The rewrite relation of the following TRS is considered.
3(5(3(x1))) | → | 1(0(3(4(4(3(1(4(5(4(x1)))))))))) | (1) |
5(0(0(x1))) | → | 5(0(3(2(1(2(3(4(0(0(x1)))))))))) | (2) |
0(1(0(4(x1)))) | → | 4(2(1(2(3(4(4(3(0(4(x1)))))))))) | (3) |
4(5(0(4(x1)))) | → | 4(0(4(0(4(0(3(4(4(4(x1)))))))))) | (4) |
5(5(5(5(x1)))) | → | 5(2(0(0(3(2(1(4(4(3(x1)))))))))) | (5) |
5(5(5(5(x1)))) | → | 5(4(0(0(1(1(1(4(3(5(x1)))))))))) | (6) |
1(5(3(1(3(x1))))) | → | 1(3(4(4(2(0(2(3(1(2(x1)))))))))) | (7) |
2(3(5(5(0(x1))))) | → | 4(0(1(4(2(1(2(0(1(0(x1)))))))))) | (8) |
2(5(5(5(5(x1))))) | → | 2(0(5(1(2(0(3(2(1(5(x1)))))))))) | (9) |
4(1(0(0(0(x1))))) | → | 4(1(4(1(0(5(1(2(4(2(x1)))))))))) | (10) |
4(1(5(5(3(x1))))) | → | 2(1(2(3(0(3(2(5(1(2(x1)))))))))) | (11) |
4(3(1(5(5(x1))))) | → | 4(0(3(1(2(3(2(1(1(5(x1)))))))))) | (12) |
5(0(2(4(2(x1))))) | → | 5(2(1(2(3(0(0(3(4(2(x1)))))))))) | (13) |
5(3(1(5(1(x1))))) | → | 3(2(1(1(0(3(0(1(5(1(x1)))))))))) | (14) |
5(5(3(0(2(x1))))) | → | 3(2(3(4(5(2(1(2(0(0(x1)))))))))) | (15) |
5(5(5(5(4(x1))))) | → | 3(4(5(4(0(0(4(0(3(4(x1)))))))))) | (16) |
0(1(5(1(0(4(x1)))))) | → | 3(2(0(4(0(1(4(3(0(4(x1)))))))))) | (17) |
0(1(5(1(5(0(x1)))))) | → | 4(4(4(2(5(5(0(1(4(0(x1)))))))))) | (18) |
0(1(5(3(0(1(x1)))))) | → | 4(4(5(1(1(1(4(0(3(1(x1)))))))))) | (19) |
0(3(1(3(0(5(x1)))))) | → | 4(4(3(3(4(4(0(5(2(3(x1)))))))))) | (20) |
1(5(5(5(5(3(x1)))))) | → | 1(2(5(1(4(0(0(2(5(4(x1)))))))))) | (21) |
2(0(5(3(4(1(x1)))))) | → | 2(3(4(0(3(3(0(1(2(1(x1)))))))))) | (22) |
2(4(0(1(3(5(x1)))))) | → | 2(3(2(0(2(0(3(1(4(3(x1)))))))))) | (23) |
2(5(4(5(5(5(x1)))))) | → | 2(4(2(1(2(4(4(4(0(5(x1)))))))))) | (24) |
3(5(3(1(5(5(x1)))))) | → | 3(2(4(4(1(1(4(0(2(4(x1)))))))))) | (25) |
4(1(3(1(5(0(x1)))))) | → | 0(2(2(2(1(1(2(3(1(4(x1)))))))))) | (26) |
4(3(5(0(4(2(x1)))))) | → | 4(3(4(3(4(1(3(1(4(2(x1)))))))))) | (27) |
5(0(5(0(4(2(x1)))))) | → | 5(4(4(4(4(0(4(4(3(0(x1)))))))))) | (28) |
5(5(1(5(3(0(x1)))))) | → | 2(2(0(1(4(3(0(3(3(4(x1)))))))))) | (29) |
5(5(3(2(3(5(x1)))))) | → | 1(4(2(4(1(2(2(4(1(5(x1)))))))))) | (30) |
5(5(5(1(3(1(x1)))))) | → | 5(1(2(4(4(4(1(3(3(4(x1)))))))))) | (31) |
1(0(4(5(3(5(0(x1))))))) | → | 1(0(2(1(2(5(2(0(5(2(x1)))))))))) | (32) |
1(5(1(3(5(5(5(x1))))))) | → | 5(1(2(3(0(2(2(0(5(5(x1)))))))))) | (33) |
3(0(1(5(1(3(0(x1))))))) | → | 3(0(0(3(1(2(1(5(4(2(x1)))))))))) | (34) |
3(2(4(1(5(5(1(x1))))))) | → | 0(5(0(3(4(1(0(3(5(1(x1)))))))))) | (35) |
3(5(5(5(1(4(1(x1))))))) | → | 1(4(4(0(0(1(0(1(3(1(x1)))))))))) | (36) |
4(0(5(5(5(5(4(x1))))))) | → | 2(1(4(3(5(4(0(1(5(4(x1)))))))))) | (37) |
4(1(5(0(0(1(3(x1))))))) | → | 0(2(1(1(1(1(4(5(1(3(x1)))))))))) | (38) |
4(1(5(0(0(1(5(x1))))))) | → | 4(3(0(5(3(5(2(1(4(5(x1)))))))))) | (39) |
4(2(3(5(0(5(0(x1))))))) | → | 4(4(4(0(0(1(5(2(3(4(x1)))))))))) | (40) |
4(2(5(5(0(2(2(x1))))))) | → | 4(2(1(0(0(1(4(5(1(2(x1)))))))))) | (41) |
4(5(5(3(5(5(3(x1))))))) | → | 0(1(4(0(1(3(2(4(1(4(x1)))))))))) | (42) |
4(5(5(5(0(4(3(x1))))))) | → | 0(3(3(3(2(0(2(3(2(3(x1)))))))))) | (43) |
5(0(5(5(3(5(4(x1))))))) | → | 5(3(5(5(0(1(1(2(3(4(x1)))))))))) | (44) |
