The relative rewrite relation R/S is considered where R is the following TRS
0(0(0(1(x1)))) | → | 2(3(2(2(4(2(2(4(0(5(x1)))))))))) | (1) |
1(0(5(0(x1)))) | → | 1(2(2(4(4(4(2(2(1(1(x1)))))))))) | (2) |
0(3(0(1(4(x1))))) | → | 2(2(4(2(4(0(5(5(1(4(x1)))))))))) | (3) |
0(4(0(1(0(x1))))) | → | 2(0(5(1(1(1(1(3(3(5(x1)))))))))) | (4) |
0(5(0(0(1(x1))))) | → | 0(5(1(1(1(4(4(3(1(5(x1)))))))))) | (5) |
0(0(3(4(5(2(x1)))))) | → | 2(3(4(2(4(1(4(2(1(1(x1)))))))))) | (6) |
0(0(3(5(2(5(x1)))))) | → | 2(4(1(1(2(2(5(2(3(5(x1)))))))))) | (7) |
0(0(4(5(1(0(x1)))))) | → | 3(1(4(4(3(1(2(4(1(1(x1)))))))))) | (8) |
0(0(4(5(1(4(x1)))))) | → | 3(4(2(4(1(4(2(0(5(4(x1)))))))))) | (9) |
0(1(4(5(5(3(x1)))))) | → | 2(2(4(4(4(5(0(3(2(4(x1)))))))))) | (10) |
0(3(0(0(2(5(x1)))))) | → | 2(4(0(3(2(4(2(5(2(5(x1)))))))))) | (11) |
0(4(0(0(2(2(x1)))))) | → | 2(2(4(0(3(2(3(0(2(2(x1)))))))))) | (12) |
0(4(3(1(0(2(x1)))))) | → | 2(2(2(4(1(1(0(3(5(2(x1)))))))))) | (13) |
0(5(0(0(3(4(x1)))))) | → | 2(4(2(0(1(4(5(2(2(4(x1)))))))))) | (14) |
0(5(0(3(4(1(x1)))))) | → | 2(4(3(2(1(4(3(1(3(1(x1)))))))))) | (15) |
1(5(0(0(0(2(x1)))))) | → | 1(1(1(5(5(1(5(2(2(4(x1)))))))))) | (16) |
1(5(5(0(4(1(x1)))))) | → | 1(1(4(4(2(4(3(3(2(1(x1)))))))))) | (17) |
2(1(0(4(5(4(x1)))))) | → | 2(2(4(2(1(0(2(3(3(4(x1)))))))))) | (18) |
4(1(0(0(5(0(x1)))))) | → | 4(1(5(1(4(4(1(1(5(1(x1)))))))))) | (19) |
4(5(0(3(2(2(x1)))))) | → | 4(2(2(4(2(5(2(2(4(2(x1)))))))))) | (20) |
5(0(0(0(4(5(x1)))))) | → | 5(0(5(4(1(1(4(4(3(5(x1)))))))))) | (21) |
5(0(3(5(0(0(x1)))))) | → | 5(2(2(3(1(5(1(1(5(5(x1)))))))))) | (22) |
5(0(4(0(5(0(x1)))))) | → | 0(5(4(4(4(2(4(4(2(0(x1)))))))))) | (23) |
5(0(4(5(4(4(x1)))))) | → | 2(1(5(2(4(4(4(1(4(2(x1)))))))))) | (24) |
5(1(3(5(5(0(x1)))))) | → | 5(2(3(2(1(5(4(4(4(1(x1)))))))))) | (25) |
5(2(5(0(1(2(x1)))))) | → | 5(2(4(2(4(0(1(5(2(4(x1)))))))))) | (26) |
0(0(0(3(4(0(5(x1))))))) | → | 0(1(5(4(1(1(5(1(1(5(x1)))))))))) | (27) |
0(0(3(4(5(0(4(x1))))))) | → | 3(2(1(1(5(4(5(3(5(3(x1)))))))))) | (28) |
0(1(0(3(0(5(3(x1))))))) | → | 2(2(0(2(1(4(3(5(5(3(x1)))))))))) | (29) |
0(1(3(1(3(4(2(x1))))))) | → | 5(4(4(2(1(1(1(1(5(4(x1)))))))))) | (30) |
0(2(5(0(3(0(5(x1))))))) | → | 2(4(5(2(4(0(0(1(1(5(x1)))))))))) | (31) |
