Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/96438)

The rewrite relation of the following TRS is considered.

0(1(2(3(x1)))) 1(4(3(x1))) (1)
1(2(0(4(2(x1))))) 3(4(5(4(x1)))) (2)
3(3(0(3(2(x1))))) 3(2(4(1(x1)))) (3)
5(2(1(0(4(x1))))) 5(5(4(5(x1)))) (4)
0(1(4(5(0(5(x1)))))) 3(0(4(0(3(5(x1)))))) (5)
0(2(5(2(1(5(x1)))))) 5(2(1(5(4(x1))))) (6)
0(3(5(1(5(5(x1)))))) 0(5(1(5(4(x1))))) (7)
2(2(5(1(4(5(4(3(x1)))))))) 2(2(3(3(0(1(0(3(x1)))))))) (8)
0(0(0(2(4(1(2(2(4(x1))))))))) 0(0(0(4(3(3(4(4(x1)))))))) (9)
2(4(4(3(4(2(0(3(2(x1))))))))) 3(4(3(4(1(3(3(1(x1)))))))) (10)
0(1(4(3(2(3(2(3(5(3(x1)))))))))) 1(4(3(0(3(4(2(5(3(x1))))))))) (11)
0(2(1(5(0(4(3(1(4(2(2(x1))))))))))) 0(0(4(0(5(1(0(5(4(4(2(x1))))))))))) (12)
4(4(3(3(0(2(4(2(4(4(1(5(x1)))))))))))) 4(4(0(4(3(1(5(5(5(2(5(x1))))))))))) (13)
5(3(0(0(5(5(2(0(2(2(3(3(x1)))))))))))) 5(5(4(1(5(2(0(5(2(4(3(x1))))))))))) (14)
0(2(0(2(5(5(1(5(0(2(5(2(2(x1))))))))))))) 5(4(3(1(4(0(1(0(1(5(2(x1))))))))))) (15)
0(3(1(4(4(2(0(5(4(0(1(0(4(x1))))))))))))) 0(0(4(4(1(0(4(0(0(2(2(4(4(x1))))))))))))) (16)
1(2(4(1(1(0(2(5(3(4(0(1(4(0(3(x1))))))))))))))) 1(1(0(4(5(0(3(2(0(5(2(0(0(3(3(x1))))))))))))))) (17)
2(3(5(2(4(4(5(1(4(4(4(1(3(2(3(x1))))))))))))))) 2(3(3(1(1(1(5(3(3(5(1(3(5(2(3(x1))))))))))))))) (18)
5(4(2(5(2(5(3(2(3(3(1(5(0(0(5(x1))))))))))))))) 5(2(3(5(4(1(3(1(4(4(4(4(1(3(5(x1))))))))))))))) (19)
0(0(2(4(1(2(2(1(3(2(0(4(5(5(4(2(x1)))))))))))))))) 0(5(1(1(0(2(3(5(4(3(0(2(5(2(3(5(1(x1))))))))))))))))) (20)
0(1(1(5(3(0(1(4(2(2(4(0(1(0(2(3(4(x1))))))))))))))))) 0(4(2(2(0(1(5(4(4(0(2(2(2(5(5(4(x1)))))))))))))))) (21)
0(2(3(2(5(2(4(3(2(4(3(0(2(4(5(1(3(x1))))))))))))))))) 3(4(3(5(2(5(3(1(5(0(1(0(5(5(2(3(x1)))))))))))))))) (22)
4(5(4(5(4(2(1(4(5(0(2(0(4(3(0(0(1(0(0(2(x1)))))))))))))))))))) 4(4(2(2(5(2(0(0(0(5(3(4(1(2(2(1(1(5(0(0(x1)))))))))))))))))))) (23)
3(0(1(0(5(2(4(4(4(5(2(4(1(1(4(5(4(0(3(2(1(x1))))))))))))))))))))) 3(4(2(0(4(5(2(2(2(3(3(3(5(0(5(5(3(2(1(1(4(x1))))))))))))))))))))) (24)
3(3(2(1(0(0(3(1(2(0(2(1(2(3(5(4(0(2(2(1(1(x1))))))))))))))))))))) 3(4(5(2(4(3(4(3(5(3(4(5(4(2(5(5(1(0(1(x1))))))))))))))))))) (25)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
3(2(1(0(x1)))) 3(4(1(x1))) (26)
2(4(0(2(1(x1))))) 4(5(4(3(x1)))) (27)
2(3(0(3(3(x1))))) 1(4(2(3(x1)))) (28)
4(0(1(2(5(x1))))) 5(4(5(5(x1)))) (29)
5(0(5(4(1(0(x1)))))) 5(3(0(4(0(3(x1)))))) (30)
5(1(2(5(2(0(x1)))))) 4(5(1(2(5(x1))))) (31)
5(5(1(5(3(0(x1)))))) 4(5(1(5(0(x1))))) (32)
3(4(5(4(1(5(2(2(x1)))))))) 3(0(1(0(3(3(2(2(x1)))))))) (33)
4(2(2(1(4(2(0(0(0(x1))))))))) 4(4(3(3(4(0(0(0(x1)))))))) (34)
2(3(0(2(4(3(4(4(2(x1))))))))) 1(3(3(1(4(3(4(3(x1)))))))) (35)
3(5(3(2(3(2(3(4(1(0(x1)))))))))) 3(5(2(4(3(0(3(4(1(x1))))))))) (36)
2(2(4(1(3(4(0(5(1(2(0(x1))))))))))) 2(4(4(5(0(1(5(0(4(0(0(x1))))))))))) (37)
5(1(4(4(2(4(2(0(3(3(4(4(x1)))))))))))) 5(2(5(5(5(1(3(4(0(4(4(x1))))))))))) (38)
3(3(2(2(0(2(5(5(0(0(3(5(x1)))))))))))) 3(4(2(5(0(2(5(1(4(5(5(x1))))))))))) (39)
2(2(5(2(0(5(1(5(5(2(0(2(0(x1))))))))))))) 2(5(1(0(1(0(4(1(3(4(5(x1))))))))))) (40)
4(0(1(0(4(5(0(2(4(4(1(3(0(x1))))))))))))) 4(4(2(2(0(0(4(0(1(4(4(0(0(x1))))))))))))) (41)
3(0(4(1(0(4(3(5(2(0(1(1(4(2(1(x1))))))))))))))) 3(3(0(0(2(5(0(2(3(0(5(4(0(1(1(x1))))))))))))))) (42)
3(2(3(1(4(4(4(1(5(4(4(2(5(3(2(x1))))))))))))))) 3(2(5(3(1(5(3(3(5(1(1(1(3(3(2(x1))))))))))))))) (43)
5(0(0(5(1(3(3(2(3(5(2(5(2(4(5(x1))))))))))))))) 5(3(1(4(4(4(4(1(3(1(4(5(3(2(5(x1))))))))))))))) (44)
2(4(5(5(4(0(2(3(1(2(2(1(4(2(0(0(x1)))))))))))))))) 1(5(3(2(5(2(0(3(4(5(3(2(0(1(1(5(0(x1))))))))))))))))) (45)
4(3(2(0(1(0(4(2(2(4(1(0(3(5(1(1(0(x1))))))))))))))))) 4(5(5(2(2(2(0(4(4(5(1(0(2(2(4(0(x1)))))))))))))))) (46)
3(1(5(4(2(0(3(4(2(3(4(2(5(2(3(2(0(x1))))))))))))))))) 3(2(5(5(0(1(0(5(1(3(5(2(5(3(4(3(x1)))))))))))))))) (47)
2(0(0(1(0(0(3(4(0(2(0(5(4(1(2(4(5(4(5(4(x1)))))))))))))))))))) 0(0(5(1(1(2(2(1(4(3(5(0(0(0(2(5(2(2(4(4(x1)))))))))))))))))))) (48)
1(2(3(0(4(5(4(1(1(4(2(5(4(4(4(2(5(0(1(0(3(x1))))))))))))))))))))) 4(1(1(2(3(5(5(0(5(3(3(3(2(2(2(5(4(0(2(4(3(x1))))))))))))))))))))) (49)
1(1(2(2(0(4(5(3(2(1(2(0(2(1(3(0(0(1(2(3(3(x1))))))))))))))))))))) 1(0(1(5(5(2(4(5(4(3(5(3(4(3(4(2(5(4(3(x1))))))))))))))))))) (50)

