The rewrite relation of the following TRS is considered.
0(0(0(x1))) | → | 0(0(1(0(2(x1))))) | (1) |
0(3(2(x1))) | → | 4(3(0(2(x1)))) | (2) |
0(0(4(2(x1)))) | → | 0(4(1(0(2(x1))))) | (3) |
0(0(5(2(x1)))) | → | 5(0(2(3(0(x1))))) | (4) |
0(1(3(2(x1)))) | → | 0(3(1(0(2(x1))))) | (5) |
0(1(3(2(x1)))) | → | 3(1(1(0(2(x1))))) | (6) |
0(1(3(2(x1)))) | → | 0(1(4(3(1(2(x1)))))) | (7) |
0(4(1(3(x1)))) | → | 1(4(3(0(2(2(x1)))))) | (8) |
0(4(2(3(x1)))) | → | 5(4(3(0(2(x1))))) | (9) |
0(4(5(2(x1)))) | → | 5(0(2(2(4(2(x1)))))) | (10) |
0(5(1(3(x1)))) | → | 3(0(1(5(1(2(x1)))))) | (11) |
0(5(3(0(x1)))) | → | 5(0(1(4(3(0(x1)))))) | (12) |
0(5(3(2(x1)))) | → | 5(1(5(0(2(3(x1)))))) | (13) |
4(0(2(3(x1)))) | → | 3(4(3(0(2(x1))))) | (14) |
4(0(2(3(x1)))) | → | 4(3(5(0(2(x1))))) | (15) |
4(4(1(3(x1)))) | → | 4(3(4(1(2(2(x1)))))) | (16) |
4(5(2(0(x1)))) | → | 4(2(1(5(0(2(x1)))))) | (17) |
4(5(2(0(x1)))) | → | 5(1(0(2(2(4(x1)))))) | (18) |
5(1(0(0(x1)))) | → | 5(1(0(2(0(x1))))) | (19) |
5(1(0(0(x1)))) | → | 5(2(1(0(2(0(x1)))))) | (20) |
5(1(3(0(x1)))) | → | 5(0(2(1(3(x1))))) | (21) |
5(1(3(2(x1)))) | → | 3(0(1(5(1(2(x1)))))) | (22) |
5(1(3(2(x1)))) | → | 3(1(1(5(2(2(x1)))))) | (23) |
5(3(0(0(x1)))) | → | 5(0(4(3(0(2(x1)))))) | (24) |
0(0(4(1(3(x1))))) | → | 4(0(1(0(2(3(x1)))))) | (25) |
0(0(4(5(2(x1))))) | → | 5(0(1(0(2(4(x1)))))) | (26) |
0(0(5(3(2(x1))))) | → | 0(1(5(0(2(3(x1)))))) | (27) |
0(1(0(5(2(x1))))) | → | 1(0(2(5(1(0(x1)))))) | (28) |
0(1(4(5(2(x1))))) | → | 2(1(5(0(2(4(x1)))))) | (29) |
0(3(1(4(0(x1))))) | → | 4(1(0(1(0(3(x1)))))) | (30) |
0(3(2(0(0(x1))))) | → | 0(0(1(0(2(3(x1)))))) | (31) |
0(3(4(0(2(x1))))) | → | 4(3(0(2(1(0(x1)))))) | (32) |
0(3(4(0(2(x1))))) | → | 4(3(0(2(3(0(x1)))))) | (33) |
0(3(4(4(2(x1))))) | → | 4(0(3(4(2(2(x1)))))) | (34) |
0(4(2(5(3(x1))))) | → | 0(4(3(5(1(2(x1)))))) | (35) |
0(5(1(2(0(x1))))) | → | 3(0(1(5(0(2(x1)))))) | (36) |
4(4(2(2(0(x1))))) | → | 4(1(0(2(2(4(x1)))))) | (37) |
4(5(1(2(0(x1))))) | → | 5(0(4(1(2(2(x1)))))) | (38) |
4(5(2(3(2(x1))))) | → | 5(4(3(5(2(2(x1)))))) | (39) |
5(1(0(3(2(x1))))) | → | 5(0(3(1(0(2(x1)))))) | (40) |
5(1(0(5(3(x1))))) | → | 5(5(0(1(3(1(x1)))))) | (41) |
5(1(3(0(0(x1))))) | → | 3(5(0(1(2(0(x1)))))) | (42) |
5(1(3(0(2(x1))))) | → | 3(0(2(1(5(2(x1)))))) | (43) |
5(1(3(0(2(x1))))) | → | 5(0(1(0(3(2(x1)))))) | (44) |
5(1(3(0(2(x1))))) | → | 5(0(1(1(2(3(x1)))))) | (45) |
5(1(3(2(0(x1))))) | → | 5(3(1(5(2(0(x1)))))) | (46) |
5(1(3(2(3(x1))))) | → | 3(4(3(5(1(2(x1)))))) | (47) |
5(1(4(5(2(x1))))) | → | 5(1(4(1(5(2(x1)))))) | (48) |
5(5(1(3(2(x1))))) | → | 3(5(5(4(1(2(x1)))))) | (49) |
{5(☐), 4(☐), 3(☐), 2(☐), 1(☐), 0(☐)}
We obtain the transformed TRSThere are 294 ruless (increase limit for explicit display).