0(3(2(0(4(0(1(x1))))))) | → | 3(2(0(0(4(2(4(1(3(1(x1)))))))))) | (32) |
0(3(5(2(0(0(3(x1))))))) | → | 2(0(2(3(3(4(3(4(2(3(x1)))))))))) | (33) |
0(5(3(0(4(0(2(x1))))))) | → | 2(2(1(0(5(1(3(2(1(4(x1)))))))))) | (34) |
0(5(3(2(2(5(0(x1))))))) | → | 2(3(2(1(2(2(4(1(5(1(x1)))))))))) | (35) |
1(0(0(1(0(4(0(x1))))))) | → | 1(4(1(3(2(2(1(5(4(5(x1)))))))))) | (36) |
1(0(0(4(1(1(2(x1))))))) | → | 2(2(4(0(2(0(5(4(1(2(x1)))))))))) | (37) |
1(0(1(1(1(0(4(x1))))))) | → | 1(4(1(1(4(0(3(3(0(2(x1)))))))))) | (38) |
1(0(1(4(5(0(5(x1))))))) | → | 4(1(1(1(1(4(1(0(1(5(x1)))))))))) | (39) |
1(0(4(5(4(5(0(x1))))))) | → | 2(2(1(2(0(2(5(3(1(1(x1)))))))))) | (40) |
1(3(5(4(1(3(3(x1))))))) | → | 1(4(4(2(0(1(1(5(3(3(x1)))))))))) | (41) |
1(5(0(0(3(0(5(x1))))))) | → | 1(1(4(1(5(0(5(5(1(5(x1)))))))))) | (42) |
2(5(1(3(3(0(1(x1))))))) | → | 2(1(3(4(3(2(4(5(5(5(x1)))))))))) | (43) |
4(0(0(1(0(3(4(x1))))))) | → | 4(3(2(3(3(1(5(5(2(0(x1)))))))))) | (44) |
5(0(0(0(0(0(4(x1))))))) | → | 2(4(2(1(3(1(1(2(3(2(x1)))))))))) | (45) |
5(0(0(1(2(5(2(x1))))))) | → | 5(2(0(2(2(1(5(4(5(2(x1)))))))))) | (46) |
5(0(0(3(1(0(4(x1))))))) | → | 3(1(2(4(3(4(3(4(2(1(x1)))))))))) | (47) |
5(0(5(1(0(3(4(x1))))))) | → | 5(5(4(1(2(2(2(4(1(5(x1)))))))))) | (48) |
5(1(0(0(4(3(4(x1))))))) | → | 5(4(3(2(3(2(2(5(4(4(x1)))))))))) | (49) |
5(1(3(0(4(0(0(x1))))))) | → | 5(1(4(1(4(5(2(2(3(5(x1)))))))))) | (50) |
5(2(0(1(0(4(2(x1))))))) | → | 2(5(1(1(4(1(1(4(1(2(x1)))))))))) | (51) |
and S is the following TRS.
1(3(5(2(0(4(x1)))))) | → | 1(5(2(2(4(2(2(1(5(2(x1)))))))))) | (52) |
0(1(0(4(4(1(x1)))))) | → | 2(2(0(2(4(5(5(4(3(1(x1)))))))))) | (53) |
4(0(0(5(2(1(4(x1))))))) | → | 4(2(5(2(3(2(2(4(1(4(x1)))))))))) | (54) |
2(0(3(0(1(2(x1)))))) | → | 2(2(1(5(2(4(2(1(0(2(x1)))))))))) | (55) |
0(5(2(5(0(0(2(x1))))))) | → | 0(3(1(5(1(5(4(4(5(2(x1)))))))))) | (56) |
4(0(4(0(3(4(x1)))))) | → | 4(2(1(4(2(2(4(5(3(2(x1)))))))))) | (57) |
0(1(0(5(3(4(x1)))))) | → | 0(1(3(3(2(4(1(3(2(4(x1)))))))))) | (58) |
0(1(0(0(5(0(4(x1))))))) | → | 2(0(5(2(3(0(3(2(5(2(x1)))))))))) | (59) |
5(3(4(5(4(5(4(x1))))))) | → | 4(4(2(4(4(0(3(1(3(4(x1)))))))))) | (60) |
{0(☐), 1(☐), 2(☐), 3(☐), 4(☐), 5(☐)}
We obtain the transformed TRSThere are 220 ruless (increase limit for explicit display).