5(2(5(5(0(0(3(x1))))))) | → | 1(4(4(3(1(0(1(3(0(3(x1)))))))))) | (45) |
5(3(5(5(5(3(0(x1))))))) | → | 5(4(3(4(5(2(5(5(5(0(x1)))))))))) | (46) |
5(4(5(3(2(5(3(x1))))))) | → | 5(4(3(1(1(4(2(0(3(5(x1)))))))))) | (47) |
5(5(0(5(5(0(1(x1))))))) | → | 2(3(4(5(4(2(1(2(5(1(x1)))))))))) | (48) |
5(5(0(5(5(5(3(x1))))))) | → | 5(0(4(4(0(1(2(3(3(3(x1)))))))))) | (49) |
5(5(2(5(3(5(0(x1))))))) | → | 5(2(0(4(0(3(2(3(3(0(x1)))))))))) | (50) |
5(5(5(3(0(4(2(x1))))))) | → | 5(5(2(1(5(4(3(4(4(2(x1)))))))))) | (51) |
{5(☐), 4(☐), 3(☐), 2(☐), 1(☐), 0(☐)}
We obtain the transformed TRSThere are 306 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 1836 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 +
|
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[40(x1)] | = |
x1 +
|
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[41(x1)] | = |
x1 +
|
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[42(x1)] | = |
x1 +
|
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[43(x1)] | = |
x1 +
|
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[44(x1)] | = |
x1 +
|
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[45(x1)] | = |
x1 +
|
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[30(x1)] | = |
x1 +
|
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[31(x1)] | = |
x1 +
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[32(x1)] | = |
x1 +
|
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[33(x1)] | = |
x1 +
|
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[34(x1)] | = |
x1 +
|
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[35(x1)] | = |
x1 +
|
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[20(x1)] | = |
x1 +
|
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[21(x1)] | = |
x1 +
|
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[22(x1)] | = |
x1 +
|
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[23(x1)] | = |
x1 +
|
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[24(x1)] | = |
x1 +
|
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[25(x1)] | = |
x1 +
|
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[10(x1)] | = |
x1 +
|
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[11(x1)] | = |
x1 +
|
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[12(x1)] | = |
x1 +
|
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[13(x1)] | = |
x1 +
|
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[14(x1)] | = |
x1 +
|
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[15(x1)] | = |
x1 +
|
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[00(x1)] | = |
x1 +
|
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[01(x1)] | = |
x1 +
|
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[02(x1)] | = |
x1 +
|
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[03(x1)] | = |
x1 +
|
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[04(x1)] | = |
x1 +
|
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[05(x1)] | = |
x1 +
|
There are 1800 ruless (increase limit for explicit display).