As carrier we take the set {0,...,5}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 6):
[5(x1)] | = | 6x1 + 0 |
[4(x1)] | = | 6x1 + 1 |
[3(x1)] | = | 6x1 + 2 |
[2(x1)] | = | 6x1 + 3 |
[1(x1)] | = | 6x1 + 4 |
[0(x1)] | = | 6x1 + 5 |
There are 1764 ruless (increase limit for explicit display).
[50(x1)] | = |
x1 +
|
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[51(x1)] | = |
x1 +
|
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[52(x1)] | = |
x1 +
|
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[53(x1)] | = |
x1 +
|
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[54(x1)] | = |
x1 +
|
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[55(x1)] | = |
x1 +
|
||||
[40(x1)] | = |
x1 +
|
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[41(x1)] | = |
x1 +
|
||||
[42(x1)] | = |
x1 +
|
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[43(x1)] | = |
x1 +
|
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[44(x1)] | = |
x1 +
|
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[45(x1)] | = |
x1 +
|
||||
[30(x1)] | = |
x1 +
|
||||
[31(x1)] | = |
x1 +
|
||||
[32(x1)] | = |
x1 +
|
||||
[33(x1)] | = |
x1 +
|
||||
[34(x1)] | = |
x1 +
|
||||
[35(x1)] | = |
x1 +
|
||||
[20(x1)] | = |
x1 +
|
||||
[21(x1)] | = |
x1 +
|
||||
[22(x1)] | = |
x1 +
|
||||
[23(x1)] | = |
x1 +
|
||||
[24(x1)] | = |
x1 +
|
||||
[25(x1)] | = |
x1 +
|
||||
[10(x1)] | = |
x1 +
|
||||
[11(x1)] | = |
x1 +
|
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[12(x1)] | = |
x1 +
|
||||
[13(x1)] | = |
x1 +
|
||||
[14(x1)] | = |
x1 +
|
||||
[15(x1)] | = |
x1 +
|
||||
[00(x1)] | = |
x1 +
|
||||
[01(x1)] | = |
x1 +
|
||||
[02(x1)] | = |
x1 +
|
||||
[03(x1)] | = |
x1 +
|
||||
[04(x1)] | = |
x1 +
|
||||
[05(x1)] | = |
x1 +
|
There are 1739 ruless (increase limit for explicit display).
50#(54(12(35(03(x1))))) | → | 50#(55(03(24(12(33(x1)))))) | (2108) |
50#(54(12(35(03(x1))))) | → | 55#(03(24(12(33(x1))))) | (2109) |
55#(04(15(00(53(20(x1)))))) | → | 20#(54(15(00(x1)))) | (2110) |
55#(04(15(00(53(20(x1)))))) | → | 00#(x1) | (2111) |
40#(54(12(35(03(x1))))) | → | 55#(03(24(12(33(x1))))) | (2112) |
40#(54(12(35(03(x1))))) | → | 40#(55(03(24(12(33(x1)))))) | (2113) |
45#(02(31(41(43(20(x1)))))) | → | 45#(02(31(43(23(20(x1)))))) | (2114) |
45#(02(31(41(43(21(x1)))))) | → | 45#(02(31(43(23(21(x1)))))) | (2115) |
45#(02(31(41(43(22(x1)))))) | → | 45#(02(31(43(23(22(x1)))))) | (2116) |
45#(02(31(41(43(23(x1)))))) | → | 45#(02(31(43(23(23(x1)))))) | (2117) |
45#(02(31(41(43(24(x1)))))) | → | 45#(02(31(43(23(24(x1)))))) | (2118) |
45#(02(31(41(43(25(x1)))))) | → | 45#(02(31(43(23(25(x1)))))) | (2119) |
30#(54(12(35(03(x1))))) | → | 55#(03(24(12(33(x1))))) | (2120) |
30#(54(12(35(03(x1))))) | → | 30#(55(03(24(12(33(x1)))))) | (2121) |
