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 119 ruless (increase limit for explicit display).
b0(a0(a1(b3(b6(b4(b0(x1))))))) |
→ |
b0(a0(b1(a2(b5(b2(b4(x1))))))) |
(238) |
b4(a0(a1(b3(b6(b4(b0(x1))))))) |
→ |
b4(a0(b1(a2(b5(b2(b4(x1))))))) |
(239) |
b2(a4(a1(b3(b6(b4(b0(x1))))))) |
→ |
b2(a4(b1(a2(b5(b2(b4(x1))))))) |
(240) |
b6(a4(a1(b3(b6(b4(b0(x1))))))) |
→ |
b6(a4(b1(a2(b5(b2(b4(x1))))))) |
(241) |
b1(a2(a5(b3(b6(b4(b0(x1))))))) |
→ |
b1(a2(b5(a2(b5(b2(b4(x1))))))) |
(242) |
b5(a2(a5(b3(b6(b4(b0(x1))))))) |
→ |
b5(a2(b5(a2(b5(b2(b4(x1))))))) |
(243) |
b3(a6(a5(b3(b6(b4(b0(x1))))))) |
→ |
b3(a6(b5(a2(b5(b2(b4(x1))))))) |
(244) |
b7(a6(a5(b3(b6(b4(b0(x1))))))) |
→ |
b7(a6(b5(a2(b5(b2(b4(x1))))))) |
(245) |
b0(a0(a1(b3(b6(b4(a0(x1))))))) |
→ |
b0(a0(b1(a2(b5(b2(a4(x1))))))) |
(246) |
b4(a0(a1(b3(b6(b4(a0(x1))))))) |
→ |
b4(a0(b1(a2(b5(b2(a4(x1))))))) |
(247) |
b2(a4(a1(b3(b6(b4(a0(x1))))))) |
→ |
b2(a4(b1(a2(b5(b2(a4(x1))))))) |
(248) |
b6(a4(a1(b3(b6(b4(a0(x1))))))) |
→ |
b6(a4(b1(a2(b5(b2(a4(x1))))))) |
(249) |
b1(a2(a5(b3(b6(b4(a0(x1))))))) |
→ |
b1(a2(b5(a2(b5(b2(a4(x1))))))) |
(250) |
b5(a2(a5(b3(b6(b4(a0(x1))))))) |
→ |
b5(a2(b5(a2(b5(b2(a4(x1))))))) |
(251) |
b3(a6(a5(b3(b6(b4(a0(x1))))))) |
→ |
b3(a6(b5(a2(b5(b2(a4(x1))))))) |
(252) |
b7(a6(a5(b3(b6(b4(a0(x1))))))) |
→ |
b7(a6(b5(a2(b5(b2(a4(x1))))))) |
(253) |
b0(a0(a1(b3(a6(b5(a2(x1))))))) |
→ |
b0(a0(b1(a2(a5(b3(a6(x1))))))) |
(254) |
b4(a0(a1(b3(a6(b5(a2(x1))))))) |
→ |
b4(a0(b1(a2(a5(b3(a6(x1))))))) |
(255) |
b2(a4(a1(b3(a6(b5(a2(x1))))))) |
→ |
b2(a4(b1(a2(a5(b3(a6(x1))))))) |
(256) |
b6(a4(a1(b3(a6(b5(a2(x1))))))) |
→ |
b6(a4(b1(a2(a5(b3(a6(x1))))))) |
(257) |
b1(a2(a5(b3(a6(b5(a2(x1))))))) |
→ |
b1(a2(b5(a2(a5(b3(a6(x1))))))) |
(258) |
b5(a2(a5(b3(a6(b5(a2(x1))))))) |
→ |
b5(a2(b5(a2(a5(b3(a6(x1))))))) |
(259) |
b3(a6(a5(b3(a6(b5(a2(x1))))))) |
→ |
b3(a6(b5(a2(a5(b3(a6(x1))))))) |
(260) |
b7(a6(a5(b3(a6(b5(a2(x1))))))) |
