0(1(1(2(x1)))) |
→ |
0(2(3(0(2(0(0(0(2(0(x1)))))))))) |
(1) |
1(1(3(3(1(x1))))) |
→ |
5(3(3(2(3(0(2(2(2(0(x1)))))))))) |
(2) |
1(3(3(4(4(x1))))) |
→ |
0(3(5(5(3(0(2(0(0(1(x1)))))))))) |
(3) |
3(1(3(5(2(x1))))) |
→ |
5(3(1(5(3(0(0(2(2(2(x1)))))))))) |
(4) |
4(2(3(3(3(x1))))) |
→ |
5(0(3(0(2(0(0(2(0(0(x1)))))))))) |
(5) |
0(1(2(1(1(4(x1)))))) |
→ |
0(0(4(2(3(0(2(2(0(4(x1)))))))))) |
(6) |
2(4(4(3(4(2(x1)))))) |
→ |
2(4(5(0(3(0(0(2(2(0(x1)))))))))) |
(7) |
3(3(0(3(3(3(x1)))))) |
→ |
5(1(4(5(4(0(3(0(2(0(x1)))))))))) |
(8) |
3(5(2(5(4(1(x1)))))) |
→ |
3(0(2(0(0(4(2(3(0(0(x1)))))))))) |
(9) |
0(1(3(1(3(1(0(x1))))))) |
→ |
2(3(0(2(0(1(4(3(1(0(x1)))))))))) |
(10) |
0(1(3(3(3(5(3(x1))))))) |
→ |
0(0(0(4(0(2(4(2(3(0(x1)))))))))) |
(11) |
0(1(3(3(4(3(4(x1))))))) |
→ |
0(3(0(2(0(4(2(0(2(4(x1)))))))))) |
(12) |
0(2(3(3(5(1(3(x1))))))) |
→ |
2(3(2(0(2(0(0(0(5(3(x1)))))))))) |
(13) |
1(1(1(3(1(2(1(x1))))))) |
→ |
1(2(5(3(0(2(2(2(5(1(x1)))))))))) |
(14) |
1(1(3(1(2(3(3(x1))))))) |
→ |
3(0(2(1(5(3(2(5(3(0(x1)))))))))) |
(15) |
1(1(3(3(4(0(1(x1))))))) |
→ |
3(2(1(0(5(1(2(3(2(2(x1)))))))))) |
(16) |
1(2(4(3(4(3(3(x1))))))) |
→ |
3(0(2(1(0(1(1(5(5(3(x1)))))))))) |
(17) |
1(3(0(5(4(1(3(x1))))))) |
→ |
1(3(2(4(0(0(2(2(5(3(x1)))))))))) |
(18) |
1(3(3(0(3(2(4(x1))))))) |
→ |
1(5(2(3(2(4(0(0(0(2(x1)))))))))) |
(19) |
1(3(3(3(3(1(3(x1))))))) |
→ |
1(3(0(2(4(1(4(2(2(3(x1)))))))))) |
(20) |
1(3(3(3(3(4(4(x1))))))) |
→ |
1(0(0(4(5(5(5(1(1(4(x1)))))))))) |
(21) |
1(3(3(4(1(1(2(x1))))))) |
→ |
3(1(5(2(4(3(0(2(2(0(x1)))))))))) |
(22) |
1(3(3(5(1(1(1(x1))))))) |
→ |
1(0(0(3(1(0(0(2(2(2(x1)))))))))) |
(23) |
1(3(4(4(1(3(5(x1))))))) |
→ |
1(3(3(3(0(2(0(2(1(5(x1)))))))))) |
(24) |
1(3(5(0(2(3(4(x1))))))) |
→ |
3(3(4(5(5(5(0(3(5(4(x1)))))))))) |
(25) |
1(3(5(1(1(5(1(x1))))))) |
→ |
1(0(0(4(4(0(0(4(0(0(x1)))))))))) |
(26) |
1(3(5(1(3(4(3(x1))))))) |
→ |
2(5(0(0(5(5(5(1(1(3(x1)))))))))) |
(27) |
2(1(3(3(3(3(1(x1))))))) |
→ |
2(3(0(2(0(4(0(0(3(1(x1)))))))))) |
(28) |