20#(54(12(35(03(x1))))) | → | 55#(03(24(12(33(x1))))) | (2122) |
20#(54(12(35(03(x1))))) | → | 20#(55(03(24(12(33(x1)))))) | (2123) |
10#(54(12(33(20(x1))))) | → | 10#(54(13(20(x1)))) | (2124) |
10#(54(12(33(21(x1))))) | → | 10#(54(13(21(x1)))) | (2125) |
10#(54(12(33(22(x1))))) | → | 10#(54(13(22(x1)))) | (2126) |
10#(54(12(33(23(x1))))) | → | 10#(54(13(23(x1)))) | (2127) |
10#(54(12(33(24(x1))))) | → | 10#(54(13(24(x1)))) | (2128) |
10#(54(12(33(25(x1))))) | → | 10#(54(13(25(x1)))) | (2129) |
10#(54(12(35(03(x1))))) | → | 55#(03(24(12(33(x1))))) | (2130) |
10#(54(12(35(03(x1))))) | → | 10#(55(03(24(12(33(x1)))))) | (2131) |
10#(54(12(35(03(20(x1)))))) | → | 10#(53(20(x1))) | (2132) |
10#(54(12(35(03(21(x1)))))) | → | 10#(53(21(x1))) | (2133) |
10#(54(12(35(03(22(x1)))))) | → | 10#(53(22(x1))) | (2134) |
10#(54(12(35(03(23(x1)))))) | → | 10#(53(23(x1))) | (2135) |
10#(54(12(35(03(24(x1)))))) | → | 10#(53(24(x1))) | (2136) |
10#(54(12(35(03(25(x1)))))) | → | 10#(53(25(x1))) | (2137) |
00#(54(12(35(03(x1))))) | → | 55#(03(24(12(33(x1))))) | (2138) |
00#(54(12(35(03(x1))))) | → | 00#(55(03(24(12(33(x1)))))) | (2139) |
[50(x1)] | = |
x1 +
|
||||
[53(x1)] | = |
x1 +
|
||||
[54(x1)] | = |
x1 +
|
||||
[55(x1)] | = |
x1 +
|
||||
[40(x1)] | = |
x1 +
|
||||
[41(x1)] | = |
x1 +
|
||||
[43(x1)] | = |
x1 +
|
||||
[45(x1)] | = |
x1 +
|
||||
[30(x1)] | = |
x1 +
|
||||
[31(x1)] | = |
x1 +
|
||||
[33(x1)] | = |
x1 +
|
||||
[35(x1)] | = |
x1 +
|
||||
[20(x1)] | = |
x1 +
|
||||
[21(x1)] | = |
x1 +
|
||||
[22(x1)] | = |
x1 +
|
||||
[23(x1)] | = |
x1 +
|
||||
[24(x1)] | = |
x1 +
|
||||
[25(x1)] | = |
x1 +
|
||||
[10(x1)] | = |
x1 +
|
||||
[12(x1)] | = |
x1 +
|
||||
[13(x1)] | = |
x1 +
|
||||
[15(x1)] | = |
x1 +
|
||||
[00(x1)] | = |
x1 +
|
||||
[02(x1)] | = |
x1 +
|
||||
[03(x1)] | = |
x1 +
|
||||
[04(x1)] | = |
x1 +
|
||||
[50#(x1)] | = |
x1 +
|
||||
[55#(x1)] | = |
x1 +
|
||||
[40#(x1)] | = |
x1 +
|
||||
[45#(x1)] | = |
x1 +
|
||||
[30#(x1)] | = |
x1 +
|
||||
[20#(x1)] | = |
x1 +
|
||||
[10#(x1)] | = |
x1 +
|
||||
[00#(x1)] | = |
x1 +
|
00(54(12(35(03(x1))))) | → | 00(55(03(24(12(33(x1)))))) | (1066) |
10(54(12(35(03(x1))))) | → | 10(55(03(24(12(33(x1)))))) | (1072) |
20(54(12(35(03(x1))))) | → | 20(55(03(24(12(33(x1)))))) | (1078) |
30(54(12(35(03(x1))))) | → | 30(55(03(24(12(33(x1)))))) | (1084) |
40(54(12(35(03(x1))))) | → | 40(55(03(24(12(33(x1)))))) | (1090) |
50(54(12(35(03(x1))))) | → | 50(55(03(24(12(33(x1)))))) | (1096) |
10(54(12(33(25(x1))))) | → | 12(35(04(10(54(13(25(x1))))))) | (1106) |
10(54(12(33(24(x1))))) | → | 12(35(04(10(54(13(24(x1))))))) | (1107) |
10(54(12(33(23(x1))))) | → | 12(35(04(10(54(13(23(x1))))))) | (1108) |
10(54(12(33(22(x1))))) | → | 12(35(04(10(54(13(22(x1))))))) | (1109) |
10(54(12(33(21(x1))))) | → | 12(35(04(10(54(13(21(x1))))))) | (1110) |