→ |
b7(a6(b5(a2(a5(b3(a6(x1))))))) |
(261) |
a2(a5(a3(a7(a7(b7(b6(x1))))))) |
→ |
b2(b4(b0(b0(a0(b1(b2(x1))))))) |
(262) |
b0(a0(b1(b2(b4(b0(b0(x1))))))) |
→ |
a0(a1(b3(b6(b4(b0(b0(x1))))))) |
(263) |
b4(a0(b1(b2(b4(b0(b0(x1))))))) |
→ |
a4(a1(b3(b6(b4(b0(b0(x1))))))) |
(264) |
b6(a4(b1(b2(b4(b0(b0(x1))))))) |
→ |
a6(a5(b3(b6(b4(b0(b0(x1))))))) |
(265) |
b1(a2(b5(b2(b4(b0(b0(x1))))))) |
→ |
a1(a3(b7(b6(b4(b0(b0(x1))))))) |
(266) |
b5(a2(b5(b2(b4(b0(b0(x1))))))) |
→ |
a5(a3(b7(b6(b4(b0(b0(x1))))))) |
(267) |
b7(a6(b5(b2(b4(b0(b0(x1))))))) |
→ |
a7(a7(b7(b6(b4(b0(b0(x1))))))) |
(268) |
b0(a0(b1(b2(a4(b1(b2(x1))))))) |
→ |
a0(a1(b3(b6(a4(b1(b2(x1))))))) |
(269) |
b4(a0(b1(b2(a4(b1(b2(x1))))))) |
→ |
a4(a1(b3(b6(a4(b1(b2(x1))))))) |
(270) |
b6(a4(b1(b2(a4(b1(b2(x1))))))) |
→ |
a6(a5(b3(b6(a4(b1(b2(x1))))))) |
(271) |
b1(a2(b5(b2(a4(b1(b2(x1))))))) |
→ |
a1(a3(b7(b6(a4(b1(b2(x1))))))) |
(272) |
b5(a2(b5(b2(a4(b1(b2(x1))))))) |
→ |
a5(a3(b7(b6(a4(b1(b2(x1))))))) |
(273) |
b7(a6(b5(b2(a4(b1(b2(x1))))))) |
→ |
a7(a7(b7(b6(a4(b1(b2(x1))))))) |
(274) |
b0(a0(b1(b2(b4(a0(b1(x1))))))) |
→ |
a0(a1(b3(b6(b4(a0(b1(x1))))))) |
(275) |
b4(a0(b1(b2(b4(a0(b1(x1))))))) |
→ |
a4(a1(b3(b6(b4(a0(b1(x1))))))) |
(276) |
b6(a4(b1(b2(b4(a0(b1(x1))))))) |
→ |
a6(a5(b3(b6(b4(a0(b1(x1))))))) |
(277) |
b1(a2(b5(b2(b4(a0(b1(x1))))))) |
→ |
a1(a3(b7(b6(b4(a0(b1(x1))))))) |
(278) |
b5(a2(b5(b2(b4(a0(b1(x1))))))) |
→ |
a5(a3(b7(b6(b4(a0(b1(x1))))))) |
(279) |
b7(a6(b5(b2(b4(a0(b1(x1))))))) |
→ |
a7(a7(b7(b6(b4(a0(b1(x1))))))) |
(280) |
b0(a0(b1(b2(a4(a1(b3(x1))))))) |
→ |
a0(a1(b3(b6(a4(a1(b3(x1))))))) |
(281) |
b4(a0(b1(b2(a4(a1(b3(x1))))))) |
→ |
a4(a1(b3(b6(a4(a1(b3(x1))))))) |
(282) |
b6(a4(b1(b2(a4(a1(b3(x1))))))) |
→ |
a6(a5(b3(b6(a4(a1(b3(x1))))))) |
(283) |
b1(a2(b5(b2(a4(a1(b3(x1))))))) |
→ |
a1(a3(b7(b6(a4(a1(b3(x1))))))) |
(284) |
b5(a2(b5(b2(a4(a1(b3(x1))))))) |
→ |
a5(a3(b7(b6(a4(a1(b3(x1))))))) |
