The rewrite relation of the following TRS is considered.
As carrier we take the set
{0,...,7}.
Symbols are labeled by the interpretation of their arguments using the interpretations
(modulo 8):
There are 192 ruless (increase limit for explicit display).
There are 192 ruless (increase limit for explicit display).
There are 128 ruless (increase limit for explicit display).
a7(b7(b6(a4(a1(a3(a7(x1))))))) |
→ |
a7(a7(b7(a6(a5(a3(a7(x1))))))) |
(302) |
a3(b7(b6(a4(a1(a3(a7(x1))))))) |
→ |
a3(a7(b7(a6(a5(a3(a7(x1))))))) |
(303) |
a5(b3(b6(a4(a1(a3(a7(x1))))))) |
→ |
a5(a3(b7(a6(a5(a3(a7(x1))))))) |
(304) |
a1(b3(b6(a4(a1(a3(a7(x1))))))) |
→ |
a1(a3(b7(a6(a5(a3(a7(x1))))))) |
(305) |
a6(b5(b2(a4(a1(a3(a7(x1))))))) |
→ |
a6(a5(b3(a6(a5(a3(a7(x1))))))) |
(306) |
a2(b5(b2(a4(a1(a3(a7(x1))))))) |
→ |
a2(a5(b3(a6(a5(a3(a7(x1))))))) |
(307) |
a4(b1(b2(a4(a1(a3(a7(x1))))))) |
→ |
a4(a1(b3(a6(a5(a3(a7(x1))))))) |
(308) |
a0(b1(b2(a4(a1(a3(a7(x1))))))) |
→ |
a0(a1(b3(a6(a5(a3(a7(x1))))))) |
(309) |
a7(b7(b6(a4(b1(a2(a5(x1))))))) |
→ |
a7(a7(b7(a6(b5(a2(a5(x1))))))) |
(310) |
a3(b7(b6(a4(b1(a2(a5(x1))))))) |
→ |
a3(a7(b7(a6(b5(a2(a5(x1))))))) |
(311) |
a5(b3(b6(a4(b1(a2(a5(x1))))))) |
→ |
a5(a3(b7(a6(b5(a2(a5(x1))))))) |
(312) |
a1(b3(b6(a4(b1(a2(a5(x1))))))) |
→ |
a1(a3(b7(a6(b5(a2(a5(x1))))))) |
(313) |
a6(b5(b2(a4(b1(a2(a5(x1))))))) |
→ |
a6(a5(b3(a6(b5(a2(a5(x1))))))) |
(314) |
a2(b5(b2(a4(b1(a2(a5(x1))))))) |
→ |
a2(a5(b3(a6(b5(a2(a5(x1))))))) |
(315) |
a4(b1(b2(a4(b1(a2(a5(x1))))))) |
→ |
a4(a1(b3(a6(b5(a2(a5(x1))))))) |
(316) |
a0(b1(b2(a4(b1(a2(a5(x1))))))) |
→ |
a0(a1(b3(a6(b5(a2(a5(x1))))))) |
(317) |
a7(b7(b6(a4(a1(b3(a6(x1))))))) |
→ |
a7(a7(b7(a6(a5(b3(a6(x1))))))) |
(318) |
a3(b7(b6(a4(a1(b3(a6(x1))))))) |
→ |
a3(a7(b7(a6(a5(b3(a6(x1))))))) |
(319) |
a5(b3(b6(a4(a1(b3(a6(x1))))))) |
→ |
a5(a3(b7(a6(a5(b3(a6(x1))))))) |
(320) |
a1(b3(b6(a4(a1(b3(a6(x1))))))) |
→ |
a1(a3(b7(a6(a5(b3(a6(x1))))))) |
(321) |
a6(b5(b2(a4(a1(b3(a6(x1))))))) |
→ |
a6(a5(b3(a6(a5(b3(a6(x1))))))) |
(322) |
a2(b5(b2(a4(a1(b3(a6(x1))))))) |
→ |
a2(a5(b3(a6(a5(b3(a6(x1))))))) |
(323) |
a4(b1(b2(a4(a1(b3(a6(x1))))))) |
→ |
a4(a1(b3(a6(a5(b3(a6(x1))))))) |
(324) |
a0(b1(b2(a4(a1(b3(a6(x1))))))) |
→ |
a0(a1(b3(a6(a5(b3(a6(x1))))))) |
(325) |
a7(b7(b6(a4(b1(b2(a4(x1))))))) |
→ |
a7(a7(b7(a6(b5(b2(a4(x1))))))) |
(326) |
a3(b7(b6(a4(b1(b2(a4(x1))))))) |
→ |
a3(a7(b7(a6(b5(b2(a4(x1))))))) |
(327) |
a5(b3(b6(a4(b1(b2(a4(x1))))))) |
→ |
a5(a3(b7(a6(b5(b2(a4(x1))))))) |
(328) |
a1(b3(b6(a4(b1(b2(a4(x1))))))) |
→ |
a1(a3(b7(a6(b5(b2(a4(x1))))))) |
(329) |
a6(b5(b2(a4(b1(b2(a4(x1))))))) |
→ |
a6(a5(b3(a6(b5(b2(a4(x1))))))) |
(330) |
a2(b5(b2(a4(b1(b2(a4(x1))))))) |
→ |
a2(a5(b3(a6(b5(b2(a4(x1))))))) |
(331) |