2(3(1(1(1(1(0(x1))))))) |
→ |
2(1(5(0(3(5(5(4(0(0(x1)))))))))) |
(29) |
2(3(1(3(3(1(1(x1))))))) |
→ |
2(2(2(2(2(0(5(5(5(1(x1)))))))))) |
(30) |
2(3(3(5(1(3(3(x1))))))) |
→ |
2(4(4(5(5(3(4(3(2(3(x1)))))))))) |
(31) |
2(4(3(3(4(2(5(x1))))))) |
→ |
0(4(2(4(0(2(5(1(0(5(x1)))))))))) |
(32) |
2(5(2(0(3(5(1(x1))))))) |
→ |
2(5(2(0(4(0(2(0(0(2(x1)))))))))) |
(33) |
3(1(3(1(1(1(4(x1))))))) |
→ |
5(3(5(3(0(0(4(0(1(4(x1)))))))))) |
(34) |
3(1(3(1(4(4(0(x1))))))) |
→ |
3(2(1(4(0(2(0(0(4(2(x1)))))))))) |
(35) |
3(2(5(4(4(2(4(x1))))))) |
→ |
5(3(1(0(2(2(2(0(0(4(x1)))))))))) |
(36) |
3(3(3(3(4(5(2(x1))))))) |
→ |
5(5(1(1(2(4(0(0(2(1(x1)))))))))) |
(37) |
3(3(5(1(5(1(1(x1))))))) |
→ |
5(3(0(2(4(5(5(4(3(1(x1)))))))))) |
(38) |
3(3(5(2(5(0(4(x1))))))) |
→ |
5(5(1(0(1(5(5(3(0(2(x1)))))))))) |
(39) |
3(3(5(3(0(1(1(x1))))))) |
→ |
5(1(4(5(5(3(5(4(5(1(x1)))))))))) |
(40) |
3(4(1(1(3(1(1(x1))))))) |
→ |
1(2(2(4(5(3(5(5(5(1(x1)))))))))) |
(41) |
3(4(2(0(4(1(1(x1))))))) |
→ |
5(3(3(0(2(0(2(5(5(1(x1)))))))))) |
(42) |
3(4(2(5(0(2(3(x1))))))) |
→ |
5(5(1(0(0(5(3(5(5(3(x1)))))))))) |
(43) |
4(1(1(1(4(5(1(x1))))))) |
→ |
5(3(0(4(3(0(2(4(0(2(x1)))))))))) |
(44) |
4(2(1(3(3(3(4(x1))))))) |
→ |
5(4(2(0(0(0(5(1(4(5(x1)))))))))) |
(45) |
4(3(3(5(1(4(1(x1))))))) |
→ |
5(3(5(0(0(5(3(2(0(4(x1)))))))))) |
(46) |
4(4(0(4(3(3(3(x1))))))) |
→ |
4(5(3(0(2(2(3(2(1(3(x1)))))))))) |
(47) |
4(4(3(3(3(4(1(x1))))))) |
→ |
4(0(1(0(2(1(0(2(0(2(x1)))))))))) |
(48) |
4(5(1(5(2(4(3(x1))))))) |
→ |
4(3(3(0(2(0(0(0(0(3(x1)))))))))) |
(49) |
4(5(2(0(3(2(5(x1))))))) |
→ |
5(0(3(4(5(4(0(0(0(5(x1)))))))))) |
(50) |
4(5(2(5(4(1(3(x1))))))) |
→ |
5(0(3(2(1(4(3(0(2(4(x1)))))))))) |
(51) |
5(0(1(3(2(5(4(x1))))))) |
→ |
4(2(3(0(0(0(0(2(5(1(x1)))))))))) |
(52) |
5(1(1(1(1(5(0(x1))))))) |
→ |
3(4(5(5(4(2(0(0(5(0(x1)))))))))) |
(53) |
5(1(1(2(1(1(1(x1))))))) |
→ |
0(5(0(0(5(1(2(0(2(1(x1)))))))))) |
(54) |
5(2(1(3(5(2(2(x1))))))) |
→ |
4(2(1(2(3(0(0(0(0(0(x1)))))))))) |
(55) |
and S is the following TRS.