(285) |
b7(a6(b5(b2(a4(a1(b3(x1))))))) |
→ |
a7(a7(b7(b6(a4(a1(b3(x1))))))) |
(286) |
b0(a0(b1(b2(b4(b0(a0(x1))))))) |
→ |
a0(a1(b3(b6(b4(b0(a0(x1))))))) |
(287) |
b4(a0(b1(b2(b4(b0(a0(x1))))))) |
→ |
a4(a1(b3(b6(b4(b0(a0(x1))))))) |
(288) |
b6(a4(b1(b2(b4(b0(a0(x1))))))) |
→ |
a6(a5(b3(b6(b4(b0(a0(x1))))))) |
(289) |
b1(a2(b5(b2(b4(b0(a0(x1))))))) |
→ |
a1(a3(b7(b6(b4(b0(a0(x1))))))) |
(290) |
b5(a2(b5(b2(b4(b0(a0(x1))))))) |
→ |
a5(a3(b7(b6(b4(b0(a0(x1))))))) |
(291) |
b7(a6(b5(b2(b4(b0(a0(x1))))))) |
→ |
a7(a7(b7(b6(b4(b0(a0(x1))))))) |
(292) |
b0(a0(b1(b2(a4(b1(a2(x1))))))) |
→ |
a0(a1(b3(b6(a4(b1(a2(x1))))))) |
(293) |
b4(a0(b1(b2(a4(b1(a2(x1))))))) |
→ |
a4(a1(b3(b6(a4(b1(a2(x1))))))) |
(294) |
b6(a4(b1(b2(a4(b1(a2(x1))))))) |
→ |
a6(a5(b3(b6(a4(b1(a2(x1))))))) |
(295) |
b1(a2(b5(b2(a4(b1(a2(x1))))))) |
→ |
a1(a3(b7(b6(a4(b1(a2(x1))))))) |
(296) |
b5(a2(b5(b2(a4(b1(a2(x1))))))) |
→ |
a5(a3(b7(b6(a4(b1(a2(x1))))))) |
(297) |
b7(a6(b5(b2(a4(b1(a2(x1))))))) |
→ |
a7(a7(b7(b6(a4(b1(a2(x1))))))) |
(298) |
b0(a0(b1(b2(b4(a0(a1(x1))))))) |
→ |
a0(a1(b3(b6(b4(a0(a1(x1))))))) |
(299) |
b4(a0(b1(b2(b4(a0(a1(x1))))))) |
→ |
a4(a1(b3(b6(b4(a0(a1(x1))))))) |
(300) |
b6(a4(b1(b2(b4(a0(a1(x1))))))) |
→ |
a6(a5(b3(b6(b4(a0(a1(x1))))))) |
(301) |
b1(a2(b5(b2(b4(a0(a1(x1))))))) |
→ |
a1(a3(b7(b6(b4(a0(a1(x1))))))) |
(302) |
b5(a2(b5(b2(b4(a0(a1(x1))))))) |
→ |
a5(a3(b7(b6(b4(a0(a1(x1))))))) |
(303) |
b7(a6(b5(b2(b4(a0(a1(x1))))))) |
→ |
a7(a7(b7(b6(b4(a0(a1(x1))))))) |
(304) |
b0(a0(b1(b2(a4(a1(a3(x1))))))) |
→ |
a0(a1(b3(b6(a4(a1(a3(x1))))))) |
(305) |
b4(a0(b1(b2(a4(a1(a3(x1))))))) |
→ |
a4(a1(b3(b6(a4(a1(a3(x1))))))) |
(306) |
b6(a4(b1(b2(a4(a1(a3(x1))))))) |
→ |
a6(a5(b3(b6(a4(a1(a3(x1))))))) |
(307) |
b1(a2(b5(b2(a4(a1(a3(x1))))))) |
→ |
a1(a3(b7(b6(a4(a1(a3(x1))))))) |
(308) |
b5(a2(b5(b2(a4(a1(a3(x1))))))) |
→ |
a5(a3(b7(b6(a4(a1(a3(x1))))))) |
(309) |
b7(a6(b5(b2(a4(a1(a3(x1))))))) |
