and S is the following TRS.
As carrier we take the set
{0,...,7}.
Symbols are labeled by the interpretation of their arguments using the interpretations
(modulo 8):
There are 128 ruless (increase limit for explicit display).
a7(a3(a5(a2(b5(a6(b7(a7(x1)))))))) |
→ |
a7(a7(a7(x1))) |
(31) |
a7(a3(a5(a2(b5(a6(b7(a3(x1)))))))) |
→ |
a7(a7(a3(x1))) |
(32) |
a7(a3(a5(a2(b5(a6(b3(a5(x1)))))))) |
→ |
a7(a3(a5(x1))) |
(33) |
a7(a3(a5(a2(b5(a6(b3(a1(x1)))))))) |
→ |
a7(a3(a1(x1))) |
(34) |
a7(a3(a5(a2(b5(a2(b5(a6(x1)))))))) |
→ |
a3(a5(a6(x1))) |
(35) |
a7(a3(a5(a2(b5(a2(b5(a2(x1)))))))) |
→ |
a3(a5(a2(x1))) |
(36) |
a7(a3(a5(a2(b5(a2(b1(a4(x1)))))))) |
→ |
a3(a1(a4(x1))) |
(37) |
a7(a3(a5(a2(b5(a2(b1(a0(x1)))))))) |
→ |
a3(a1(a0(x1))) |
(38) |
a5(a2(b5(a2(b5(a6(b7(a7(x1)))))))) |
→ |
a5(a6(b7(x1))) |
(39) |
a5(a2(b5(a2(b5(a6(b7(a3(x1)))))))) |
→ |
a5(a6(b3(x1))) |
(40) |
a5(a2(b5(a2(b5(a6(b3(a5(x1)))))))) |
→ |
a5(a2(b5(x1))) |
(41) |
a5(a2(b5(a2(b5(a6(b3(a1(x1)))))))) |
→ |
a5(a2(b1(x1))) |
(42) |
a5(a2(b5(a2(b5(a2(b5(a6(x1)))))))) |
→ |
a1(a4(b6(x1))) |
(43) |
a5(a2(b5(a2(b5(a2(b5(a2(x1)))))))) |
→ |
a1(a4(b2(x1))) |
(44) |
a5(a2(b5(a2(b5(a2(b1(a4(x1)))))))) |
→ |
a1(a0(b4(x1))) |
(45) |
a5(a2(b5(a2(b5(a2(b1(a0(x1)))))))) |
→ |
a1(a0(b0(x1))) |
(46) |
a6(b3(a5(a2(b5(a6(b7(a7(x1)))))))) |
→ |
a6(b7(a7(x1))) |
(47) |
a6(b3(a5(a2(b5(a6(b7(a3(x1)))))))) |
→ |
a6(b7(a3(x1))) |
(48) |
a6(b3(a5(a2(b5(a6(b3(a5(x1)))))))) |
→ |
a6(b3(a5(x1))) |
(49) |
a6(b3(a5(a2(b5(a6(b3(a1(x1)))))))) |
→ |
a6(b3(a1(x1))) |
(50) |
a6(b3(a5(a2(b5(a2(b5(a6(x1)))))))) |
→ |
a2(b5(a6(x1))) |
(51) |
a6(b3(a5(a2(b5(a2(b5(a2(x1)))))))) |
→ |
a2(b5(a2(x1))) |
(52) |
a6(b3(a5(a2(b5(a2(b1(a4(x1)))))))) |
→ |
a2(b1(a4(x1))) |
(53) |
a6(b3(a5(a2(b5(a2(b1(a0(x1)))))))) |
→ |
a2(b1(a0(x1))) |
(54) |
a4(b2(b5(a2(b5(a6(b7(a7(x1)))))))) |
→ |
a4(b6(b7(x1))) |
(55) |
a4(b2(b5(a2(b5(a6(b7(a3(x1)))))))) |
→ |
a4(b6(b3(x1))) |
(56) |
a4(b2(b5(a2(b5(a6(b3(a5(x1)))))))) |
→ |
a4(b2(b5(x1))) |
(57) |
a4(b2(b5(a2(b5(a6(b3(a1(x1)))))))) |
→ |
a4(b2(b1(x1))) |