1.1 Closure Under Flat Contexts

Using the flat contexts

{3(), 2(), 1(), 0(), 4(), 5()}

We obtain the transformed TRS
3(2(1(0(x1)))) 3(4(1(x1))) (26)
5(0(5(4(1(0(x1)))))) 5(3(0(4(0(3(x1)))))) (30)
3(4(5(4(1(5(2(2(x1)))))))) 3(0(1(0(3(3(2(2(x1)))))))) (33)
4(2(2(1(4(2(0(0(0(x1))))))))) 4(4(3(3(4(0(0(0(x1)))))))) (34)
3(5(3(2(3(2(3(4(1(0(x1)))))))))) 3(5(2(4(3(0(3(4(1(x1))))))))) (36)
2(2(4(1(3(4(0(5(1(2(0(x1))))))))))) 2(4(4(5(0(1(5(0(4(0(0(x1))))))))))) (37)
5(1(4(4(2(4(2(0(3(3(4(4(x1)))))))))))) 5(2(5(5(5(1(3(4(0(4(4(x1))))))))))) (38)
3(3(2(2(0(2(5(5(0(0(3(5(x1)))))))))))) 3(4(2(5(0(2(5(1(4(5(5(x1))))))))))) (39)
2(2(5(2(0(5(1(5(5(2(0(2(0(x1))))))))))))) 2(5(1(0(1(0(4(1(3(4(5(x1))))))))))) (40)
4(0(1(0(4(5(0(2(4(4(1(3(0(x1))))))))))))) 4(4(2(2(0(0(4(0(1(4(4(0(0(x1))))))))))))) (41)
3(0(4(1(0(4(3(5(2(0(1(1(4(2(1(x1))))))))))))))) 3(3(0(0(2(5(0(2(3(0(5(4(0(1(1(x1))))))))))))))) (42)
3(2(3(1(4(4(4(1(5(4(4(2(5(3(2(x1))))))))))))))) 3(2(5(3(1(5(3(3(5(1(1(1(3(3(2(x1))))))))))))))) (43)
5(0(0(5(1(3(3(2(3(5(2(5(2(4(5(x1))))))))))))))) 5(3(1(4(4(4(4(1(3(1(4(5(3(2(5(x1))))))))))))))) (44)
4(3(2(0(1(0(4(2(2(4(1(0(3(5(1(1(0(x1))))))))))))))))) 4(5(5(2(2(2(0(4(4(5(1(0(2(2(4(0(x1)))))))))))))))) (46)
3(1(5(4(2(0(3(4(2(3(4(2(5(2(3(2(0(x1))))))))))))))))) 3(2(5(5(0(1(0(5(1(3(5(2(5(3(4(3(x1)))))))))))))))) (47)
1(1(2(2(0(4(5(3(2(1(2(0(2(1(3(0(0(1(2(3(3(x1))))))))))))))))))))) 1(0(1(5(5(2(4(5(4(3(5(3(4(3(4(2(5(4(3(x1))))))))))))))))))) (50)
3(2(4(0(2(1(x1)))))) 3(4(5(4(3(x1))))) (51)
2(2(4(0(2(1(x1)))))) 2(4(5(4(3(x1))))) (52)
1(2(4(0(2(1(x1)))))) 1(4(5(4(3(x1))))) (53)
0(2(4(0(2(1(x1)))))) 0(4(5(4(3(x1))))) (54)
4(2(4(0(2(1(x1)))))) 4(4(5(4(3(x1))))) (55)
5(2(4(0(2(1(x1)))))) 5(4(5(4(3(x1))))) (56)
3(2(3(0(3(3(x1)))))) 3(1(4(2(3(x1))))) (57)
2(2(3(0(3(3(x1)))))) 2(1(4(2(3(x1))))) (58)
1(2(3(0(3(3(x1)))))) 1(1(4(2(3(x1))))) (59)
0(2(3(0(3(3(x1)))))) 0(1(4(2(3(x1))))) (60)
4(2(3(0(3(3(x1)))))) 4(1(4(2(3(x1))))) (61)
5(2(3(0(3(3(x1)))))) 5(1(4(2(3(x1))))) (62)
3(4(0(1(2(5(x1)))))) 3(5(4(5(5(x1))))) (63)
2(4(0(1(2(5(x1)))))) 2(5(4(5(5(x1))))) (64)
1(4(0(1(2(5(x1)))))) 1(5(4(5(5(x1))))) (65)
0(4(0(1(2(5(x1)))))) 0(5(4(5(5(x1))))) (66)
4(4(0(1(2(5(x1)))))) 4(5(4(5(5(x1))))) (67)
5(4(0(1(2(5(x1)))))) 5(5(4(5(5(x1))))) (68)
3(5(1(2(5(2(0(x1))))))) 3(4(5(1(2(5(x1)))))) (69)
2(5(1(2(5(2(0(x1))))))) 2(4(5(1(2(5(x1)))))) (70)
1(5(1(2(5(2(0(x1))))))) 1(4(5(1(2(5(x1)))))) (71)
0(5(1(2(5(2(0(x1))))))) 0(4(5(1(2(5(x1)))))) (72)
4(5(1(2(5(2(0(x1))))))) 4(4(5(1(2(5(x1)))))) (73)
5(5(1(2(5(2(0(x1))))))) 5(4(5(1(2(5(x1)))))) (74)
3(5(5(1(5(3(0(x1))))))) 3(4(5(1(5(0(x1)))))) (75)
2(5(5(1(5(3(0(x1))))))) 2(4(5(1(5(0(x1)))))) (76)
1(5(5(1(5(3(0(x1))))))) 1(4(5(1(5(0(x1)))))) (77)
0(5(5(1(5(3(0(x1))))))) 0(4(5(1(5(0(x1)))))) (78)
4(5(5(1(5(3(0(x1))))))) 4(4(5(1(5(0(x1)))))) (79)
5(5(5(1(5(3(0(x1))))))) 5(4(5(1(5(0(x1)))))) (80)
3(2(3(0(2(4(3(4(4(2(x1)))))))))) 3(1(3(3(1(4(3(4(3(x1))))))))) (81)
2(2(3(0(2(4(3(4(4(2(x1)))))))))) 2(1(3(3(1(4(3(4(3(x1))))))))) (82)
1(2(3(0(2(4(3(4(4(2(x1)))))))))) 1(1(3(3(1(4(3(4(3(x1))))))))) (83)
0(2(3(0(2(4(3(4(4(2(x1)))))))))) 0(1(3(3(1(4(3(4(3(x1))))))))) (84)
4(2(3(0(2(4(3(4(4(2(x1)))))))))) 4(1(3(3(1(4(3(4(3(x1))))))))) (85)
5(2(3(0(2(4(3(4(4(2(x1)))))))))) 5(1(3(3(1(4(3(4(3(x1))))))))) (86)
3(2(4(5(5(4(0(2(3(1(2(2(1(4(2(0(0(x1))))))))))))))))) 3(1(5(3(2(5(2(0(3(4(5(3(2(0(1(1(5(0(x1)))))))))))))))))) (87)
2(2(4(5(5(4(0(2(3(1(2(2(1(4(2(0(0(x1))))))))))))))))) 2(1(5(3(2(5(2(0(3(4(5(3(2(0(1(1(5(0(x1)))))))))))))))))) (88)
1(2(4(5(5(4(0(2(3(1(2(2(1(4(2(0(0(x1))))))))))))))))) 1(1(5(3(2(5(2(0(3(4(5(3(2(0(1(1(5(0(x1)))))))))))))))))) (89)
0(2(4(5(5(4(0(2(3(1(2(2(1(4(2(0(0(x1))))))))))))))))) 0(1(5(3(2(5(2(0(3(4(5(3(2(0(1(1(5(0(x1)))))))))))))))))) (90)
4(2(4(5(5(4(0(2(3(1(2(2(1(4(2(0(0(x1))))))))))))))))) 4(1(5(3(2(5(2(0(3(4(5(3(2(0(1(1(5(0(x1)))))))))))))))))) (91)
5(2(4(5(5(4(0(2(3(1(2(2(1(4(2(0(0(x1))))))))))))))))) 5(1(5(3(2(5(2(0(3(4(5(3(2(0(1(1(5(0(x1)))))))))))))))))) (92)
3(2(0(0(1(0(0(3(4(0(2(0(5(4(1(2(4(5(4(5(4(x1))))))))))))))))))))) 3(0(0(5(1(1(2(2(1(4(3(5(0(0(0(2(5(2(2(4(4(x1))))))))))))))))))))) (93)
2(2(0(0(1(0(0(3(4(0(2(0(5(4(1(2(4(5(4(5(4(x1))))))))))))))))))))) 2(0(0(5(1(1(2(2(1(4(3(5(0(0(0(2(5(2(2(4(4(x1))))))))))))))))))))) (94)
1(2(0(0(1(0(0(3(4(0(2(0(5(4(1(2(4(5(4(5(4(x1))))))))))))))))))))) 1(0(0(5(1(1(2(2(1(4(3(5(0(0(0(2(5(2(2(4(4(x1))))))))))))))))))))) (95)
0(2(0(0(1(0(0(3(4(0(2(0(5(4(1(2(4(5(4(5(4(x1))))))))))))))))))))) 0(0(0(5(1(1(2(2(1(4(3(5(0(0(0(2(5(2(2(4(4(x1))))))))))))))))))))) (96)
4(2(0(0(1(0(0(3(4(0(2(0(5(4(1(2(4(5(4(5(4(x1))))))))))))))))))))) 4(0(0(5(1(1(2(2(1(4(3(5(0(0(0(2(5(2(2(4(4(x1))))))))))))))))))))) (97)
5(2(0(0(1(0(0(3(4(0(2(0(5(4(1(2(4(5(4(5(4(x1))))))))))))))))))))) 5(0(0(5(1(1(2(2(1(4(3(5(0(0(0(2(5(2(2(4(4(x1))))))))))))))))))))) (98)
3(1(2(3(0(4(5(4(1(1(4(2(5(4(4(4(2(5(0(1(0(3(x1)))))))))))))))))))))) 3(4(1(1(2(3(5(5(0(5(3(3(3(2(2(2(5(4(0(2(4(3(x1)))))))))))))))))))))) (99)
2(1(2(3(0(4(5(4(1(1(4(2(5(4(4(4(2(5(0(1(0(3(x1)))))))))))))))))))))) 2(4(1(1(2(3(5(5(0(5(3(3(3(2(2(2(5(4(0(2(4(3(x1)))))))))))))))))))))) (100)
1(1(2(3(0(4(5(4(1(1(4(2(5(4(4(4(2(5(0(1(0(3(x1)))))))))))))))))))))) 1(4(1(1(2(3(5(5(0(5(3(3(3(2(2(2(5(4(0(2(4(3(x1)))))))))))))))))))))) (101)
0(1(2(3(0(4(5(4(1(1(4(2(5(4(4(4(2(5(0(1(0(3(x1)))))))))))))))))))))) 0(4(1(1(2(3(5(5(0(5(3(3(3(2(2(2(5(4(0(2(4(3(x1)))))))))))))))))))))) (102)
4(1(2(3(0(4(5(4(1(1(4(2(5(4(4(4(2(5(0(1(0(3(x1)))))))))))))))))))))) 4(4(1(1(2(3(5(5(0(5(3(3(3(2(2(2(5(4(0(2(4(3(x1)))))))))))))))))))))) (103)
5(1(2(3(0(4(5(4(1(1(4(2(5(4(4(4(2(5(0(1(0(3(x1)))))))))))))))))))))) 5(4(1(1(2(3(5(5(0(5(3(3(3(2(2(2(5(4(0(2(4(3(x1)))))))))))))))))))))) (104)