→ |
a7(a7(b7(b6(a4(a1(a3(x1))))))) |
(310) |
b0(a0(a1(b3(b6(b4(b0(x1))))))) |
→ |
b0(a0(b1(a2(b5(b2(b4(x1))))))) |
(238) |
b4(a0(a1(b3(b6(b4(b0(x1))))))) |
→ |
b4(a0(b1(a2(b5(b2(b4(x1))))))) |
(239) |
b2(a4(a1(b3(b6(b4(b0(x1))))))) |
→ |
b2(a4(b1(a2(b5(b2(b4(x1))))))) |
(240) |
b6(a4(a1(b3(b6(b4(b0(x1))))))) |
→ |
b6(a4(b1(a2(b5(b2(b4(x1))))))) |
(241) |
b1(a2(a5(b3(b6(b4(b0(x1))))))) |
→ |
b1(a2(b5(a2(b5(b2(b4(x1))))))) |
(242) |
b5(a2(a5(b3(b6(b4(b0(x1))))))) |
→ |
b5(a2(b5(a2(b5(b2(b4(x1))))))) |
(243) |
b3(a6(a5(b3(b6(b4(b0(x1))))))) |
→ |
b3(a6(b5(a2(b5(b2(b4(x1))))))) |
(244) |
b7(a6(a5(b3(b6(b4(b0(x1))))))) |
→ |
b7(a6(b5(a2(b5(b2(b4(x1))))))) |
(245) |
b0(a0(a1(b3(b6(b4(a0(x1))))))) |
→ |
b0(a0(b1(a2(b5(b2(a4(x1))))))) |
(246) |
b4(a0(a1(b3(b6(b4(a0(x1))))))) |
→ |
b4(a0(b1(a2(b5(b2(a4(x1))))))) |
(247) |
b2(a4(a1(b3(b6(b4(a0(x1))))))) |
→ |
b2(a4(b1(a2(b5(b2(a4(x1))))))) |
(248) |
b6(a4(a1(b3(b6(b4(a0(x1))))))) |
→ |
b6(a4(b1(a2(b5(b2(a4(x1))))))) |
(249) |
b1(a2(a5(b3(b6(b4(a0(x1))))))) |
→ |
b1(a2(b5(a2(b5(b2(a4(x1))))))) |
(250) |
b5(a2(a5(b3(b6(b4(a0(x1))))))) |
→ |
b5(a2(b5(a2(b5(b2(a4(x1))))))) |
(251) |
b3(a6(a5(b3(b6(b4(a0(x1))))))) |
→ |
b3(a6(b5(a2(b5(b2(a4(x1))))))) |
(252) |
b7(a6(a5(b3(b6(b4(a0(x1))))))) |
→ |
b7(a6(b5(a2(b5(b2(a4(x1))))))) |
(253) |
b0(a0(a1(b3(a6(b5(a2(x1))))))) |
→ |
b0(a0(b1(a2(a5(b3(a6(x1))))))) |
(254) |
b4(a0(a1(b3(a6(b5(a2(x1))))))) |
→ |
b4(a0(b1(a2(a5(b3(a6(x1))))))) |
(255) |
b2(a4(a1(b3(a6(b5(a2(x1))))))) |
→ |
b2(a4(b1(a2(a5(b3(a6(x1))))))) |
(256) |
b6(a4(a1(b3(a6(b5(a2(x1))))))) |
→ |
b6(a4(b1(a2(a5(b3(a6(x1))))))) |
(257) |
b1(a2(a5(b3(a6(b5(a2(x1))))))) |
→ |
b1(a2(b5(a2(a5(b3(a6(x1))))))) |
(258) |
b5(a2(a5(b3(a6(b5(a2(x1))))))) |
→ |
b5(a2(b5(a2(a5(b3(a6(x1))))))) |
(259) |
b3(a6(a5(b3(a6(b5(a2(x1))))))) |
→ |
b3(a6(b5(a2(a5(b3(a6(x1))))))) |
(260) |
b7(a6(a5(b3(a6(b5(a2(x1))))))) |
→ |
b7(a6(b5(a2(a5(b3(a6(x1))))))) |