50#(55(05(00(x1)))) | → | 50#(55(02(33(24(13(22(31(45(05(00(x1))))))))))) | (2194) |
50#(55(05(01(x1)))) | → | 50#(55(02(33(24(13(22(31(45(05(01(x1))))))))))) | (2195) |
50#(55(05(02(x1)))) | → | 50#(55(02(33(24(13(22(31(45(05(02(x1))))))))))) | (2196) |
50#(55(05(03(x1)))) | → | 50#(55(02(33(24(13(22(31(45(05(03(x1))))))))))) | (2197) |
50#(55(05(04(x1)))) | → | 50#(55(02(33(24(13(22(31(45(05(04(x1))))))))))) | (2198) |
50#(55(05(05(x1)))) | → | 50#(55(02(33(24(13(22(31(45(05(05(x1))))))))))) | (2199) |
40#(55(05(00(x1)))) | → | 40#(55(02(33(24(13(22(31(45(05(00(x1))))))))))) | (2200) |
40#(55(05(01(x1)))) | → | 40#(55(02(33(24(13(22(31(45(05(01(x1))))))))))) | (2201) |
40#(55(05(02(x1)))) | → | 40#(55(02(33(24(13(22(31(45(05(02(x1))))))))))) | (2202) |
40#(55(05(03(x1)))) | → | 40#(55(02(33(24(13(22(31(45(05(03(x1))))))))))) | (2203) |
40#(55(05(04(x1)))) | → | 40#(55(02(33(24(13(22(31(45(05(04(x1))))))))))) | (2204) |
40#(55(05(05(x1)))) | → | 40#(55(02(33(24(13(22(31(45(05(05(x1))))))))))) | (2205) |
30#(55(05(00(x1)))) | → | 30#(55(02(33(24(13(22(31(45(05(00(x1))))))))))) | (2206) |
30#(55(05(01(x1)))) | → | 30#(55(02(33(24(13(22(31(45(05(01(x1))))))))))) | (2207) |
30#(55(05(02(x1)))) | → | 30#(55(02(33(24(13(22(31(45(05(02(x1))))))))))) | (2208) |
30#(55(05(03(x1)))) | → | 30#(55(02(33(24(13(22(31(45(05(03(x1))))))))))) | (2209) |
30#(55(05(04(x1)))) | → | 30#(55(02(33(24(13(22(31(45(05(04(x1))))))))))) | (2210) |
30#(55(05(05(x1)))) | → | 30#(55(02(33(24(13(22(31(45(05(05(x1))))))))))) | (2211) |
20#(55(05(00(x1)))) | → | 20#(55(02(33(24(13(22(31(45(05(00(x1))))))))))) | (2212) |
20#(55(05(01(x1)))) | → | 20#(55(02(33(24(13(22(31(45(05(01(x1))))))))))) | (2213) |
20#(55(05(02(x1)))) | → | 20#(55(02(33(24(13(22(31(45(05(02(x1))))))))))) | (2214) |
20#(55(05(03(x1)))) | → | 20#(55(02(33(24(13(22(31(45(05(03(x1))))))))))) | (2215) |
20#(55(05(04(x1)))) | → | 20#(55(02(33(24(13(22(31(45(05(04(x1))))))))))) | (2216) |
20#(55(05(05(x1)))) | → | 20#(55(02(33(24(13(22(31(45(05(05(x1))))))))))) | (2217) |
10#(55(05(00(x1)))) | → | 10#(55(02(33(24(13(22(31(45(05(00(x1))))))))))) | (2218) |
10#(55(05(01(x1)))) | → | 10#(55(02(33(24(13(22(31(45(05(01(x1))))))))))) | (2219) |
10#(55(05(02(x1)))) | → | 10#(55(02(33(24(13(22(31(45(05(02(x1))))))))))) | (2220) |
10#(55(05(03(x1)))) | → | 10#(55(02(33(24(13(22(31(45(05(03(x1))))))))))) | (2221) |
10#(55(05(04(x1)))) | → | 10#(55(02(33(24(13(22(31(45(05(04(x1))))))))))) | (2222) |
10#(55(05(05(x1)))) | → | 10#(55(02(33(24(13(22(31(45(05(05(x1))))))))))) | (2223) |
00#(55(05(00(x1)))) | → | 00#(55(02(33(24(13(22(31(45(05(00(x1))))))))))) | (2224) |
00#(55(05(01(x1)))) | → | 00#(55(02(33(24(13(22(31(45(05(01(x1))))))))))) | (2225) |
00#(55(05(02(x1)))) | → | 00#(55(02(33(24(13(22(31(45(05(02(x1))))))))))) | (2226) |
00#(55(05(03(x1)))) | → | 00#(55(02(33(24(13(22(31(45(05(03(x1))))))))))) | (2227) |
00#(55(05(04(x1)))) | → | 00#(55(02(33(24(13(22(31(45(05(04(x1))))))))))) | (2228) |
00#(55(05(05(x1)))) | → | 00#(55(02(33(24(13(22(31(45(05(05(x1))))))))))) | (2229) |
The dependency pairs are split into 0 components.