1.1.1 Semantic Labeling

Root-labeling is applied.

We obtain the labeled TRS

There are 420 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[32(x1)] = 1 · x1 + 1340
[21(x1)] = 1 · x1 + 280
[10(x1)] = 1 · x1 + 2617
[03(x1)] = 1 · x1 + 1447
[34(x1)] = 1 · x1 + 46
[41(x1)] = 1 · x1 + 1663
[13(x1)] = 1 · x1 + 2706
[02(x1)] = 1 · x1 + 1323
[12(x1)] = 1 · x1 + 3071
[01(x1)] = 1 · x1
[11(x1)] = 1 · x1 + 1748
[00(x1)] = 1 · x1 + 869
[04(x1)] = 1 · x1 + 29
[14(x1)] = 1 · x1 + 1777
[05(x1)] = 1 · x1 + 1641
[15(x1)] = 1 · x1 + 4167
[50(x1)] = 1 · x1 + 949
[54(x1)] = 1 · x1 + 109
[53(x1)] = 1 · x1 + 34
[30(x1)] = 1 · x1 + 886
[40(x1)] = 1 · x1 + 2532
[33(x1)] = 1 · x1 + 2622
[31(x1)] = 1 · x1 + 17
[35(x1)] = 1 · x1 + 1658
[45(x1)] = 1 · x1 + 3304
[52(x1)] = 1 · x1 + 1403
[22(x1)] = 1 · x1 + 1603
[23(x1)] = 1 · x1 + 1825
[20(x1)] = 1 · x1 + 1149
[24(x1)] = 1 · x1 + 309
[25(x1)] = 1 · x1 + 1921
[42(x1)] = 1 · x1 + 2986
[44(x1)] = 1 · x1 + 1692
[43(x1)] = 1 · x1 + 2409
[51(x1)] = 1 · x1 + 80
[55(x1)] = 1 · x1 + 1721
all of the following rules can be deleted.

There are 252 ruless (increase limit for explicit display).

1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[22(x1)] = 1 · x1 + 4
[24(x1)] = 1 · x1
[41(x1)] = 1 · x1 + 2
[13(x1)] = 1 · x1
[34(x1)] = 1 · x1
[40(x1)] = 1 · x1 + 3
[05(x1)] = 1 · x1
[51(x1)] = 1 · x1 + 1
[12(x1)] = 1 · x1 + 4
[20(x1)] = 1 · x1 + 1
[03(x1)] = 1 · x1 + 7
[44(x1)] = 1 · x1 + 2
[45(x1)] = 1 · x1 + 2
[50(x1)] = 1 · x1 + 2
[01(x1)] = 1 · x1
[15(x1)] = 1 · x1 + 3
[04(x1)] = 1 · x1
[00(x1)] = 1 · x1 + 1
[02(x1)] = 1 · x1 + 4
[30(x1)] = 1 · x1 + 1
[10(x1)] = 1 · x1 + 1
[43(x1)] = 1 · x1 + 6
[35(x1)] = 1 · x1
[52(x1)] = 1 · x1 + 5
[11(x1)] = 1 · x1
[14(x1)] = 1 · x1
[42(x1)] = 1 · x1 + 6
[21(x1)] = 1 · x1
[33(x1)] = 1 · x1
[25(x1)] = 1 · x1
[23(x1)] = 1 · x1 + 5
[54(x1)] = 1 · x1 + 1
[32(x1)] = 1 · x1 + 4
[55(x1)] = 1 · x1 + 1
[53(x1)] = 1 · x1 + 2
[31(x1)] = 1 · x1
all of the following rules can be deleted.
32(24(40(02(21(13(x1)))))) 34(45(54(43(33(x1))))) (201)
22(24(40(02(21(13(x1)))))) 24(45(54(43(33(x1))))) (207)
12(24(40(02(21(13(x1)))))) 14(45(54(43(33(x1))))) (213)
02(24(40(02(21(13(x1)))))) 04(45(54(43(33(x1))))) (219)
42(24(40(02(21(13(x1)))))) 44(45(54(43(33(x1))))) (225)
52(24(40(02(21(13(x1)))))) 54(45(54(43(33(x1))))) (231)

1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[22(x1)] = 1 · x1
[24(x1)] = 1 · x1
[41(x1)] = 1 · x1
[13(x1)] = 1 · x1 + 1
[34(x1)] = 1 · x1
[40(x1)] = 1 · x1
[05(x1)] = 1 · x1
[51(x1)] = 1 · x1
[12(x1)] = 1 · x1
[20(x1)] = 1 · x1
[03(x1)] = 1 · x1
[44(x1)] = 1 · x1
[45(x1)] = 1 · x1
[50(x1)] = 1 · x1
[01(x1)] = 1 · x1
[15(x1)] = 1 · x1
[04(x1)] = 1 · x1
[00(x1)] = 1 · x1
[02(x1)] = 1 · x1
[30(x1)] = 1 · x1
[10(x1)] = 1 · x1
[43(x1)] = 1 · x1
[35(x1)] = 1 · x1
[52(x1)] = 1 · x1
[11(x1)] = 1 · x1
[14(x1)] = 1 · x1
[42(x1)] = 1 · x1
[21(x1)] = 1 · x1
[33(x1)] = 1 · x1
[25(x1)] = 1 · x1
[23(x1)] = 1 · x1
[54(x1)] = 1 · x1
[32(x1)] = 1 · x1
[55(x1)] = 1 · x1
[53(x1)] = 1 · x1
[31(x1)] = 1 · x1
all of the following rules can be deleted.
22(24(41(13(34(40(05(51(12(20(03(x1))))))))))) 24(44(45(50(01(15(50(04(40(00(03(x1))))))))))) (135)
22(24(41(13(34(40(05(51(12(20(02(x1))))))))))) 24(44(45(50(01(15(50(04(40(00(02(x1))))))))))) (136)
22(24(41(13(34(40(05(51(12(20(01(x1))))))))))) 24(44(45(50(01(15(50(04(40(00(01(x1))))))))))) (137)
22(24(41(13(34(40(05(51(12(20(00(x1))))))))))) 24(44(45(50(01(15(50(04(40(00(00(x1))))))))))) (138)
22(24(41(13(34(40(05(51(12(20(04(x1))))))))))) 24(44(45(50(01(15(50(04(40(00(04(x1))))))))))) (139)
22(24(41(13(34(40(05(51(12(20(05(x1))))))))))) 24(44(45(50(01(15(50(04(40(00(05(x1))))))))))) (140)