Root-labeling is applied.
We obtain the labeled TRSThere are 1320 ruless (increase limit for explicit display).
[10(x1)] | = | 1 + 1 · x1 |
[05(x1)] | = | 1 + 1 · x1 |
[50(x1)] | = | 1 + 1 · x1 |
[01(x1)] | = | 1 + 1 · x1 |
[12(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 + 1 · x1 |
[15(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 + 1 · x1 |
[14(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 + 1 · x1 |
[51(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[55(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[53(x1)] | = | 1 + 1 · x1 |
[41(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 + 1 · x1 |
[40(x1)] | = | 1 + 1 · x1 |
[25(x1)] | = | 1 + 1 · x1 |
[45(x1)] | = | 1 + 1 · x1 |
[23(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 + 1 · x1 |
[35(x1)] | = | 1 + 1 · x1 |
[30(x1)] | = | 1 + 1 · x1 |
There are 1250 ruless (increase limit for explicit display).
31(33(13(41(54(35(13(x1))))))) | → | 31(33(53(15(11(01(20(42(44(14(x1)))))))))) | (1573) |
30(33(13(41(54(35(13(x1))))))) | → | 30(33(53(15(11(01(20(42(44(14(x1)))))))))) | (1574) |
35(33(13(41(54(35(13(x1))))))) | → | 35(33(53(15(11(01(20(42(44(14(x1)))))))))) | (1575) |
32(33(13(41(54(35(13(x1))))))) | → | 32(33(53(15(11(01(20(42(44(14(x1)))))))))) | (1576) |
34(33(13(41(54(35(13(x1))))))) | → | 34(33(53(15(11(01(20(42(44(14(x1)))))))))) | (1577) |
33(33(13(41(54(35(13(x1))))))) | → | 33(33(53(15(11(01(20(42(44(14(x1)))))))))) | (1578) |
03(10(01(40(04(00(x1)))))) | → | 53(35(33(13(11(11(11(51(05(20(02(x1))))))))))) | (1579) |
03(10(01(40(04(10(x1)))))) | → | 53(35(33(13(11(11(11(51(05(20(12(x1))))))))))) | (1580) |
03(10(01(40(04(20(x1)))))) | → | 53(35(33(13(11(11(11(51(05(20(22(x1))))))))))) | (1581) |
03(10(01(40(04(30(x1)))))) | → | 53(35(33(13(11(11(11(51(05(20(32(x1))))))))))) | (1582) |
03(10(01(40(04(40(x1)))))) | → | 53(35(33(13(11(11(11(51(05(20(42(x1))))))))))) | (1583) |
03(10(01(40(04(50(x1)))))) | → | 53(35(33(13(11(11(11(51(05(20(52(x1))))))))))) | (1584) |
41(14(51(45(04(00(10(x1))))))) | → | 41(54(05(20(42(14(41(24(42(34(13(x1))))))))))) | (1585) |
40(14(51(45(04(00(10(x1))))))) | → | 40(54(05(20(42(14(41(24(42(34(13(x1))))))))))) | (1586) |
45(14(51(45(04(00(10(x1))))))) | → | 45(54(05(20(42(14(41(24(42(34(13(x1))))))))))) | (1587) |
42(14(51(45(04(00(10(x1))))))) | → | 42(54(05(20(42(14(41(24(42(34(13(x1))))))))))) | (1588) |
44(14(51(45(04(00(10(x1))))))) | → | 44(54(05(20(42(14(41(24(42(34(13(x1))))))))))) | (1589) |
43(14(51(45(04(00(10(x1))))))) | → | 43(54(05(20(42(14(41(24(42(34(13(x1))))))))))) | (1590) |
41(14(51(45(04(00(50(x1))))))) | → | 41(54(05(20(42(14(41(24(42(34(53(x1))))))))))) | (1591) |
40(14(51(45(04(00(50(x1))))))) | → | 40(54(05(20(42(14(41(24(42(34(53(x1))))))))))) | (1592) |
45(14(51(45(04(00(50(x1))))))) | → | 45(54(05(20(42(14(41(24(42(34(53(x1))))))))))) | (1593) |
42(14(51(45(04(00(50(x1))))))) | → | 42(54(05(20(42(14(41(24(42(34(53(x1))))))))))) | (1594) |