a4(b1(b2(a4(b1(b2(a4(x1))))))) |
→ |
a4(a1(b3(a6(b5(b2(a4(x1))))))) |
(332) |
a0(b1(b2(a4(b1(b2(a4(x1))))))) |
→ |
a0(a1(b3(a6(b5(b2(a4(x1))))))) |
(333) |
a7(b7(b6(a4(a1(a3(b7(x1))))))) |
→ |
a7(a7(b7(a6(a5(a3(b7(x1))))))) |
(334) |
a3(b7(b6(a4(a1(a3(b7(x1))))))) |
→ |
a3(a7(b7(a6(a5(a3(b7(x1))))))) |
(335) |
a5(b3(b6(a4(a1(a3(b7(x1))))))) |
→ |
a5(a3(b7(a6(a5(a3(b7(x1))))))) |
(336) |
a1(b3(b6(a4(a1(a3(b7(x1))))))) |
→ |
a1(a3(b7(a6(a5(a3(b7(x1))))))) |
(337) |
a6(b5(b2(a4(a1(a3(b7(x1))))))) |
→ |
a6(a5(b3(a6(a5(a3(b7(x1))))))) |
(338) |
a2(b5(b2(a4(a1(a3(b7(x1))))))) |
→ |
a2(a5(b3(a6(a5(a3(b7(x1))))))) |
(339) |
a4(b1(b2(a4(a1(a3(b7(x1))))))) |
→ |
a4(a1(b3(a6(a5(a3(b7(x1))))))) |
(340) |
a0(b1(b2(a4(a1(a3(b7(x1))))))) |
→ |
a0(a1(b3(a6(a5(a3(b7(x1))))))) |
(341) |
a7(b7(b6(a4(b1(a2(b5(x1))))))) |
→ |
a7(a7(b7(a6(b5(a2(b5(x1))))))) |
(342) |
a3(b7(b6(a4(b1(a2(b5(x1))))))) |
→ |
a3(a7(b7(a6(b5(a2(b5(x1))))))) |
(343) |
a5(b3(b6(a4(b1(a2(b5(x1))))))) |
→ |
a5(a3(b7(a6(b5(a2(b5(x1))))))) |
(344) |
a1(b3(b6(a4(b1(a2(b5(x1))))))) |
→ |
a1(a3(b7(a6(b5(a2(b5(x1))))))) |
(345) |
a6(b5(b2(a4(b1(a2(b5(x1))))))) |
→ |
a6(a5(b3(a6(b5(a2(b5(x1))))))) |
(346) |
a2(b5(b2(a4(b1(a2(b5(x1))))))) |
→ |
a2(a5(b3(a6(b5(a2(b5(x1))))))) |
(347) |
a4(b1(b2(a4(b1(a2(b5(x1))))))) |
→ |
a4(a1(b3(a6(b5(a2(b5(x1))))))) |
(348) |
a0(b1(b2(a4(b1(a2(b5(x1))))))) |
→ |
a0(a1(b3(a6(b5(a2(b5(x1))))))) |
(349) |
a7(b7(b6(a4(a1(b3(b6(x1))))))) |
→ |
a7(a7(b7(a6(a5(b3(b6(x1))))))) |
(350) |
a3(b7(b6(a4(a1(b3(b6(x1))))))) |
→ |
a3(a7(b7(a6(a5(b3(b6(x1))))))) |
(351) |
a5(b3(b6(a4(a1(b3(b6(x1))))))) |
→ |
a5(a3(b7(a6(a5(b3(b6(x1))))))) |
(352) |
a1(b3(b6(a4(a1(b3(b6(x1))))))) |
→ |
a1(a3(b7(a6(a5(b3(b6(x1))))))) |
(353) |
a6(b5(b2(a4(a1(b3(b6(x1))))))) |
→ |
a6(a5(b3(a6(a5(b3(b6(x1))))))) |
(354) |
a2(b5(b2(a4(a1(b3(b6(x1))))))) |
→ |
a2(a5(b3(a6(a5(b3(b6(x1))))))) |
(355) |
a4(b1(b2(a4(a1(b3(b6(x1))))))) |
→ |
a4(a1(b3(a6(a5(b3(b6(x1))))))) |
(356) |
a0(b1(b2(a4(a1(b3(b6(x1))))))) |
→ |
a0(a1(b3(a6(a5(b3(b6(x1))))))) |
(357) |
a7(b7(b6(a4(b1(b2(b4(x1))))))) |
→ |
a7(a7(b7(a6(b5(b2(b4(x1))))))) |
(358) |
a3(b7(b6(a4(b1(b2(b4(x1))))))) |
→ |
a3(a7(b7(a6(b5(b2(b4(x1))))))) |
(359) |
a5(b3(b6(a4(b1(b2(b4(x1))))))) |
→ |
a5(a3(b7(a6(b5(b2(b4(x1))))))) |
(360) |
a1(b3(b6(a4(b1(b2(b4(x1))))))) |
→ |
a1(a3(b7(a6(b5(b2(b4(x1))))))) |
(361) |
a6(b5(b2(a4(b1(b2(b4(x1))))))) |
→ |
a6(a5(b3(a6(b5(b2(b4(x1))))))) |
(362) |
a2(b5(b2(a4(b1(b2(b4(x1))))))) |
→ |
a2(a5(b3(a6(b5(b2(b4(x1))))))) |
(363) |
a4(b1(b2(a4(b1(b2(b4(x1))))))) |
→ |
a4(a1(b3(a6(b5(b2(b4(x1))))))) |
(364) |
a0(b1(b2(a4(b1(b2(b4(x1))))))) |
→ |
a0(a1(b3(a6(b5(b2(b4(x1))))))) |
(365) |
There are no rules.
There are no rules in the TRS. Hence, it is terminating.