1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[30(x1)] = 1 · x1
[04(x1)] = 1 · x1 + 10
[41(x1)] = 1 · x1
[10(x1)] = 1 · x1 + 4
[43(x1)] = 1 · x1 + 12
[35(x1)] = 1 · x1
[52(x1)] = 1 · x1 + 5
[20(x1)] = 1 · x1 + 4
[01(x1)] = 1 · x1
[11(x1)] = 1 · x1 + 4
[14(x1)] = 1 · x1 + 14
[42(x1)] = 1 · x1
[21(x1)] = 1 · x1 + 4
[13(x1)] = 1 · x1
[33(x1)] = 1 · x1 + 6
[00(x1)] = 1 · x1
[02(x1)] = 1 · x1
[25(x1)] = 1 · x1 + 4
[50(x1)] = 1 · x1 + 5
[23(x1)] = 1 · x1
[05(x1)] = 1 · x1
[54(x1)] = 1 · x1 + 15
[40(x1)] = 1 · x1
[12(x1)] = 1 · x1 + 4
[15(x1)] = 1 · x1 + 2
[32(x1)] = 1 · x1
[22(x1)] = 1 · x1 + 4
[24(x1)] = 1 · x1 + 14
[03(x1)] = 1 · x1 + 4
[51(x1)] = 1 · x1 + 5
[45(x1)] = 1 · x1
[55(x1)] = 1 · x1 + 5
[44(x1)] = 1 · x1 + 10
[53(x1)] = 1 · x1 + 10
[34(x1)] = 1 · x1 + 10
[31(x1)] = 1 · x1
all of the following rules can be deleted.
30(04(41(10(04(43(35(52(20(01(11(14(42(21(13(x1))))))))))))))) 33(30(00(02(25(50(02(23(30(05(54(40(01(11(13(x1))))))))))))))) (165)
30(04(41(10(04(43(35(52(20(01(11(14(42(21(12(x1))))))))))))))) 33(30(00(02(25(50(02(23(30(05(54(40(01(11(12(x1))))))))))))))) (166)
30(04(41(10(04(43(35(52(20(01(11(14(42(21(11(x1))))))))))))))) 33(30(00(02(25(50(02(23(30(05(54(40(01(11(11(x1))))))))))))))) (167)
30(04(41(10(04(43(35(52(20(01(11(14(42(21(10(x1))))))))))))))) 33(30(00(02(25(50(02(23(30(05(54(40(01(11(10(x1))))))))))))))) (168)
30(04(41(10(04(43(35(52(20(01(11(14(42(21(14(x1))))))))))))))) 33(30(00(02(25(50(02(23(30(05(54(40(01(11(14(x1))))))))))))))) (169)
30(04(41(10(04(43(35(52(20(01(11(14(42(21(15(x1))))))))))))))) 33(30(00(02(25(50(02(23(30(05(54(40(01(11(15(x1))))))))))))))) (170)

1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[43(x1)] = 1 · x1 + 3
[32(x1)] = 1 · x1
[20(x1)] = 1 · x1
[01(x1)] = 1 · x1
[10(x1)] = 1 · x1
[04(x1)] = 1 · x1
[42(x1)] = 1 · x1 + 1
[22(x1)] = 1 · x1
[24(x1)] = 1 · x1
[41(x1)] = 1 · x1 + 1
[03(x1)] = 1 · x1
[35(x1)] = 1 · x1
[51(x1)] = 1 · x1
[11(x1)] = 1 · x1
[45(x1)] = 1 · x1 + 1
[55(x1)] = 1 · x1
[52(x1)] = 1 · x1
[44(x1)] = 1 · x1 + 1
[02(x1)] = 1 · x1
[40(x1)] = 1 · x1 + 1
[00(x1)] = 1 · x1
[05(x1)] = 1 · x1
[14(x1)] = 1 · x1
[12(x1)] = 1 · x1
[25(x1)] = 1 · x1
[53(x1)] = 1 · x1 + 1
[15(x1)] = 1 · x1
[54(x1)] = 1 · x1
[50(x1)] = 1 · x1
[30(x1)] = 1 · x1
[34(x1)] = 1 · x1
[23(x1)] = 1 · x1
[31(x1)] = 1 · x1
[21(x1)] = 1 · x1
[33(x1)] = 1 · x1
all of the following rules can be deleted.
43(32(20(01(10(04(42(22(24(41(10(03(35(51(11(10(03(x1))))))))))))))))) 45(55(52(22(22(20(04(44(45(51(10(02(22(24(40(03(x1)))))))))))))))) (183)
43(32(20(01(10(04(42(22(24(41(10(03(35(51(11(10(02(x1))))))))))))))))) 45(55(52(22(22(20(04(44(45(51(10(02(22(24(40(02(x1)))))))))))))))) (184)
43(32(20(01(10(04(42(22(24(41(10(03(35(51(11(10(01(x1))))))))))))))))) 45(55(52(22(22(20(04(44(45(51(10(02(22(24(40(01(x1)))))))))))))))) (185)
43(32(20(01(10(04(42(22(24(41(10(03(35(51(11(10(00(x1))))))))))))))))) 45(55(52(22(22(20(04(44(45(51(10(02(22(24(40(00(x1)))))))))))))))) (186)
43(32(20(01(10(04(42(22(24(41(10(03(35(51(11(10(04(x1))))))))))))))))) 45(55(52(22(22(20(04(44(45(51(10(02(22(24(40(04(x1)))))))))))))))) (187)
43(32(20(01(10(04(42(22(24(41(10(03(35(51(11(10(05(x1))))))))))))))))) 45(55(52(22(22(20(04(44(45(51(10(02(22(24(40(05(x1)))))))))))))))) (188)

1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[14(x1)] = 1 · x1
[40(x1)] = 1 · x1
[01(x1)] = 1 · x1
[12(x1)] = 1 · x1
[25(x1)] = 1 · x1 + 1
[53(x1)] = 1 · x1
[15(x1)] = 1 · x1
[54(x1)] = 1 · x1
[45(x1)] = 1 · x1
[55(x1)] = 1 · x1
[52(x1)] = 1 · x1
[51(x1)] = 1 · x1
[50(x1)] = 1 · x1
[35(x1)] = 1 · x1
[30(x1)] = 1 · x1
[03(x1)] = 1 · x1 + 2
[34(x1)] = 1 · x1
[02(x1)] = 1 · x1
[00(x1)] = 1 · x1
[04(x1)] = 1 · x1
[05(x1)] = 1 · x1
[24(x1)] = 1 · x1 + 1
[44(x1)] = 1 · x1
[32(x1)] = 1 · x1
[23(x1)] = 1 · x1 + 1
[31(x1)] = 1 · x1
[22(x1)] = 1 · x1 + 1
[21(x1)] = 1 · x1 + 1
[42(x1)] = 1 · x1
[20(x1)] = 1 · x1 + 1
[11(x1)] = 1 · x1
[41(x1)] = 1 · x1
[10(x1)] = 1 · x1
[43(x1)] = 1 · x1
[33(x1)] = 1 · x1
all of the following rules can be deleted.
14(40(01(12(25(53(x1)))))) 15(54(45(55(53(x1))))) (285)
14(40(01(12(25(52(x1)))))) 15(54(45(55(52(x1))))) (286)
14(40(01(12(25(51(x1)))))) 15(54(45(55(51(x1))))) (287)
14(40(01(12(25(50(x1)))))) 15(54(45(55(50(x1))))) (288)
14(40(01(12(25(54(x1)))))) 15(54(45(55(54(x1))))) (289)
14(40(01(12(25(55(x1)))))) 15(54(45(55(55(x1))))) (290)