44(14(51(45(04(00(50(x1))))))) | → | 44(54(05(20(42(14(41(24(42(34(53(x1))))))))))) | (1595) |
43(14(51(45(04(00(50(x1))))))) | → | 43(54(05(20(42(14(41(24(42(34(53(x1))))))))))) | (1596) |
44(04(50(45(34(03(00(10(x1)))))))) | → | 34(53(35(53(45(54(15(11(21(32(13(x1))))))))))) | (1597) |
44(04(50(45(34(03(00(50(x1)))))))) | → | 34(53(35(53(45(54(15(11(21(32(53(x1))))))))))) | (1598) |
11(01(40(04(20(32(03(10(x1)))))))) | → | 11(31(13(41(24(42(04(00(20(32(13(x1))))))))))) | (1599) |
10(01(40(04(20(32(03(10(x1)))))))) | → | 10(31(13(41(24(42(04(00(20(32(13(x1))))))))))) | (1600) |
15(01(40(04(20(32(03(10(x1)))))))) | → | 15(31(13(41(24(42(04(00(20(32(13(x1))))))))))) | (1601) |
12(01(40(04(20(32(03(10(x1)))))))) | → | 12(31(13(41(24(42(04(00(20(32(13(x1))))))))))) | (1602) |
14(01(40(04(20(32(03(10(x1)))))))) | → | 14(31(13(41(24(42(04(00(20(32(13(x1))))))))))) | (1603) |
13(01(40(04(20(32(03(10(x1)))))))) | → | 13(31(13(41(24(42(04(00(20(32(13(x1))))))))))) | (1604) |
11(01(40(04(20(32(03(50(x1)))))))) | → | 11(31(13(41(24(42(04(00(20(32(53(x1))))))))))) | (1605) |
10(01(40(04(20(32(03(50(x1)))))))) | → | 10(31(13(41(24(42(04(00(20(32(53(x1))))))))))) | (1606) |
15(01(40(04(20(32(03(50(x1)))))))) | → | 15(31(13(41(24(42(04(00(20(32(53(x1))))))))))) | (1607) |
12(01(40(04(20(32(03(50(x1)))))))) | → | 12(31(13(41(24(42(04(00(20(32(53(x1))))))))))) | (1608) |
14(01(40(04(20(32(03(50(x1)))))))) | → | 14(31(13(41(24(42(04(00(20(32(53(x1))))))))))) | (1609) |
13(01(40(04(20(32(03(50(x1)))))))) | → | 13(31(13(41(24(42(04(00(20(32(53(x1))))))))))) | (1610) |
21(12(11(41(04(00(10(11(x1)))))))) | → | 21(12(41(54(05(20(02(40(24(22(12(x1))))))))))) | (1611) |
20(12(11(41(04(00(10(11(x1)))))))) | → | 20(12(41(54(05(20(02(40(24(22(12(x1))))))))))) | (1612) |
25(12(11(41(04(00(10(11(x1)))))))) | → | 25(12(41(54(05(20(02(40(24(22(12(x1))))))))))) | (1613) |
22(12(11(41(04(00(10(11(x1)))))))) | → | 22(12(41(54(05(20(02(40(24(22(12(x1))))))))))) | (1614) |
24(12(11(41(04(00(10(11(x1)))))))) | → | 24(12(41(54(05(20(02(40(24(22(12(x1))))))))))) | (1615) |
23(12(11(41(04(00(10(11(x1)))))))) | → | 23(12(41(54(05(20(02(40(24(22(12(x1))))))))))) | (1616) |
21(12(11(41(04(00(10(21(x1)))))))) | → | 21(12(41(54(05(20(02(40(24(22(22(x1))))))))))) | (1617) |
20(12(11(41(04(00(10(21(x1)))))))) | → | 20(12(41(54(05(20(02(40(24(22(22(x1))))))))))) | (1618) |
25(12(11(41(04(00(10(21(x1)))))))) | → | 25(12(41(54(05(20(02(40(24(22(22(x1))))))))))) | (1619) |
22(12(11(41(04(00(10(21(x1)))))))) | → | 22(12(41(54(05(20(02(40(24(22(22(x1))))))))))) | (1620) |
24(12(11(41(04(00(10(21(x1)))))))) | → | 24(12(41(54(05(20(02(40(24(22(22(x1))))))))))) | (1621) |
23(12(11(41(04(00(10(21(x1)))))))) | → | 23(12(41(54(05(20(02(40(24(22(22(x1))))))))))) | (1622) |
21(12(11(41(04(00(10(31(x1)))))))) | → | 21(12(41(54(05(20(02(40(24(22(32(x1))))))))))) | (1623) |