(261) |
b0(a0(b1(b2(b4(b0(b0(x1))))))) |
→ |
a0(a1(b3(b6(b4(b0(b0(x1))))))) |
(263) |
b4(a0(b1(b2(b4(b0(b0(x1))))))) |
→ |
a4(a1(b3(b6(b4(b0(b0(x1))))))) |
(264) |
b6(a4(b1(b2(b4(b0(b0(x1))))))) |
→ |
a6(a5(b3(b6(b4(b0(b0(x1))))))) |
(265) |
b1(a2(b5(b2(b4(b0(b0(x1))))))) |
→ |
a1(a3(b7(b6(b4(b0(b0(x1))))))) |
(266) |
b5(a2(b5(b2(b4(b0(b0(x1))))))) |
→ |
a5(a3(b7(b6(b4(b0(b0(x1))))))) |
(267) |
b7(a6(b5(b2(b4(b0(b0(x1))))))) |
→ |
a7(a7(b7(b6(b4(b0(b0(x1))))))) |
(268) |
b0(a0(b1(b2(a4(b1(b2(x1))))))) |
→ |
a0(a1(b3(b6(a4(b1(b2(x1))))))) |
(269) |
b4(a0(b1(b2(a4(b1(b2(x1))))))) |
→ |
a4(a1(b3(b6(a4(b1(b2(x1))))))) |
(270) |
b6(a4(b1(b2(a4(b1(b2(x1))))))) |
→ |
a6(a5(b3(b6(a4(b1(b2(x1))))))) |
(271) |
b1(a2(b5(b2(a4(b1(b2(x1))))))) |
→ |
a1(a3(b7(b6(a4(b1(b2(x1))))))) |
(272) |
b5(a2(b5(b2(a4(b1(b2(x1))))))) |
→ |
a5(a3(b7(b6(a4(b1(b2(x1))))))) |
(273) |
b7(a6(b5(b2(a4(b1(b2(x1))))))) |
→ |
a7(a7(b7(b6(a4(b1(b2(x1))))))) |
(274) |
b0(a0(b1(b2(b4(a0(b1(x1))))))) |
→ |
a0(a1(b3(b6(b4(a0(b1(x1))))))) |
(275) |
b4(a0(b1(b2(b4(a0(b1(x1))))))) |
→ |
a4(a1(b3(b6(b4(a0(b1(x1))))))) |
(276) |
b6(a4(b1(b2(b4(a0(b1(x1))))))) |
→ |
a6(a5(b3(b6(b4(a0(b1(x1))))))) |
(277) |
b1(a2(b5(b2(b4(a0(b1(x1))))))) |
→ |
a1(a3(b7(b6(b4(a0(b1(x1))))))) |
(278) |
b5(a2(b5(b2(b4(a0(b1(x1))))))) |
→ |
a5(a3(b7(b6(b4(a0(b1(x1))))))) |
(279) |
b7(a6(b5(b2(b4(a0(b1(x1))))))) |
→ |
a7(a7(b7(b6(b4(a0(b1(x1))))))) |
(280) |
b0(a0(b1(b2(a4(a1(b3(x1))))))) |
→ |
a0(a1(b3(b6(a4(a1(b3(x1))))))) |
(281) |
b4(a0(b1(b2(a4(a1(b3(x1))))))) |
→ |
a4(a1(b3(b6(a4(a1(b3(x1))))))) |
(282) |
b6(a4(b1(b2(a4(a1(b3(x1))))))) |
→ |
a6(a5(b3(b6(a4(a1(b3(x1))))))) |
(283) |
b1(a2(b5(b2(a4(a1(b3(x1))))))) |
→ |
a1(a3(b7(b6(a4(a1(b3(x1))))))) |
(284) |
b5(a2(b5(b2(a4(a1(b3(x1))))))) |
→ |
a5(a3(b7(b6(a4(a1(b3(x1))))))) |
(285) |
b7(a6(b5(b2(a4(a1(b3(x1))))))) |
→ |
a7(a7(b7(b6(a4(a1(b3(x1))))))) |
(286) |
b0(a0(b1(b2(b4(b0(a0(x1))))))) |
