(x1)] | = |
x1 +
|
||||
| [212(x1)] | = |
x1 +
|
||||
| [218(x1)] | = |
x1 +
|
||||
| [224(x1)] | = |
x1 +
|
||||
| [230(x1)] | = |
x1 +
|
||||
| [21(x1)] | = |
x1 +
|
||||
| [27(x1)] | = |
x1 +
|
||||
| [213(x1)] | = |
x1 +
|
||||
| [219(x1)] | = |
x1 +
|
||||
| [225(x1)] | = |
x1 +
|
||||
| [231(x1)] | = |
x1 +
|
||||
| [22(x1)] | = |
x1 +
|
||||
| [28(x1)] | = |
x1 +
|
||||
| [214(x1)] | = |
x1 +
|
||||
| [220(x1)] | = |
x1 +
|
||||
| [226(x1)] | = |
x1 +
|
||||
| [232(x1)] | = |
x1 +
|
||||
| [23(x1)] | = |
x1 +
|
||||
| [29(x1)] | = |
x1 +
|
||||
| [215(x1)] | = |
x1 +
|
||||
| [221(x1)] | = |
x1 +
|
||||
| [227(x1)] | = |
x1 +
|
||||
| [233(x1)] | = |
x1 +
|
||||
| [24(x1)] | = |
x1 +
|
||||
| [210(x1)] | = |
x1 +
|
||||
| [216(x1)] | = |
x1 +
|
||||
| [222(x1)] | = |
x1 +
|
||||
| [228(x1)] | = |
x1 +
|
||||
| [234(x1)] | = |
x1 +
|
||||
| [25(x1)] | = |
x1 +
|
||||
| [211(x1)] | = |
x1 +
|
||||
| [217(x1)] | = |
x1 +
|
||||
| [223(x1)] | = |
x1 +
|
||||
| [229(x1)] | = |
x1 +
|
||||
| [235(x1)] | = |
x1 +
|
||||
| [10(x1)] | = |
x1 +
|
||||
| [16(x1)] | = |
x1 +
|
||||
| [112(x1)] | = |
x1 +
|
||||
| [118(x1)] | = |
x1 +
|
||||
| [124(x1)] | = |
x1 +
|
||||
| [130(x1)] | = |
x1 +
|
||||
| [11(x1)] | = |
x1 +
|
||||
| [17(x1)] | = |
x1 +
|
||||
| [113(x1)] | = |
x1 +
|
||||
| [119(x1)] | = |
x1 +
|
||||
| [125(x1)] | = |
x1 +
|
||||
| [131(x1)] | = |
x1 +
|
||||
| [12(x1)] | = |
x1 +
|
||||
| [18(x1)] | = |
x1 +
|
||||
| [114(x1)] | = |
x1 +
|
||||
| [120(x1)] | = |
x1 +
|
||||
| [126(x1)] | = |
x1 +
|
||||
| [132(x1)] | = |
x1 +
|
||||
| [13(x1)] | = |
x1 +
|
||||
| [19(x1)] | = |
x1 +
|
||||
| [115(x1)] | = |
x1 +
|
||||
| [121(x1)] | = |
x1 +
|
||||
| [127(x1)] | = |
x1 +
|
||||
| [133(x1)] | = |
x1 +
|
||||
| [14(x1)] | = |
x1 +
|
||||
| [110(x1)] | = |
x1 +
|
||||
| [116(x1)] | = |
x1 +
|
||||
| [122(x1)] | = |
x1 +
|
||||
| [128(x1)] | = |
x1 +
|
||||
| [134(x1)] | = |
x1 +
|
||||
| [15(x1)] | = |
x1 +
|
||||
| [111(x1)] | = |
x1 +
|
||||
| [117(x1)] | = |
x1 +
|
||||
| [123(x1)] | = |
x1 +
|
||||
| [129(x1)] | = |
x1 +
|
||||
| [135(x1)] | = |
x1 +
|
||||
| [00(x1)] | = |
x1 +
|
||||
| [06(x1)] | = |
x1 +
|
||||
| [012(x1)] | = |
x1 +
|
||||
| [018(x1)] | = |
x1 +
|
||||
| [024(x1)] | = |
x1 +
|
||||
| [030(x1)] | = |
x1 +
|
||||
| [01(x1)] | = |
x1 +
|
||||
| [07(x1)] | = |
x1 +
|
||||
| [013(x1)] | = |
x1 +
|
||||
| [019(x1)] | = |
x1 +
|
||||
| [025(x1)] | = |
x1 +
|
||||
| [031(x1)] | = |
x1 +
|
||||
| [02(x1)] | = |
x1 +
|
||||
| [08(x1)] | = |
x1 +
|
||||
| [014(x1)] | = |
x1 +
|
||||
| [020(x1)] | = |
x1 +
|
||||
| [026(x1)] | = |
x1 +
|
||||
| [032(x1)] | = |
x1 +
|
||||
| [03(x1)] | = |
x1 +
|
||||
| [09(x1)] | = |
x1 +
|
||||
| [015(x1)] | = |
x1 +
|
||||
| [021(x1)] | = |
x1 +
|
||||
| [027(x1)] | = |
x1 +
|
||||
| [033(x1)] | = |
x1 +
|
||||
| [04(x1)] | = |
x1 +
|
||||
| [010(x1)] | = |
x1 +
|
||||
| [016(x1)] | = |
x1 +
|
||||
| [022(x1)] | = |
x1 +
|
||||
| [028(x1)] | = |
x1 +
|
||||
| [034(x1)] | = |
x1 +
|
||||
| [05(x1)] | = |
x1 +
|
||||
| [011(x1)] | = |
x1 +
|
||||
| [017(x1)] | = |
x1 +
|
||||
| [023(x1)] | = |
x1 +
|
||||
| [029(x1)] | = |
x1 +
|
||||
| [035(x1)] | = |
x1 +
|
There are 51840 ruless (increase limit for explicit display).
There are no rules in the TRS. Hence, it is terminating.