2(1(1(0(x1)))) |
→ |
0(2(0(0(0(2(0(3(2(0(x1)))))))))) |
(61) |
1(3(3(1(1(x1))))) |
→ |
0(2(2(2(0(3(2(3(3(5(x1)))))))))) |
(62) |
4(4(3(3(1(x1))))) |
→ |
1(0(0(2(0(3(5(5(3(0(x1)))))))))) |
(63) |
2(5(3(1(3(x1))))) |
→ |
2(2(2(0(0(3(5(1(3(5(x1)))))))))) |
(64) |
3(3(3(2(4(x1))))) |
→ |
0(0(2(0(0(2(0(3(0(5(x1)))))))))) |
(65) |
4(1(1(2(1(0(x1)))))) |
→ |
4(0(2(2(0(3(2(4(0(0(x1)))))))))) |
(66) |
2(4(3(4(4(2(x1)))))) |
→ |
0(2(2(0(0(3(0(5(4(2(x1)))))))))) |
(67) |
3(3(3(0(3(3(x1)))))) |
→ |
0(2(0(3(0(4(5(4(1(5(x1)))))))))) |
(68) |
1(4(5(2(5(3(x1)))))) |
→ |
0(0(3(2(4(0(0(2(0(3(x1)))))))))) |
(69) |
0(1(3(1(3(1(0(x1))))))) |
→ |
0(1(3(4(1(0(2(0(3(2(x1)))))))))) |
(70) |
3(5(3(3(3(1(0(x1))))))) |
→ |
0(3(2(4(2(0(4(0(0(0(x1)))))))))) |
(71) |
4(3(4(3(3(1(0(x1))))))) |
→ |
4(2(0(2(4(0(2(0(3(0(x1)))))))))) |
(72) |
3(1(5(3(3(2(0(x1))))))) |
→ |
3(5(0(0(0(2(0(2(3(2(x1)))))))))) |
(73) |
1(2(1(3(1(1(1(x1))))))) |
→ |
1(5(2(2(2(0(3(5(2(1(x1)))))))))) |
(74) |
3(3(2(1(3(1(1(x1))))))) |
→ |
0(3(5(2(3(5(1(2(0(3(x1)))))))))) |
(75) |
1(0(4(3(3(1(1(x1))))))) |
→ |
2(2(3(2(1(5(0(1(2(3(x1)))))))))) |
(76) |
3(3(4(3(4(2(1(x1))))))) |
→ |
3(5(5(1(1(0(1(2(0(3(x1)))))))))) |
(77) |
3(1(4(5(0(3(1(x1))))))) |
→ |
3(5(2(2(0(0(4(2(3(1(x1)))))))))) |
(78) |
4(2(3(0(3(3(1(x1))))))) |
→ |
2(0(0(0(4(2(3(2(5(1(x1)))))))))) |
(79) |
3(1(3(3(3(3(1(x1))))))) |
→ |
3(2(2(4(1(4(2(0(3(1(x1)))))))))) |
(80) |
4(4(3(3(3(3(1(x1))))))) |
→ |
4(1(1(5(5(5(4(0(0(1(x1)))))))))) |
(81) |
2(1(1(4(3(3(1(x1))))))) |
→ |
0(2(2(0(3(4(2(5(1(3(x1)))))))))) |
(82) |
1(1(1(5(3(3(1(x1))))))) |
→ |
2(2(2(0(0(1(3(0(0(1(x1)))))))))) |
(83) |
5(3(1(4(4(3(1(x1))))))) |
→ |
5(1(2(0(2(0(3(3(3(1(x1)))))))))) |
(84) |
4(3(2(0(5(3(1(x1))))))) |
→ |
4(5(3(0(5(5(5(4(3(3(x1)))))))))) |
(85) |
1(5(1(1(5(3(1(x1))))))) |
→ |
0(0(4(0(0(4(4(0(0(1(x1)))))))))) |
(86) |
3(4(3(1(5(3(1(x1))))))) |
→ |
3(1(1(5(5(5(0(0(5(2(x1)))))))))) |
(87) |
1(3(3(3(3(1(2(x1))))))) |
→ |
1(3(0(0(4(0(2(0(3(2(x1)))))))))) |
(88) |
0(1(1(1(1(3(2(x1))))))) |
→ |
0(0(4(5(5(3(0(5(1(2(x1)))))))))) |
(89) |
1(1(3(3(1(3(2(x1))))))) |
→ |
1(5(5(5(0(2(2(2(2(2(x1)))))))))) |
(90) |
3(3(1(5(3(3(2(x1))))))) |
→ |
3(2(3(4(3(5(5(4(4(2(x1)))))))))) |