→ |
a0(a1(b3(b6(b4(b0(a0(x1))))))) |
(287) |
b4(a0(b1(b2(b4(b0(a0(x1))))))) |
→ |
a4(a1(b3(b6(b4(b0(a0(x1))))))) |
(288) |
b6(a4(b1(b2(b4(b0(a0(x1))))))) |
→ |
a6(a5(b3(b6(b4(b0(a0(x1))))))) |
(289) |
b1(a2(b5(b2(b4(b0(a0(x1))))))) |
→ |
a1(a3(b7(b6(b4(b0(a0(x1))))))) |
(290) |
b5(a2(b5(b2(b4(b0(a0(x1))))))) |
→ |
a5(a3(b7(b6(b4(b0(a0(x1))))))) |
(291) |
b7(a6(b5(b2(b4(b0(a0(x1))))))) |
→ |
a7(a7(b7(b6(b4(b0(a0(x1))))))) |
(292) |
b0(a0(b1(b2(a4(b1(a2(x1))))))) |
→ |
a0(a1(b3(b6(a4(b1(a2(x1))))))) |
(293) |
b4(a0(b1(b2(a4(b1(a2(x1))))))) |
→ |
a4(a1(b3(b6(a4(b1(a2(x1))))))) |
(294) |
b6(a4(b1(b2(a4(b1(a2(x1))))))) |
→ |
a6(a5(b3(b6(a4(b1(a2(x1))))))) |
(295) |
b1(a2(b5(b2(a4(b1(a2(x1))))))) |
→ |
a1(a3(b7(b6(a4(b1(a2(x1))))))) |
(296) |
b5(a2(b5(b2(a4(b1(a2(x1))))))) |
→ |
a5(a3(b7(b6(a4(b1(a2(x1))))))) |
(297) |
b7(a6(b5(b2(a4(b1(a2(x1))))))) |
→ |
a7(a7(b7(b6(a4(b1(a2(x1))))))) |
(298) |
b0(a0(b1(b2(b4(a0(a1(x1))))))) |
→ |
a0(a1(b3(b6(b4(a0(a1(x1))))))) |
(299) |
b4(a0(b1(b2(b4(a0(a1(x1))))))) |
→ |
a4(a1(b3(b6(b4(a0(a1(x1))))))) |
(300) |
b6(a4(b1(b2(b4(a0(a1(x1))))))) |
→ |
a6(a5(b3(b6(b4(a0(a1(x1))))))) |
(301) |
b1(a2(b5(b2(b4(a0(a1(x1))))))) |
→ |
a1(a3(b7(b6(b4(a0(a1(x1))))))) |
(302) |
b5(a2(b5(b2(b4(a0(a1(x1))))))) |
→ |
a5(a3(b7(b6(b4(a0(a1(x1))))))) |
(303) |
b7(a6(b5(b2(b4(a0(a1(x1))))))) |
→ |
a7(a7(b7(b6(b4(a0(a1(x1))))))) |
(304) |
b0(a0(b1(b2(a4(a1(a3(x1))))))) |
→ |
a0(a1(b3(b6(a4(a1(a3(x1))))))) |
(305) |
b4(a0(b1(b2(a4(a1(a3(x1))))))) |
→ |
a4(a1(b3(b6(a4(a1(a3(x1))))))) |
(306) |
b6(a4(b1(b2(a4(a1(a3(x1))))))) |
→ |
a6(a5(b3(b6(a4(a1(a3(x1))))))) |
(307) |
b1(a2(b5(b2(a4(a1(a3(x1))))))) |
→ |
a1(a3(b7(b6(a4(a1(a3(x1))))))) |
(308) |
b5(a2(b5(b2(a4(a1(a3(x1))))))) |
→ |
a5(a3(b7(b6(a4(a1(a3(x1))))))) |
(309) |
b7(a6(b5(b2(a4(a1(a3(x1))))))) |
→ |
a7(a7(b7(b6(a4(a1(a3(x1))))))) |
(310) |
There are no rules.
There are no rules in the TRS. Hence, it is terminating.