1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[35(x1)] = 1 · x1 + 1
[55(x1)] = 1 · x1
[51(x1)] = 1 · x1
[15(x1)] = 1 · x1
[53(x1)] = 1 · x1
[30(x1)] = 1 · x1
[03(x1)] = 1 · x1 + 1
[34(x1)] = 1 · x1
[45(x1)] = 1 · x1
[50(x1)] = 1 · x1
[02(x1)] = 1 · x1
[01(x1)] = 1 · x1
[00(x1)] = 1 · x1
[04(x1)] = 1 · x1
[05(x1)] = 1 · x1
[25(x1)] = 1 · x1
[24(x1)] = 1 · x1
[44(x1)] = 1 · x1
[54(x1)] = 1 · x1
[32(x1)] = 1 · x1
[40(x1)] = 1 · x1
[23(x1)] = 1 · x1 + 1
[31(x1)] = 1 · x1
[12(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1
[42(x1)] = 1 · x1
[20(x1)] = 1 · x1
[52(x1)] = 1 · x1
[11(x1)] = 1 · x1
[41(x1)] = 1 · x1
[10(x1)] = 1 · x1
[43(x1)] = 1 · x1
[33(x1)] = 1 · x1
all of the following rules can be deleted.
35(55(51(15(53(30(03(x1))))))) 34(45(51(15(50(03(x1)))))) (345)
35(55(51(15(53(30(02(x1))))))) 34(45(51(15(50(02(x1)))))) (346)
35(55(51(15(53(30(01(x1))))))) 34(45(51(15(50(01(x1)))))) (347)
35(55(51(15(53(30(00(x1))))))) 34(45(51(15(50(00(x1)))))) (348)
35(55(51(15(53(30(04(x1))))))) 34(45(51(15(50(04(x1)))))) (349)
35(55(51(15(53(30(05(x1))))))) 34(45(51(15(50(05(x1)))))) (350)

1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[25(x1)] = 1 · x1 + 1
[55(x1)] = 1 · x1
[51(x1)] = 1 · x1
[15(x1)] = 1 · x1
[53(x1)] = 1 · x1
[30(x1)] = 1 · x1
[03(x1)] = 1 · x1 + 1
[24(x1)] = 1 · x1
[45(x1)] = 1 · x1
[50(x1)] = 1 · x1
[02(x1)] = 1 · x1
[01(x1)] = 1 · x1
[00(x1)] = 1 · x1
[04(x1)] = 1 · x1
[05(x1)] = 1 · x1
[44(x1)] = 1 · x1
[54(x1)] = 1 · x1
[32(x1)] = 1 · x1
[40(x1)] = 1 · x1
[23(x1)] = 1 · x1 + 2
[31(x1)] = 1 · x1
[12(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1
[42(x1)] = 1 · x1
[20(x1)] = 1 · x1
[52(x1)] = 1 · x1
[34(x1)] = 1 · x1
[11(x1)] = 1 · x1
[41(x1)] = 1 · x1
[10(x1)] = 1 · x1
[43(x1)] = 1 · x1
[35(x1)] = 1 · x1
[33(x1)] = 1 · x1 + 1
all of the following rules can be deleted.
25(55(51(15(53(30(03(x1))))))) 24(45(51(15(50(03(x1)))))) (351)
25(55(51(15(53(30(02(x1))))))) 24(45(51(15(50(02(x1)))))) (352)
25(55(51(15(53(30(01(x1))))))) 24(45(51(15(50(01(x1)))))) (353)
25(55(51(15(53(30(00(x1))))))) 24(45(51(15(50(00(x1)))))) (354)
25(55(51(15(53(30(04(x1))))))) 24(45(51(15(50(04(x1)))))) (355)
25(55(51(15(53(30(05(x1))))))) 24(45(51(15(50(05(x1)))))) (356)

1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[05(x1)] = 1 · x1 + 2
[55(x1)] = 1 · x1 + 1
[51(x1)] = 1 · x1
[15(x1)] = 1 · x1 + 2
[53(x1)] = 1 · x1
[30(x1)] = 1 · x1
[03(x1)] = 1 · x1
[04(x1)] = 1 · x1 + 1
[45(x1)] = 1 · x1 + 1
[50(x1)] = 1 · x1
[02(x1)] = 1 · x1
[01(x1)] = 1 · x1
[00(x1)] = 1 · x1
[44(x1)] = 1 · x1 + 1
[54(x1)] = 1 · x1 + 1
[32(x1)] = 1 · x1
[24(x1)] = 1 · x1 + 1
[40(x1)] = 1 · x1
[23(x1)] = 1 · x1
[31(x1)] = 1 · x1
[12(x1)] = 1 · x1 + 1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1 + 2
[42(x1)] = 1 · x1
[20(x1)] = 1 · x1
[25(x1)] = 1 · x1
[52(x1)] = 1 · x1
[34(x1)] = 1 · x1 + 1
[11(x1)] = 1 · x1 + 1
[41(x1)] = 1 · x1
[10(x1)] = 1 · x1 + 1
[43(x1)] = 1 · x1 + 3
[35(x1)] = 1 · x1
[33(x1)] = 1 · x1
all of the following rules can be deleted.
05(55(51(15(53(30(03(x1))))))) 04(45(51(15(50(03(x1)))))) (363)
05(55(51(15(53(30(02(x1))))))) 04(45(51(15(50(02(x1)))))) (364)
05(55(51(15(53(30(01(x1))))))) 04(45(51(15(50(01(x1)))))) (365)
05(55(51(15(53(30(00(x1))))))) 04(45(51(15(50(00(x1)))))) (366)
05(55(51(15(53(30(04(x1))))))) 04(45(51(15(50(04(x1)))))) (367)
05(55(51(15(53(30(05(x1))))))) 04(45(51(15(50(05(x1)))))) (368)

1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[45(x1)] = 1 · x1 + 1
[55(x1)] = 1 · x1
[51(x1)] = 1 · x1
[15(x1)] = 1 · x1
[53(x1)] = 1 · x1
[30(x1)] = 1 · x1 + 1
[03(x1)] = 1 · x1
[44(x1)] = 1 · x1
[50(x1)] = 1 · x1
[02(x1)] = 1 · x1
[01(x1)] = 1 · x1
[00(x1)] = 1 · x1
[04(x1)] = 1 · x1
[05(x1)] = 1 · x1
[54(x1)] = 1 · x1
[32(x1)] = 1 · x1 + 1
[24(x1)] = 1 · x1
[40(x1)] = 1 · x1
[23(x1)] = 1 · x1 + 5
[31(x1)] = 1 · x1 + 1
[12(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1
[42(x1)] = 1 · x1
[20(x1)] = 1 · x1
[25(x1)] = 1 · x1 + 3
[52(x1)] = 1 · x1
[34(x1)] = 1 · x1 + 1
[11(x1)] = 1 · x1
[41(x1)] = 1 · x1
[10(x1)] = 1 · x1
[43(x1)] = 1 · x1
[35(x1)] = 1 · x1
[33(x1)] = 1 · x1 + 2
all of the following rules can be deleted.
45(55(51(15(53(30(03(x1))))))) 44(45(51(15(50(03(x1)))))) (369)
45(55(51(15(53(30(02(x1))))))) 44(45(51(15(50(02(x1)))))) (370)
45(55(51(15(53(30(01(x1))))))) 44(45(51(15(50(01(x1)))))) (371)
45(55(51(15(53(30(00(x1))))))) 44(45(51(15(50(00(x1)))))) (372)
45(55(51(15(53(30(04(x1))))))) 44(45(51(15(50(04(x1)))))) (373)
45(55(51(15(53(30(05(x1))))))) 44(45(51(15(50(05(x1)))))) (374)