(91) |
5(2(4(3(3(4(2(x1))))))) |
→ |
5(0(1(5(2(0(4(2(4(0(x1)))))))))) |
(92) |
1(5(3(0(2(5(2(x1))))))) |
→ |
2(0(0(2(0(4(0(2(5(2(x1)))))))))) |
(93) |
4(1(1(1(3(1(3(x1))))))) |
→ |
4(1(0(4(0(0(3(5(3(5(x1)))))))))) |
(94) |
0(4(4(1(3(1(3(x1))))))) |
→ |
2(4(0(0(2(0(4(1(2(3(x1)))))))))) |
(95) |
4(2(4(4(5(2(3(x1))))))) |
→ |
4(0(0(2(2(2(0(1(3(5(x1)))))))))) |
(96) |
2(5(4(3(3(3(3(x1))))))) |
→ |
1(2(0(0(4(2(1(1(5(5(x1)))))))))) |
(97) |
1(1(5(1(5(3(3(x1))))))) |
→ |
1(3(4(5(5(4(2(0(3(5(x1)))))))))) |
(98) |
4(0(5(2(5(3(3(x1))))))) |
→ |
2(0(3(5(5(1(0(1(5(5(x1)))))))))) |
(99) |
1(1(0(3(5(3(3(x1))))))) |
→ |
1(5(4(5(3(5(5(4(1(5(x1)))))))))) |
(100) |
1(1(3(1(1(4(3(x1))))))) |
→ |
1(5(5(5(3(5(4(2(2(1(x1)))))))))) |
(101) |
1(1(4(0(2(4(3(x1))))))) |
→ |
1(5(5(2(0(2(0(3(3(5(x1)))))))))) |
(102) |
3(2(0(5(2(4(3(x1))))))) |
→ |
3(5(5(3(5(0(0(1(5(5(x1)))))))))) |
(103) |
1(5(4(1(1(1(4(x1))))))) |
→ |
2(0(4(2(0(3(4(0(3(5(x1)))))))))) |
(104) |
4(3(3(3(1(2(4(x1))))))) |
→ |
5(4(1(5(0(0(0(2(4(5(x1)))))))))) |
(105) |
1(4(1(5(3(3(4(x1))))))) |
→ |
4(0(2(3(5(0(0(5(3(5(x1)))))))))) |
(106) |
3(3(3(4(0(4(4(x1))))))) |
→ |
3(1(2(3(2(2(0(3(5(4(x1)))))))))) |
(107) |
1(4(3(3(3(4(4(x1))))))) |
→ |
2(0(2(0(1(2(0(1(0(4(x1)))))))))) |
(108) |
3(4(2(5(1(5(4(x1))))))) |
→ |
3(0(0(0(0(2(0(3(3(4(x1)))))))))) |
(109) |
5(2(3(0(2(5(4(x1))))))) |
→ |
5(0(0(0(4(5(4(3(0(5(x1)))))))))) |
(110) |
3(1(4(5(2(5(4(x1))))))) |
→ |
4(2(0(3(4(1(2(3(0(5(x1)))))))))) |
(111) |
4(5(2(3(1(0(5(x1))))))) |
→ |
1(5(2(0(0(0(0(3(2(4(x1)))))))))) |
(112) |
0(5(1(1(1(1(5(x1))))))) |
→ |
0(5(0(0(2(4(5(5(4(3(x1)))))))))) |
(113) |
1(1(1(2(1(1(5(x1))))))) |
→ |
1(2(0(2(1(5(0(0(5(0(x1)))))))))) |
(114) |
2(2(5(3(1(2(5(x1))))))) |
→ |
0(0(0(0(0(3(2(1(2(4(x1)))))))))) |
(115) |
1(1(3(2(x1)))) |
→ |
0(0(2(0(0(3(5(5(4(1(x1)))))))))) |
(116) |
3(3(3(1(1(1(0(x1))))))) |
→ |
3(2(5(1(2(3(5(4(5(3(x1)))))))))) |
(117) |
5(1(2(5(4(1(1(x1))))))) |
→ |
5(1(0(2(0(4(1(2(1(5(x1)))))))))) |
(118) |
3(1(1(2(3(x1))))) |
→ |
0(4(0(1(0(2(0(2(0(3(x1)))))))))) |
(119) |
4(2(1(1(5(3(0(x1))))))) |
→ |
4(0(0(2(5(0(0(4(5(0(x1)))))))))) |
(120) |
There are 195 ruless (increase limit for explicit display).