20(12(11(41(04(00(10(31(x1)))))))) | → | 20(12(41(54(05(20(02(40(24(22(32(x1))))))))))) | (1624) |
25(12(11(41(04(00(10(31(x1)))))))) | → | 25(12(41(54(05(20(02(40(24(22(32(x1))))))))))) | (1625) |
22(12(11(41(04(00(10(31(x1)))))))) | → | 22(12(41(54(05(20(02(40(24(22(32(x1))))))))))) | (1626) |
24(12(11(41(04(00(10(31(x1)))))))) | → | 24(12(41(54(05(20(02(40(24(22(32(x1))))))))))) | (1627) |
23(12(11(41(04(00(10(31(x1)))))))) | → | 23(12(41(54(05(20(02(40(24(22(32(x1))))))))))) | (1628) |
21(12(11(41(04(00(10(41(x1)))))))) | → | 21(12(41(54(05(20(02(40(24(22(42(x1))))))))))) | (1629) |
20(12(11(41(04(00(10(41(x1)))))))) | → | 20(12(41(54(05(20(02(40(24(22(42(x1))))))))))) | (1630) |
25(12(11(41(04(00(10(41(x1)))))))) | → | 25(12(41(54(05(20(02(40(24(22(42(x1))))))))))) | (1631) |
22(12(11(41(04(00(10(41(x1)))))))) | → | 22(12(41(54(05(20(02(40(24(22(42(x1))))))))))) | (1632) |
24(12(11(41(04(00(10(41(x1)))))))) | → | 24(12(41(54(05(20(02(40(24(22(42(x1))))))))))) | (1633) |
23(12(11(41(04(00(10(41(x1)))))))) | → | 23(12(41(54(05(20(02(40(24(22(42(x1))))))))))) | (1634) |
21(12(11(41(04(00(10(51(x1)))))))) | → | 21(12(41(54(05(20(02(40(24(22(52(x1))))))))))) | (1635) |
20(12(11(41(04(00(10(51(x1)))))))) | → | 20(12(41(54(05(20(02(40(24(22(52(x1))))))))))) | (1636) |
25(12(11(41(04(00(10(51(x1)))))))) | → | 25(12(41(54(05(20(02(40(24(22(52(x1))))))))))) | (1637) |
22(12(11(41(04(00(10(51(x1)))))))) | → | 22(12(41(54(05(20(02(40(24(22(52(x1))))))))))) | (1638) |
24(12(11(41(04(00(10(51(x1)))))))) | → | 24(12(41(54(05(20(02(40(24(22(52(x1))))))))))) | (1639) |
23(12(11(41(04(00(10(51(x1)))))))) | → | 23(12(41(54(05(20(02(40(24(22(52(x1))))))))))) | (1640) |
43(04(10(31(03(00(50(15(x1)))))))) | → | 13(21(42(34(43(34(43(24(12(31(13(x1))))))))))) | (1641) |
43(04(10(31(03(00(50(55(x1)))))))) | → | 13(21(42(34(43(34(43(24(12(31(53(x1))))))))))) | (1642) |
[31(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[35(x1)] | = | 1 · x1 + 1 |
[53(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 + 1 |
[20(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 + 2 |
[00(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 + 1 |
[02(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[50(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
[45(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 + 1 |
[43(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[55(x1)] | = | 1 · x1 |
03(10(01(40(04(00(x1)))))) | → | 53(35(33(13(11(11(11(51(05(20(02(x1))))))))))) | (1579) |
03(10(01(40(04(10(x1)))))) | → | 53(35(33(13(11(11(11(51(05(20(12(x1))))))))))) | (1580) |
03(10(01(40(04(20(x1)))))) | → | 53(35(33(13(11(11(11(51(05(20(22(x1))))))))))) | (1581) |
03(10(01(40(04(30(x1)))))) | → | 53(35(33(13(11(11(11(51(05(20(32(x1))))))))))) | (1582) |
03(10(01(40(04(40(x1)))))) | → | 53(35(33(13(11(11(11(51(05(20(42(x1))))))))))) | (1583) |
03(10(01(40(04(50(x1)))))) | → | 53(35(33(13(11(11(11(51(05(20(52(x1))))))))))) | (1584) |