1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[55(x1)] = 1 · x1
[51(x1)] = 1 · x1
[15(x1)] = 1 · x1
[53(x1)] = 1 · x1
[30(x1)] = 1 · x1 + 1
[03(x1)] = 1 · x1
[54(x1)] = 1 · x1
[45(x1)] = 1 · x1
[50(x1)] = 1 · x1
[02(x1)] = 1 · x1
[01(x1)] = 1 · x1
[00(x1)] = 1 · x1
[04(x1)] = 1 · x1
[05(x1)] = 1 · x1 + 1
[32(x1)] = 1 · x1 + 1
[24(x1)] = 1 · x1
[40(x1)] = 1 · x1
[23(x1)] = 1 · x1 + 3
[31(x1)] = 1 · x1 + 1
[12(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1
[42(x1)] = 1 · x1
[20(x1)] = 1 · x1
[25(x1)] = 1 · x1 + 1
[52(x1)] = 1 · x1
[34(x1)] = 1 · x1 + 1
[11(x1)] = 1 · x1
[41(x1)] = 1 · x1
[10(x1)] = 1 · x1
[43(x1)] = 1 · x1
[35(x1)] = 1 · x1
[44(x1)] = 1 · x1
[33(x1)] = 1 · x1
all of the following rules can be deleted.
55(55(51(15(53(30(03(x1))))))) 54(45(51(15(50(03(x1)))))) (375)
55(55(51(15(53(30(02(x1))))))) 54(45(51(15(50(02(x1)))))) (376)
55(55(51(15(53(30(01(x1))))))) 54(45(51(15(50(01(x1)))))) (377)
55(55(51(15(53(30(00(x1))))))) 54(45(51(15(50(00(x1)))))) (378)
55(55(51(15(53(30(04(x1))))))) 54(45(51(15(50(04(x1)))))) (379)
55(55(51(15(53(30(05(x1))))))) 54(45(51(15(50(05(x1)))))) (380)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[32(x1)] = 1 · x1
[24(x1)] = 1 · x1 + 1
[45(x1)] = 1 · x1
[55(x1)] = 1 · x1
[54(x1)] = 1 · x1 + 1
[40(x1)] = 1 · x1
[02(x1)] = 1 · x1
[23(x1)] = 1 · x1
[31(x1)] = 1 · x1
[12(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1 + 1
[14(x1)] = 1 · x1 + 1
[42(x1)] = 1 · x1
[20(x1)] = 1 · x1
[00(x1)] = 1 · x1
[03(x1)] = 1 · x1 + 1
[15(x1)] = 1 · x1
[53(x1)] = 1 · x1
[25(x1)] = 1 · x1
[52(x1)] = 1 · x1
[34(x1)] = 1 · x1
[01(x1)] = 1 · x1 + 1
[11(x1)] = 1 · x1 + 1
[50(x1)] = 1 · x1
[04(x1)] = 1 · x1 + 1
[05(x1)] = 1 · x1 + 1
[41(x1)] = 1 · x1 + 1
[51(x1)] = 1 · x1 + 1
[10(x1)] = 1 · x1
[43(x1)] = 1 · x1
[30(x1)] = 1 · x1
[35(x1)] = 1 · x1 + 1
[44(x1)] = 1 · x1 + 1
[33(x1)] = 1 · x1 + 2
all of the following rules can be deleted.
32(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(03(x1))))))))))))))))) 31(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(03(x1)))))))))))))))))) (417)
32(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(02(x1))))))))))))))))) 31(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(02(x1)))))))))))))))))) (418)
32(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(01(x1))))))))))))))))) 31(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(01(x1)))))))))))))))))) (419)
32(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(00(x1))))))))))))))))) 31(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(00(x1)))))))))))))))))) (420)
32(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(04(x1))))))))))))))))) 31(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(04(x1)))))))))))))))))) (421)
32(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(05(x1))))))))))))))))) 31(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(05(x1)))))))))))))))))) (422)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[22(x1)] = 1 · x1
[24(x1)] = 1 · x1
[45(x1)] = 1 · x1
[55(x1)] = 1 · x1
[54(x1)] = 1 · x1 + 1
[40(x1)] = 1 · x1
[02(x1)] = 1 · x1
[23(x1)] = 1 · x1 + 1
[31(x1)] = 1 · x1
[12(x1)] = 1 · x1
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1 + 1
[42(x1)] = 1 · x1
[20(x1)] = 1 · x1
[00(x1)] = 1 · x1
[03(x1)] = 1 · x1
[15(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
[25(x1)] = 1 · x1
[52(x1)] = 1 · x1
[34(x1)] = 1 · x1
[01(x1)] = 1 · x1 + 1
[11(x1)] = 1 · x1 + 1
[50(x1)] = 1 · x1
[04(x1)] = 1 · x1 + 1
[05(x1)] = 1 · x1 + 5
[41(x1)] = 1 · x1 + 1
[51(x1)] = 1 · x1 + 1
[10(x1)] = 1 · x1
[43(x1)] = 1 · x1 + 1
[30(x1)] = 1 · x1
[35(x1)] = 1 · x1
[44(x1)] = 1 · x1 + 1
[33(x1)] = 1 · x1
all of the following rules can be deleted.
22(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(03(x1))))))))))))))))) 21(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(03(x1)))))))))))))))))) (423)
22(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(02(x1))))))))))))))))) 21(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(02(x1)))))))))))))))))) (424)
22(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(01(x1))))))))))))))))) 21(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(01(x1)))))))))))))))))) (425)
22(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(00(x1))))))))))))))))) 21(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(00(x1)))))))))))))))))) (426)
22(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(04(x1))))))))))))))))) 21(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(04(x1)))))))))))))))))) (427)
22(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(05(x1))))))))))))))))) 21(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(05(x1)))))))))))))))))) (428)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[12(x1)] = 1 · x1 + 1
[24(x1)] = 1 · x1
[45(x1)] = 1 · x1
[55(x1)] = 1 · x1
[54(x1)] = 1 · x1
[40(x1)] = 1 · x1
[02(x1)] = 1 · x1
[23(x1)] = 1 · x1
[31(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1
[42(x1)] = 1 · x1
[20(x1)] = 1 · x1
[00(x1)] = 1 · x1
[03(x1)] = 1 · x1 + 1
[11(x1)] = 1 · x1
[15(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
[25(x1)] = 1 · x1
[52(x1)] = 1 · x1
[34(x1)] = 1 · x1
[01(x1)] = 1 · x1
[50(x1)] = 1 · x1
[04(x1)] = 1 · x1
[05(x1)] = 1 · x1
[41(x1)] = 1 · x1
[51(x1)] = 1 · x1
[10(x1)] = 1 · x1 + 1
[43(x1)] = 1 · x1 + 2
[30(x1)] = 1 · x1
[35(x1)] = 1 · x1
[44(x1)] = 1 · x1
[33(x1)] = 1 · x1
all of the following rules can be deleted.
12(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(03(x1))))))))))))))))) 11(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(03(x1)))))))))))))))))) (429)
12(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(02(x1))))))))))))))))) 11(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(02(x1)))))))))))))))))) (430)
12(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(01(x1))))))))))))))))) 11(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(01(x1)))))))))))))))))) (431)
12(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(00(x1))))))))))))))))) 11(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(00(x1)))))))))))))))))) (432)
12(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(04(x1))))))))))))))))) 11(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(04(x1)))))))))))))))))) (433)
12(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(05(x1))))))))))))))))) 11(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(05(x1)))))))))))))))))) (434)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[02(x1)] = 1 · x1
[24(x1)] = 1 · x1
[45(x1)] = 1 · x1
[55(x1)] = 1 · x1
[54(x1)] = 1 · x1 + 1
[40(x1)] = 1 · x1
[23(x1)] = 1 · x1
[31(x1)] = 1 · x1
[12(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1
[42(x1)] = 1 · x1
[20(x1)] = 1 · x1
[00(x1)] = 1 · x1
[03(x1)] = 1 · x1
[01(x1)] = 1 · x1
[15(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
[25(x1)] = 1 · x1
[52(x1)] = 1 · x1
[34(x1)] = 1 · x1
[11(x1)] = 1 · x1
[50(x1)] = 1 · x1
[04(x1)] = 1 · x1
[05(x1)] = 1 · x1 + 1
[41(x1)] = 1 · x1 + 1
[51(x1)] = 1 · x1 + 1
[10(x1)] = 1 · x1
[43(x1)] = 1 · x1 + 2
[30(x1)] = 1 · x1
[35(x1)] = 1 · x1
[44(x1)] = 1 · x1 + 1
[33(x1)] = 1 · x1
all of the following rules can be deleted.
02(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(03(x1))))))))))))))))) 01(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(03(x1)))))))))))))))))) (435)
02(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(02(x1))))))))))))))))) 01(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(02(x1)))))))))))))))))) (436)
02(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(01(x1))))))))))))))))) 01(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(01(x1)))))))))))))))))) (437)
02(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(00(x1))))))))))))))))) 01(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(00(x1)))))))))))))))))) (438)
02(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(04(x1))))))))))))))))) 01(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(04(x1)))))))))))))))))) (439)
02(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(05(x1))))))))))))))))) 01(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(05(x1)))))))))))))))))) (440)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[42(x1)] = 1 · x1
[24(x1)] = 1 · x1
[45(x1)] = 1 · x1
[55(x1)] = 1 · x1
[54(x1)] = 1 · x1 + 1