Root-labeling is applied.
We obtain the labeled TRS
There are 1170 ruless (increase limit for explicit display).
There are 1084 ruless (increase limit for explicit display).
33(34(43(34(42(21(15(x1))))))) |
→ |
35(55(51(11(10(01(12(20(03(35(x1)))))))))) |
(320) |
33(34(43(34(42(21(13(x1))))))) |
→ |
35(55(51(11(10(01(12(20(03(33(x1)))))))))) |
(321) |
33(34(43(34(42(21(11(x1))))))) |
→ |
35(55(51(11(10(01(12(20(03(31(x1)))))))))) |
(322) |
33(34(43(34(42(21(14(x1))))))) |
→ |
35(55(51(11(10(01(12(20(03(34(x1)))))))))) |
(324) |
43(32(20(05(53(31(15(x1))))))) |
→ |
45(53(30(05(55(55(54(43(33(35(x1)))))))))) |
(350) |
43(32(20(05(53(31(13(x1))))))) |
→ |
45(53(30(05(55(55(54(43(33(33(x1)))))))))) |
(351) |
43(32(20(05(53(31(11(x1))))))) |
→ |
45(53(30(05(55(55(54(43(33(31(x1)))))))))) |
(352) |
43(32(20(05(53(31(14(x1))))))) |
→ |
45(53(30(05(55(55(54(43(33(34(x1)))))))))) |
(354) |
42(24(44(45(52(23(32(x1))))))) |
→ |
40(00(02(22(22(20(01(13(35(52(x1)))))))))) |
(397) |
42(24(44(45(52(23(35(x1))))))) |
→ |
40(00(02(22(22(20(01(13(35(55(x1)))))))))) |
(398) |
42(24(44(45(52(23(33(x1))))))) |
→ |
40(00(02(22(22(20(01(13(35(53(x1)))))))))) |
(399) |
42(24(44(45(52(23(30(x1))))))) |
→ |
40(00(02(22(22(20(01(13(35(50(x1)))))))))) |
(401) |
42(24(44(45(52(23(34(x1))))))) |
→ |
40(00(02(22(22(20(01(13(35(54(x1)))))))))) |
(402) |
32(20(05(52(24(43(32(x1))))))) |
→ |
35(55(53(35(50(00(01(15(55(52(x1)))))))))) |
(427) |
32(20(05(52(24(43(35(x1))))))) |
→ |
35(55(53(35(50(00(01(15(55(55(x1)))))))))) |
(428) |
32(20(05(52(24(43(33(x1))))))) |
→ |
35(55(53(35(50(00(01(15(55(53(x1)))))))))) |
(429) |
32(20(05(52(24(43(30(x1))))))) |
→ |
35(55(53(35(50(00(01(15(55(50(x1)))))))))) |
(431) |
32(20(05(52(24(43(34(x1))))))) |
→ |
35(55(53(35(50(00(01(15(55(54(x1)))))))))) |
(432) |
52(23(30(02(25(54(45(x1))))))) |
→ |
50(00(00(04(45(54(43(30(05(55(x1)))))))))) |
(446) |
52(23(30(02(25(54(43(x1))))))) |
→ |
50(00(00(04(45(54(43(30(05(53(x1)))))))))) |
(447) |
52(23(30(02(25(54(41(x1))))))) |
→ |
50(00(00(04(45(54(43(30(05(51(x1)))))))))) |
(448) |
52(23(30(02(25(54(40(x1))))))) |
→ |
50(00(00(04(45(54(43(30(05(50(x1)))))))))) |
(449) |
52(23(30(02(25(54(44(x1))))))) |