44(04(50(45(34(03(00(10(x1)))))))) | → | 34(53(35(53(45(54(15(11(21(32(13(x1))))))))))) | (1597) |
44(04(50(45(34(03(00(50(x1)))))))) | → | 34(53(35(53(45(54(15(11(21(32(53(x1))))))))))) | (1598) |
43(04(10(31(03(00(50(15(x1)))))))) | → | 13(21(42(34(43(34(43(24(12(31(13(x1))))))))))) | (1641) |
43(04(10(31(03(00(50(55(x1)))))))) | → | 13(21(42(34(43(34(43(24(12(31(53(x1))))))))))) | (1642) |
[31(x1)] | = | 1 · x1 |
[33(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[35(x1)] | = | 1 · x1 + 1 |
[53(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[30(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[45(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 · x1 |
[50(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
31(33(13(41(54(35(13(x1))))))) | → | 31(33(53(15(11(01(20(42(44(14(x1)))))))))) | (1573) |
30(33(13(41(54(35(13(x1))))))) | → | 30(33(53(15(11(01(20(42(44(14(x1)))))))))) | (1574) |
35(33(13(41(54(35(13(x1))))))) | → | 35(33(53(15(11(01(20(42(44(14(x1)))))))))) | (1575) |
32(33(13(41(54(35(13(x1))))))) | → | 32(33(53(15(11(01(20(42(44(14(x1)))))))))) | (1576) |
34(33(13(41(54(35(13(x1))))))) | → | 34(33(53(15(11(01(20(42(44(14(x1)))))))))) | (1577) |
33(33(13(41(54(35(13(x1))))))) | → | 33(33(53(15(11(01(20(42(44(14(x1)))))))))) | (1578) |
[41(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[45(x1)] | = | 1 · x1 + 1 |
[04(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[34(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[44(x1)] | = | 1 · x1 |
[43(x1)] | = | 1 · x1 |
[50(x1)] | = | 1 · x1 |
[53(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
41(14(51(45(04(00(10(x1))))))) | → | 41(54(05(20(42(14(41(24(42(34(13(x1))))))))))) | (1585) |
40(14(51(45(04(00(10(x1))))))) | → | 40(54(05(20(42(14(41(24(42(34(13(x1))))))))))) | (1586) |
45(14(51(45(04(00(10(x1))))))) | → | 45(54(05(20(42(14(41(24(42(34(13(x1))))))))))) | (1587) |
42(14(51(45(04(00(10(x1))))))) | → | 42(54(05(20(42(14(41(24(42(34(13(x1))))))))))) | (1588) |
44(14(51(45(04(00(10(x1))))))) | → | 44(54(05(20(42(14(41(24(42(34(13(x1))))))))))) | (1589) |
43(14(51(45(04(00(10(x1))))))) | → | 43(54(05(20(42(14(41(24(42(34(13(x1))))))))))) | (1590) |
41(14(51(45(04(00(50(x1))))))) | → | 41(54(05(20(42(14(41(24(42(34(53(x1))))))))))) | (1591) |
40(14(51(45(04(00(50(x1))))))) | → | 40(54(05(20(42(14(41(24(42(34(53(x1))))))))))) | (1592) |
45(14(51(45(04(00(50(x1))))))) | → | 45(54(05(20(42(14(41(24(42(34(53(x1))))))))))) | (1593) |
42(14(51(45(04(00(50(x1))))))) | → | 42(54(05(20(42(14(41(24(42(34(53(x1))))))))))) | (1594) |
44(14(51(45(04(00(50(x1))))))) | → | 44(54(05(20(42(14(41(24(42(34(53(x1))))))))))) | (1595) |
43(14(51(45(04(00(50(x1))))))) | → | 43(54(05(20(42(14(41(24(42(34(53(x1))))))))))) | (1596) |
[11(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 + 1 |
[10(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[50(x1)] | = | 1 · x1 |