(58) |
a4(b2(b5(a2(b5(a2(b5(a6(x1)))))))) |
→ |
a0(b4(b6(x1))) |
(59) |
a4(b2(b5(a2(b5(a2(b5(a2(x1)))))))) |
→ |
a0(b4(b2(x1))) |
(60) |
a4(b2(b5(a2(b5(a2(b1(a4(x1)))))))) |
→ |
a0(b0(b4(x1))) |
(61) |
a4(b2(b5(a2(b5(a2(b1(a0(x1)))))))) |
→ |
a0(b0(b0(x1))) |
(62) |
b7(a3(a5(a2(b5(a6(b7(a7(x1)))))))) |
→ |
b7(a7(a7(x1))) |
(63) |
b7(a3(a5(a2(b5(a6(b7(a3(x1)))))))) |
→ |
b7(a7(a3(x1))) |
(64) |
b7(a3(a5(a2(b5(a6(b3(a5(x1)))))))) |
→ |
b7(a3(a5(x1))) |
(65) |
b7(a3(a5(a2(b5(a6(b3(a1(x1)))))))) |
→ |
b7(a3(a1(x1))) |
(66) |
b7(a3(a5(a2(b5(a2(b5(a6(x1)))))))) |
→ |
b3(a5(a6(x1))) |
(67) |
b7(a3(a5(a2(b5(a2(b5(a2(x1)))))))) |
→ |
b3(a5(a2(x1))) |
(68) |
b7(a3(a5(a2(b5(a2(b1(a4(x1)))))))) |
→ |
b3(a1(a4(x1))) |
(69) |
b7(a3(a5(a2(b5(a2(b1(a0(x1)))))))) |
→ |
b3(a1(a0(x1))) |
(70) |
b5(a2(b5(a2(b5(a6(b7(a7(x1)))))))) |
→ |
b5(a6(b7(x1))) |
(71) |
b5(a2(b5(a2(b5(a6(b7(a3(x1)))))))) |
→ |
b5(a6(b3(x1))) |
(72) |
b5(a2(b5(a2(b5(a6(b3(a5(x1)))))))) |
→ |
b5(a2(b5(x1))) |
(73) |
b5(a2(b5(a2(b5(a6(b3(a1(x1)))))))) |
→ |
b5(a2(b1(x1))) |
(74) |
b5(a2(b5(a2(b5(a2(b5(a6(x1)))))))) |
→ |
b1(a4(b6(x1))) |
(75) |
b5(a2(b5(a2(b5(a2(b5(a2(x1)))))))) |
→ |
b1(a4(b2(x1))) |
(76) |
b5(a2(b5(a2(b5(a2(b1(a4(x1)))))))) |
→ |
b1(a0(b4(x1))) |
(77) |
b5(a2(b5(a2(b5(a2(b1(a0(x1)))))))) |
→ |
b1(a0(b0(x1))) |
(78) |
b6(b3(a5(a2(b5(a6(b7(a7(x1)))))))) |
→ |
b6(b7(a7(x1))) |
(79) |
b6(b3(a5(a2(b5(a6(b7(a3(x1)))))))) |
→ |
b6(b7(a3(x1))) |
(80) |
b6(b3(a5(a2(b5(a6(b3(a5(x1)))))))) |
→ |
b6(b3(a5(x1))) |
(81) |
b6(b3(a5(a2(b5(a6(b3(a1(x1)))))))) |
→ |
b6(b3(a1(x1))) |
(82) |
b6(b3(a5(a2(b5(a2(b5(a6(x1)))))))) |
→ |
b2(b5(a6(x1))) |
(83) |
b6(b3(a5(a2(b5(a2(b5(a2(x1)))))))) |
→ |
b2(b5(a2(x1))) |
(84) |
b6(b3(a5(a2(b5(a2(b1(a4(x1)))))))) |
→ |
b2(b1(a4(x1))) |
(85) |
b6(b3(a5(a2(b5(a2(b1(a0(x1)))))))) |
→ |
b2(b1(a0(x1))) |
(86) |
b4(b2(b5(a2(b5(a6(b7(a7(x1)))))))) |
→ |
b4(b6(b7(x1))) |
(87) |
b4(b2(b5(a2(b5(a6(b7(a3(x1)))))))) |
→ |
b4(b6(b3(x1))) |
(88) |
b4(b2(b5(a2(b5(a6(b3(a5(x1)))))))) |
→ |
b4(b2(b5(x1))) |
(89) |
b4(b2(b5(a2(b5(a6(b3(a1(x1)))))))) |