→ |
50(00(00(04(45(54(43(30(05(54(x1)))))))))) |
(450) |
14(44(43(33(31(15(x1)))))) |
→ |
11(10(00(02(20(03(35(55(53(30(05(x1))))))))))) |
(542) |
14(44(43(33(31(14(x1)))))) |
→ |
11(10(00(02(20(03(35(55(53(30(04(x1))))))))))) |
(546) |
34(44(43(33(31(15(x1)))))) |
→ |
31(10(00(02(20(03(35(55(53(30(05(x1))))))))))) |
(554) |
34(44(43(33(31(14(x1)))))) |
→ |
31(10(00(02(20(03(35(55(53(30(04(x1))))))))))) |
(558) |
41(15(54(41(11(11(14(45(x1)))))))) |
→ |
42(20(04(42(20(03(34(40(03(35(55(x1))))))))))) |
(1142) |
41(15(54(41(11(11(14(43(x1)))))))) |
→ |
42(20(04(42(20(03(34(40(03(35(53(x1))))))))))) |
(1143) |
41(15(54(41(11(11(14(41(x1)))))))) |
→ |
42(20(04(42(20(03(34(40(03(35(51(x1))))))))))) |
(1144) |
41(15(54(41(11(11(14(40(x1)))))))) |
→ |
42(20(04(42(20(03(34(40(03(35(50(x1))))))))))) |
(1145) |
41(15(54(41(11(11(14(44(x1)))))))) |
→ |
42(20(04(42(20(03(34(40(03(35(54(x1))))))))))) |
(1146) |
23(31(14(45(52(25(54(45(x1)))))))) |
→ |
24(42(20(03(34(41(12(23(30(05(55(x1))))))))))) |
(1256) |
23(31(14(45(52(25(54(43(x1)))))))) |
→ |
24(42(20(03(34(41(12(23(30(05(53(x1))))))))))) |
(1257) |
23(31(14(45(52(25(54(41(x1)))))))) |
→ |
24(42(20(03(34(41(12(23(30(05(51(x1))))))))))) |
(1258) |
23(31(14(45(52(25(54(40(x1)))))))) |
→ |
24(42(20(03(34(41(12(23(30(05(50(x1))))))))))) |
(1259) |
23(31(14(45(52(25(54(44(x1)))))))) |
→ |
24(42(20(03(34(41(12(23(30(05(54(x1))))))))))) |
(1260) |
03(31(14(45(52(25(54(45(x1)))))))) |
→ |
04(42(20(03(34(41(12(23(30(05(55(x1))))))))))) |
(1268) |
03(31(14(45(52(25(54(43(x1)))))))) |
→ |
04(42(20(03(34(41(12(23(30(05(53(x1))))))))))) |
(1269) |
03(31(14(45(52(25(54(41(x1)))))))) |
→ |
04(42(20(03(34(41(12(23(30(05(51(x1))))))))))) |
(1270) |
03(31(14(45(52(25(54(40(x1)))))))) |
→ |
04(42(20(03(34(41(12(23(30(05(50(x1))))))))))) |
(1271) |
03(31(14(45(52(25(54(44(x1)))))))) |
→ |
04(42(20(03(34(41(12(23(30(05(54(x1))))))))))) |
(1272) |
14(45(52(23(31(10(05(52(x1)))))))) |
→ |
11(15(52(20(00(00(00(03(32(24(42(x1))))))))))) |
(1297) |
34(45(52(23(31(10(05(52(x1)))))))) |
→ |
31(15(52(20(00(00(00(03(32(24(42(x1))))))))))) |
(1309) |
There are no rules in the TRS. Hence, it is terminating.