[53(x1)] | = | 1 · x1 + 1 |
[21(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
11(01(40(04(20(32(03(10(x1)))))))) | → | 11(31(13(41(24(42(04(00(20(32(13(x1))))))))))) | (1599) |
10(01(40(04(20(32(03(10(x1)))))))) | → | 10(31(13(41(24(42(04(00(20(32(13(x1))))))))))) | (1600) |
15(01(40(04(20(32(03(10(x1)))))))) | → | 15(31(13(41(24(42(04(00(20(32(13(x1))))))))))) | (1601) |
12(01(40(04(20(32(03(10(x1)))))))) | → | 12(31(13(41(24(42(04(00(20(32(13(x1))))))))))) | (1602) |
14(01(40(04(20(32(03(10(x1)))))))) | → | 14(31(13(41(24(42(04(00(20(32(13(x1))))))))))) | (1603) |
13(01(40(04(20(32(03(10(x1)))))))) | → | 13(31(13(41(24(42(04(00(20(32(13(x1))))))))))) | (1604) |
[11(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[03(x1)] | = | 1 · x1 + 1 |
[50(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[13(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[53(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[15(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[14(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
11(01(40(04(20(32(03(50(x1)))))))) | → | 11(31(13(41(24(42(04(00(20(32(53(x1))))))))))) | (1605) |
10(01(40(04(20(32(03(50(x1)))))))) | → | 10(31(13(41(24(42(04(00(20(32(53(x1))))))))))) | (1606) |
15(01(40(04(20(32(03(50(x1)))))))) | → | 15(31(13(41(24(42(04(00(20(32(53(x1))))))))))) | (1607) |
12(01(40(04(20(32(03(50(x1)))))))) | → | 12(31(13(41(24(42(04(00(20(32(53(x1))))))))))) | (1608) |
14(01(40(04(20(32(03(50(x1)))))))) | → | 14(31(13(41(24(42(04(00(20(32(53(x1))))))))))) | (1609) |
13(01(40(04(20(32(03(50(x1)))))))) | → | 13(31(13(41(24(42(04(00(20(32(53(x1))))))))))) | (1610) |
[21(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 + 2 |
[00(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 + 1 |
[25(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 + 1 |
[42(x1)] | = | 1 · x1 + 1 |
[51(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 + 1 |
21(12(11(41(04(00(10(11(x1)))))))) | → | 21(12(41(54(05(20(02(40(24(22(12(x1))))))))))) | (1611) |
20(12(11(41(04(00(10(11(x1)))))))) | → | 20(12(41(54(05(20(02(40(24(22(12(x1))))))))))) | (1612) |
25(12(11(41(04(00(10(11(x1)))))))) | → | 25(12(41(54(05(20(02(40(24(22(12(x1))))))))))) | (1613) |
22(12(11(41(04(00(10(11(x1)))))))) | → | 22(12(41(54(05(20(02(40(24(22(12(x1))))))))))) | (1614) |
24(12(11(41(04(00(10(11(x1)))))))) | → | 24(12(41(54(05(20(02(40(24(22(12(x1))))))))))) | (1615) |
23(12(11(41(04(00(10(11(x1)))))))) | → | 23(12(41(54(05(20(02(40(24(22(12(x1))))))))))) | (1616) |
[21(x1)] | = | 1 · x1 + 1 |
[12(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
21(12(11(41(04(00(10(21(x1)))))))) | → | 21(12(41(54(05(20(02(40(24(22(22(x1))))))))))) | (1617) |
20(12(11(41(04(00(10(21(x1)))))))) | → | 20(12(41(54(05(20(02(40(24(22(22(x1))))))))))) | (1618) |
25(12(11(41(04(00(10(21(x1)))))))) | → | 25(12(41(54(05(20(02(40(24(22(22(x1))))))))))) | (1619) |