[40(x1)] = 1 · x1
[02(x1)] = 1 · x1
[23(x1)] = 1 · x1 + 1
[31(x1)] = 1 · x1
[12(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1
[20(x1)] = 1 · x1
[00(x1)] = 1 · x1
[03(x1)] = 1 · x1
[41(x1)] = 1 · x1
[15(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
[25(x1)] = 1 · x1
[52(x1)] = 1 · x1
[34(x1)] = 1 · x1
[01(x1)] = 1 · x1 + 1
[11(x1)] = 1 · x1
[50(x1)] = 1 · x1
[04(x1)] = 1 · x1 + 1
[05(x1)] = 1 · x1
[51(x1)] = 1 · x1 + 1
[10(x1)] = 1 · x1
[43(x1)] = 1 · x1 + 3
[30(x1)] = 1 · x1
[35(x1)] = 1 · x1
[44(x1)] = 1 · x1
[33(x1)] = 1 · x1
all of the following rules can be deleted.
42(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(03(x1))))))))))))))))) 41(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(03(x1)))))))))))))))))) (441)
42(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(02(x1))))))))))))))))) 41(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(02(x1)))))))))))))))))) (442)
42(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(01(x1))))))))))))))))) 41(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(01(x1)))))))))))))))))) (443)
42(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(00(x1))))))))))))))))) 41(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(00(x1)))))))))))))))))) (444)
42(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(04(x1))))))))))))))))) 41(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(04(x1)))))))))))))))))) (445)
42(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(05(x1))))))))))))))))) 41(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(05(x1)))))))))))))))))) (446)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[52(x1)] = 1 · x1
[24(x1)] = 1 · x1
[45(x1)] = 1 · x1
[55(x1)] = 1 · x1
[54(x1)] = 1 · x1
[40(x1)] = 1 · x1
[02(x1)] = 1 · x1
[23(x1)] = 1 · x1 + 1
[31(x1)] = 1 · x1
[12(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1
[42(x1)] = 1 · x1
[20(x1)] = 1 · x1
[00(x1)] = 1 · x1
[03(x1)] = 1 · x1
[51(x1)] = 1 · x1
[15(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
[25(x1)] = 1 · x1
[34(x1)] = 1 · x1
[01(x1)] = 1 · x1
[11(x1)] = 1 · x1
[50(x1)] = 1 · x1
[04(x1)] = 1 · x1
[05(x1)] = 1 · x1
[10(x1)] = 1 · x1
[41(x1)] = 1 · x1
[43(x1)] = 1 · x1
[30(x1)] = 1 · x1
[35(x1)] = 1 · x1
[44(x1)] = 1 · x1
[33(x1)] = 1 · x1
all of the following rules can be deleted.
52(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(03(x1))))))))))))))))) 51(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(03(x1)))))))))))))))))) (447)
52(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(02(x1))))))))))))))))) 51(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(02(x1)))))))))))))))))) (448)
52(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(01(x1))))))))))))))))) 51(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(01(x1)))))))))))))))))) (449)
52(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(00(x1))))))))))))))))) 51(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(00(x1)))))))))))))))))) (450)
52(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(04(x1))))))))))))))))) 51(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(04(x1)))))))))))))))))) (451)
52(24(45(55(54(40(02(23(31(12(22(21(14(42(20(00(05(x1))))))))))))))))) 51(15(53(32(25(52(20(03(34(45(53(32(20(01(11(15(50(05(x1)))))))))))))))))) (452)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[32(x1)] = 1 · x1
[20(x1)] = 1 · x1 + 1
[00(x1)] = 1 · x1 + 1
[01(x1)] = 1 · x1
[10(x1)] = 1 · x1 + 1
[03(x1)] = 1 · x1
[34(x1)] = 1 · x1
[40(x1)] = 1 · x1 + 1
[02(x1)] = 1 · x1
[05(x1)] = 1 · x1
[54(x1)] = 1 · x1
[41(x1)] = 1 · x1
[12(x1)] = 1 · x1
[24(x1)] = 1 · x1
[45(x1)] = 1 · x1
[43(x1)] = 1 · x1
[30(x1)] = 1 · x1
[51(x1)] = 1 · x1
[11(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1
[35(x1)] = 1 · x1
[50(x1)] = 1 · x1 + 1
[25(x1)] = 1 · x1 + 1
[52(x1)] = 1 · x1
[44(x1)] = 1 · x1
[42(x1)] = 1 · x1
[31(x1)] = 1 · x1
[23(x1)] = 1 · x1
[04(x1)] = 1 · x1
[33(x1)] = 1 · x1
[55(x1)] = 1 · x1 + 1
[53(x1)] = 1 · x1
all of the following rules can be deleted.
32(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(43(x1))))))))))))))))))))) 30(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(43(x1))))))))))))))))))))) (453)
32(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(42(x1))))))))))))))))))))) 30(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(42(x1))))))))))))))))))))) (454)
32(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(41(x1))))))))))))))))))))) 30(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(41(x1))))))))))))))))))))) (455)
32(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(40(x1))))))))))))))))))))) 30(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(40(x1))))))))))))))))))))) (456)
32(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(44(x1))))))))))))))))))))) 30(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(44(x1))))))))))))))))))))) (457)
32(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(45(x1))))))))))))))))))))) 30(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(45(x1))))))))))))))))))))) (458)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[22(x1)] = 1 · x1 + 1
[20(x1)] = 1 · x1
[00(x1)] = 1 · x1
[01(x1)] = 1 · x1
[10(x1)] = 1 · x1
[03(x1)] = 1 · x1
[34(x1)] = 1 · x1 + 6
[40(x1)] = 1 · x1
[02(x1)] = 1 · x1
[05(x1)] = 1 · x1
[54(x1)] = 1 · x1
[41(x1)] = 1 · x1
[12(x1)] = 1 · x1
[24(x1)] = 1 · x1
[45(x1)] = 1 · x1
[43(x1)] = 1 · x1
[51(x1)] = 1 · x1
[11(x1)] = 1 · x1 + 2
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1 + 2
[35(x1)] = 1 · x1
[50(x1)] = 1 · x1
[25(x1)] = 1 · x1
[52(x1)] = 1 · x1
[44(x1)] = 1 · x1
[42(x1)] = 1 · x1
[31(x1)] = 1 · x1 + 6
[23(x1)] = 1 · x1
[30(x1)] = 1 · x1
[04(x1)] = 1 · x1
[33(x1)] = 1 · x1
[55(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
all of the following rules can be deleted.
22(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(43(x1))))))))))))))))))))) 20(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(43(x1))))))))))))))))))))) (459)
22(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(42(x1))))))))))))))))))))) 20(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(42(x1))))))))))))))))))))) (460)
22(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(41(x1))))))))))))))))))))) 20(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(41(x1))))))))))))))))))))) (461)
22(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(40(x1))))))))))))))))))))) 20(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(40(x1))))))))))))))))))))) (462)
22(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(44(x1))))))))))))))))))))) 20(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(44(x1))))))))))))))))))))) (463)
22(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(45(x1))))))))))))))))))))) 20(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(45(x1))))))))))))))))))))) (464)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[12(x1)] = 1 · x1 + 1
[20(x1)] = 1 · x1
[00(x1)] = 1 · x1
[01(x1)] = 1 · x1
[10(x1)] = 1 · x1
[03(x1)] = 1 · x1
[34(x1)] = 1 · x1
[40(x1)] = 1 · x1
[02(x1)] = 1 · x1
[05(x1)] = 1 · x1
[54(x1)] = 1 · x1
[41(x1)] = 1 · x1
[24(x1)] = 1 · x1
[45(x1)] = 1 · x1
[43(x1)] = 1 · x1
[51(x1)] = 1 · x1
[11(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1
[35(x1)] = 1 · x1
[50(x1)] = 1 · x1
[25(x1)] = 1 · x1
[52(x1)] = 1 · x1
[44(x1)] = 1 · x1
[42(x1)] = 1 · x1
[31(x1)] = 1 · x1
[23(x1)] = 1 · x1
[30(x1)] = 1 · x1
[04(x1)] = 1 · x1
[33(x1)] = 1 · x1
[55(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
all of the following rules can be deleted.
12(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(43(x1))))))))))))))))))))) 10(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(43(x1))))))))))))))))))))) (465)
12(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(42(x1))))))))))))))))))))) 10(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(42(x1))))))))))))))))))))) (466)
12(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(41(x1))))))))))))))))))))) 10(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(41(x1))))))))))))))))))))) (467)
12(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(40(x1))))))))))))))))))))) 10(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(40(x1))))))))))))))))))))) (468)