→ |
b4(b2(b1(x1))) |
(90) |
b4(b2(b5(a2(b5(a2(b5(a6(x1)))))))) |
→ |
b0(b4(b6(x1))) |
(91) |
b4(b2(b5(a2(b5(a2(b5(a2(x1)))))))) |
→ |
b0(b4(b2(x1))) |
(92) |
b4(b2(b5(a2(b5(a2(b1(a4(x1)))))))) |
→ |
b0(b0(b4(x1))) |
(93) |
b4(b2(b5(a2(b5(a2(b1(a0(x1)))))))) |
→ |
b0(b0(b0(x1))) |
(94) |
a7(a3(a5(a2(b5(x1))))) |
→ |
a3(a1(a4(b6(b7(a3(a5(x1))))))) |
(97) |
a5(a2(b5(a6(b7(x1))))) |
→ |
a1(a0(b4(b6(b7(a7(a7(x1))))))) |
(103) |
a5(a2(b5(a6(b3(x1))))) |
→ |
a1(a0(b4(b6(b7(a7(a3(x1))))))) |
(104) |
a5(a2(b5(a2(b5(x1))))) |
→ |
a1(a0(b4(b6(b7(a3(a5(x1))))))) |
(105) |
a5(a2(b5(a2(b1(x1))))) |
→ |
a1(a0(b4(b6(b7(a3(a1(x1))))))) |
(106) |
a6(b3(a5(a2(b5(x1))))) |
→ |
a2(b1(a4(b6(b7(a3(a5(x1))))))) |
(113) |
a4(b2(b5(a6(b7(x1))))) |
→ |
a0(b0(b4(b6(b7(a7(a7(x1))))))) |
(119) |
a4(b2(b5(a6(b3(x1))))) |
→ |
a0(b0(b4(b6(b7(a7(a3(x1))))))) |
(120) |
a4(b2(b5(a2(b5(x1))))) |
→ |
a0(b0(b4(b6(b7(a3(a5(x1))))))) |
(121) |
a4(b2(b5(a2(b1(x1))))) |
→ |
a0(b0(b4(b6(b7(a3(a1(x1))))))) |
(122) |
b7(a3(a5(a2(b5(x1))))) |
→ |
b3(a1(a4(b6(b7(a3(a5(x1))))))) |
(129) |
b5(a2(b5(a6(b7(x1))))) |
→ |
b1(a0(b4(b6(b7(a7(a7(x1))))))) |
(135) |
b5(a2(b5(a6(b3(x1))))) |
→ |
b1(a0(b4(b6(b7(a7(a3(x1))))))) |
(136) |
b5(a2(b5(a2(b5(x1))))) |
→ |
b1(a0(b4(b6(b7(a3(a5(x1))))))) |
(137) |
b5(a2(b5(a2(b1(x1))))) |
→ |
b1(a0(b4(b6(b7(a3(a1(x1))))))) |
(138) |
b5(a2(b1(a4(b6(x1))))) |
→ |
b1(a0(b4(b6(b3(a5(a6(x1))))))) |
(139) |
b5(a2(b1(a4(b2(x1))))) |
→ |
b1(a0(b4(b6(b3(a5(a2(x1))))))) |
(140) |
b5(a2(b1(a0(b4(x1))))) |
→ |
b1(a0(b4(b6(b3(a1(a4(x1))))))) |
(141) |
b5(a2(b1(a0(b0(x1))))) |
→ |
b1(a0(b4(b6(b3(a1(a0(x1))))))) |
(142) |
b6(b3(a5(a2(b5(x1))))) |
→ |
b2(b1(a4(b6(b7(a3(a5(x1))))))) |
(145) |
b4(b2(b5(a6(b7(x1))))) |
→ |
b0(b0(b4(b6(b7(a7(a7(x1))))))) |
(151) |
b4(b2(b5(a6(b3(x1))))) |
→ |
b0(b0(b4(b6(b7(a7(a3(x1))))))) |
(152) |
b4(b2(b5(a2(b5(x1))))) |
→ |
b0(b0(b4(b6(b7(a3(a5(x1))))))) |
(153) |
b4(b2(b5(a2(b1(x1))))) |
→ |
b0(b0(b4(b6(b7(a3(a1(x1))))))) |
(154) |
There are no rules in the TRS. Hence, it is terminating.