22(12(11(41(04(00(10(21(x1)))))))) | → | 22(12(41(54(05(20(02(40(24(22(22(x1))))))))))) | (1620) |
24(12(11(41(04(00(10(21(x1)))))))) | → | 24(12(41(54(05(20(02(40(24(22(22(x1))))))))))) | (1621) |
23(12(11(41(04(00(10(21(x1)))))))) | → | 23(12(41(54(05(20(02(40(24(22(22(x1))))))))))) | (1622) |
[21(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[31(x1)] | = | 1 · x1 + 1 |
[54(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[32(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
21(12(11(41(04(00(10(31(x1)))))))) | → | 21(12(41(54(05(20(02(40(24(22(32(x1))))))))))) | (1623) |
20(12(11(41(04(00(10(31(x1)))))))) | → | 20(12(41(54(05(20(02(40(24(22(32(x1))))))))))) | (1624) |
25(12(11(41(04(00(10(31(x1)))))))) | → | 25(12(41(54(05(20(02(40(24(22(32(x1))))))))))) | (1625) |
22(12(11(41(04(00(10(31(x1)))))))) | → | 22(12(41(54(05(20(02(40(24(22(32(x1))))))))))) | (1626) |
24(12(11(41(04(00(10(31(x1)))))))) | → | 24(12(41(54(05(20(02(40(24(22(32(x1))))))))))) | (1627) |
23(12(11(41(04(00(10(31(x1)))))))) | → | 23(12(41(54(05(20(02(40(24(22(32(x1))))))))))) | (1628) |
[21(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 + 1 |
[04(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[42(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
21(12(11(41(04(00(10(41(x1)))))))) | → | 21(12(41(54(05(20(02(40(24(22(42(x1))))))))))) | (1629) |
20(12(11(41(04(00(10(41(x1)))))))) | → | 20(12(41(54(05(20(02(40(24(22(42(x1))))))))))) | (1630) |
25(12(11(41(04(00(10(41(x1)))))))) | → | 25(12(41(54(05(20(02(40(24(22(42(x1))))))))))) | (1631) |
22(12(11(41(04(00(10(41(x1)))))))) | → | 22(12(41(54(05(20(02(40(24(22(42(x1))))))))))) | (1632) |
24(12(11(41(04(00(10(41(x1)))))))) | → | 24(12(41(54(05(20(02(40(24(22(42(x1))))))))))) | (1633) |
23(12(11(41(04(00(10(41(x1)))))))) | → | 23(12(41(54(05(20(02(40(24(22(42(x1))))))))))) | (1634) |
[21(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[41(x1)] | = | 1 · x1 |
[04(x1)] | = | 1 · x1 + 1 |
[00(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[51(x1)] | = | 1 · x1 |
[54(x1)] | = | 1 · x1 |
[05(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[40(x1)] | = | 1 · x1 |
[24(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[52(x1)] | = | 1 · x1 |
[25(x1)] | = | 1 · x1 |
[23(x1)] | = | 1 · x1 |
21(12(11(41(04(00(10(51(x1)))))))) | → | 21(12(41(54(05(20(02(40(24(22(52(x1))))))))))) | (1635) |
20(12(11(41(04(00(10(51(x1)))))))) | → | 20(12(41(54(05(20(02(40(24(22(52(x1))))))))))) | (1636) |
25(12(11(41(04(00(10(51(x1)))))))) | → | 25(12(41(54(05(20(02(40(24(22(52(x1))))))))))) | (1637) |
22(12(11(41(04(00(10(51(x1)))))))) | → | 22(12(41(54(05(20(02(40(24(22(52(x1))))))))))) | (1638) |
24(12(11(41(04(00(10(51(x1)))))))) | → | 24(12(41(54(05(20(02(40(24(22(52(x1))))))))))) | (1639) |
23(12(11(41(04(00(10(51(x1)))))))) | → | 23(12(41(54(05(20(02(40(24(22(52(x1))))))))))) | (1640) |
There are no rules in the TRS. Hence, it is terminating.