10(54(12(33(20(x1))))) | → | 12(35(04(10(54(13(20(x1))))))) | (1111) |
55(04(15(00(53(20(x1)))))) | → | 54(15(03(20(54(15(00(x1))))))) | (1351) |
45(02(31(41(43(25(x1)))))) | → | 41(45(02(31(43(23(25(x1))))))) | (1556) |
45(02(31(41(43(24(x1)))))) | → | 41(45(02(31(43(23(24(x1))))))) | (1557) |
45(02(31(41(43(23(x1)))))) | → | 41(45(02(31(43(23(23(x1))))))) | (1558) |
45(02(31(41(43(22(x1)))))) | → | 41(45(02(31(43(23(22(x1))))))) | (1559) |
45(02(31(41(43(21(x1)))))) | → | 41(45(02(31(43(23(21(x1))))))) | (1560) |
45(02(31(41(43(20(x1)))))) | → | 41(45(02(31(43(23(20(x1))))))) | (1561) |
10(54(12(35(03(25(x1)))))) | → | 12(35(03(24(10(53(25(x1))))))) | (1862) |
10(54(12(35(03(24(x1)))))) | → | 12(35(03(24(10(53(24(x1))))))) | (1863) |
10(54(12(35(03(23(x1)))))) | → | 12(35(03(24(10(53(23(x1))))))) | (1864) |
10(54(12(35(03(22(x1)))))) | → | 12(35(03(24(10(53(22(x1))))))) | (1865) |
10(54(12(35(03(21(x1)))))) | → | 12(35(03(24(10(53(21(x1))))))) | (1866) |
10(54(12(35(03(20(x1)))))) | → | 12(35(03(24(10(53(20(x1))))))) | (1867) |
50#(54(12(35(03(x1))))) | → | 55#(03(24(12(33(x1))))) | (2109) |
55#(04(15(00(53(20(x1)))))) | → | 20#(54(15(00(x1)))) | (2110) |
55#(04(15(00(53(20(x1)))))) | → | 00#(x1) | (2111) |
40#(54(12(35(03(x1))))) | → | 55#(03(24(12(33(x1))))) | (2112) |
45#(02(31(41(43(20(x1)))))) | → | 45#(02(31(43(23(20(x1)))))) | (2114) |
45#(02(31(41(43(21(x1)))))) | → | 45#(02(31(43(23(21(x1)))))) | (2115) |
45#(02(31(41(43(22(x1)))))) | → | 45#(02(31(43(23(22(x1)))))) | (2116) |
45#(02(31(41(43(23(x1)))))) | → | 45#(02(31(43(23(23(x1)))))) | (2117) |
45#(02(31(41(43(24(x1)))))) | → | 45#(02(31(43(23(24(x1)))))) | (2118) |
45#(02(31(41(43(25(x1)))))) | → | 45#(02(31(43(23(25(x1)))))) | (2119) |
30#(54(12(35(03(x1))))) | → | 55#(03(24(12(33(x1))))) | (2120) |
20#(54(12(35(03(x1))))) | → | 55#(03(24(12(33(x1))))) | (2122) |
10#(54(12(33(20(x1))))) | → | 10#(54(13(20(x1)))) | (2124) |
10#(54(12(33(21(x1))))) | → | 10#(54(13(21(x1)))) | (2125) |
10#(54(12(33(22(x1))))) | → | 10#(54(13(22(x1)))) | (2126) |
10#(54(12(33(23(x1))))) | → | 10#(54(13(23(x1)))) | (2127) |
10#(54(12(33(24(x1))))) | → | 10#(54(13(24(x1)))) | (2128) |
10#(54(12(33(25(x1))))) | → | 10#(54(13(25(x1)))) | (2129) |
10#(54(12(35(03(x1))))) | → | 55#(03(24(12(33(x1))))) | (2130) |
10#(54(12(35(03(20(x1)))))) | → | 10#(53(20(x1))) | (2132) |
10#(54(12(35(03(21(x1)))))) | → | 10#(53(21(x1))) | (2133) |
10#(54(12(35(03(22(x1)))))) | → | 10#(53(22(x1))) | (2134) |
10#(54(12(35(03(23(x1)))))) | → | 10#(53(23(x1))) | (2135) |
10#(54(12(35(03(24(x1)))))) | → | 10#(53(24(x1))) | (2136) |
10#(54(12(35(03(25(x1)))))) | → | 10#(53(25(x1))) | (2137) |
00#(54(12(35(03(x1))))) | → | 55#(03(24(12(33(x1))))) | (2138) |
The dependency pairs are split into 0 components.