12(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(44(x1))))))))))))))))))))) 10(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(44(x1))))))))))))))))))))) (469)
12(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(45(x1))))))))))))))))))))) 10(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(45(x1))))))))))))))))))))) (470)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[02(x1)] = 1 · x1 + 1
[20(x1)] = 1 · x1 + 1
[00(x1)] = 1 · x1
[01(x1)] = 1 · x1
[10(x1)] = 1 · x1
[03(x1)] = 1 · x1
[34(x1)] = 1 · x1
[40(x1)] = 1 · x1
[05(x1)] = 1 · x1
[54(x1)] = 1 · x1
[41(x1)] = 1 · x1
[12(x1)] = 1 · x1
[24(x1)] = 1 · x1
[45(x1)] = 1 · x1
[43(x1)] = 1 · x1
[51(x1)] = 1 · x1
[11(x1)] = 1 · x1 + 1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1 + 1
[35(x1)] = 1 · x1
[50(x1)] = 1 · x1
[25(x1)] = 1 · x1
[52(x1)] = 1 · x1
[44(x1)] = 1 · x1
[42(x1)] = 1 · x1
[31(x1)] = 1 · x1
[23(x1)] = 1 · x1
[30(x1)] = 1 · x1
[04(x1)] = 1 · x1
[33(x1)] = 1 · x1
[55(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
all of the following rules can be deleted.
02(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(43(x1))))))))))))))))))))) 00(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(43(x1))))))))))))))))))))) (471)
02(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(42(x1))))))))))))))))))))) 00(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(42(x1))))))))))))))))))))) (472)
02(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(41(x1))))))))))))))))))))) 00(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(41(x1))))))))))))))))))))) (473)
02(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(40(x1))))))))))))))))))))) 00(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(40(x1))))))))))))))))))))) (474)
02(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(44(x1))))))))))))))))))))) 00(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(44(x1))))))))))))))))))))) (475)
02(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(45(x1))))))))))))))))))))) 00(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(45(x1))))))))))))))))))))) (476)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[42(x1)] = 1 · x1
[20(x1)] = 1 · x1 + 1
[00(x1)] = 1 · x1
[01(x1)] = 1 · x1
[10(x1)] = 1 · x1
[03(x1)] = 1 · x1
[34(x1)] = 1 · x1
[40(x1)] = 1 · x1
[02(x1)] = 1 · x1
[05(x1)] = 1 · x1
[54(x1)] = 1 · x1
[41(x1)] = 1 · x1
[12(x1)] = 1 · x1
[24(x1)] = 1 · x1
[45(x1)] = 1 · x1
[43(x1)] = 1 · x1
[51(x1)] = 1 · x1
[11(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1
[35(x1)] = 1 · x1
[50(x1)] = 1 · x1 + 1
[25(x1)] = 1 · x1
[52(x1)] = 1 · x1
[44(x1)] = 1 · x1
[31(x1)] = 1 · x1
[23(x1)] = 1 · x1
[30(x1)] = 1 · x1
[04(x1)] = 1 · x1
[33(x1)] = 1 · x1
[55(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
all of the following rules can be deleted.
42(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(43(x1))))))))))))))))))))) 40(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(43(x1))))))))))))))))))))) (477)
42(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(42(x1))))))))))))))))))))) 40(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(42(x1))))))))))))))))))))) (478)
42(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(41(x1))))))))))))))))))))) 40(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(41(x1))))))))))))))))))))) (479)
42(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(40(x1))))))))))))))))))))) 40(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(40(x1))))))))))))))))))))) (480)
42(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(44(x1))))))))))))))))))))) 40(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(44(x1))))))))))))))))))))) (481)
42(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(45(x1))))))))))))))))))))) 40(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(45(x1))))))))))))))))))))) (482)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[52(x1)] = 1 · x1
[20(x1)] = 1 · x1
[00(x1)] = 1 · x1
[01(x1)] = 1 · x1
[10(x1)] = 1 · x1
[03(x1)] = 1 · x1
[34(x1)] = 1 · x1 + 1
[40(x1)] = 1 · x1
[02(x1)] = 1 · x1
[05(x1)] = 1 · x1
[54(x1)] = 1 · x1
[41(x1)] = 1 · x1
[12(x1)] = 1 · x1
[24(x1)] = 1 · x1
[45(x1)] = 1 · x1
[43(x1)] = 1 · x1
[50(x1)] = 1 · x1
[51(x1)] = 1 · x1
[11(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[14(x1)] = 1 · x1
[35(x1)] = 1 · x1
[25(x1)] = 1 · x1
[44(x1)] = 1 · x1
[42(x1)] = 1 · x1
[31(x1)] = 1 · x1 + 1
[23(x1)] = 1 · x1
[30(x1)] = 1 · x1
[04(x1)] = 1 · x1
[33(x1)] = 1 · x1
[55(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
all of the following rules can be deleted.
52(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(43(x1))))))))))))))))))))) 50(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(43(x1))))))))))))))))))))) (483)
52(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(42(x1))))))))))))))))))))) 50(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(42(x1))))))))))))))))))))) (484)
52(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(41(x1))))))))))))))))))))) 50(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(41(x1))))))))))))))))))))) (485)
52(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(40(x1))))))))))))))))))))) 50(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(40(x1))))))))))))))))))))) (486)
52(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(44(x1))))))))))))))))))))) 50(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(44(x1))))))))))))))))))))) (487)
52(20(00(01(10(00(03(34(40(02(20(05(54(41(12(24(45(54(45(54(45(x1))))))))))))))))))))) 50(00(05(51(11(12(22(21(14(43(35(50(00(00(02(25(52(22(24(44(45(x1))))))))))))))))))))) (488)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[31(x1)] = 1 · x1 + 1
[12(x1)] = 1 · x1
[23(x1)] = 1 · x1
[30(x1)] = 1 · x1
[04(x1)] = 1 · x1
[45(x1)] = 1 · x1
[54(x1)] = 1 · x1
[41(x1)] = 1 · x1
[11(x1)] = 1 · x1
[14(x1)] = 1 · x1
[42(x1)] = 1 · x1
[25(x1)] = 1 · x1
[44(x1)] = 1 · x1
[50(x1)] = 1 · x1
[01(x1)] = 1 · x1
[10(x1)] = 1 · x1
[03(x1)] = 1 · x1
[33(x1)] = 1 · x1
[34(x1)] = 1 · x1
[35(x1)] = 1 · x1
[55(x1)] = 1 · x1
[05(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
[22(x1)] = 1 · x1
[40(x1)] = 1 · x1
[02(x1)] = 1 · x1
[24(x1)] = 1 · x1
[43(x1)] = 1 · x1
[21(x1)] = 1 · x1
[51(x1)] = 1 · x1
all of the following rules can be deleted.
31(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(33(x1)))))))))))))))))))))) 34(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(33(x1)))))))))))))))))))))) (489)
31(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(32(x1)))))))))))))))))))))) 34(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(32(x1)))))))))))))))))))))) (490)
31(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(31(x1)))))))))))))))))))))) 34(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(31(x1)))))))))))))))))))))) (491)
31(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(30(x1)))))))))))))))))))))) 34(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(30(x1)))))))))))))))))))))) (492)
31(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(34(x1)))))))))))))))))))))) 34(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(34(x1)))))))))))))))))))))) (493)
31(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(35(x1)))))))))))))))))))))) 34(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(35(x1)))))))))))))))))))))) (494)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[21(x1)] = 1 · x1 + 1
[12(x1)] = 1 · x1
[23(x1)] = 1 · x1
[30(x1)] = 1 · x1
[04(x1)] = 1 · x1
[45(x1)] = 1 · x1
[54(x1)] = 1 · x1
[41(x1)] = 1 · x1
[11(x1)] = 1 · x1
[14(x1)] = 1 · x1
[42(x1)] = 1 · x1
[25(x1)] = 1 · x1
[44(x1)] = 1 · x1
[50(x1)] = 1 · x1
[01(x1)] = 1 · x1
[10(x1)] = 1 · x1
[03(x1)] = 1 · x1
[33(x1)] = 1 · x1
[24(x1)] = 1 · x1
[35(x1)] = 1 · x1
[55(x1)] = 1 · x1
[05(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
[22(x1)] = 1 · x1
[40(x1)] = 1 · x1
[02(x1)] = 1 · x1
[43(x1)] = 1 · x1
[31(x1)] = 1 · x1
[34(x1)] = 1 · x1
[51(x1)] = 1 · x1
all of the following rules can be deleted.
21(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(33(x1)))))))))))))))))))))) 24(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(33(x1)))))))))))))))))))))) (495)
21(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(32(x1)))))))))))))))))))))) 24(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(32(x1)))))))))))))))))))))) (496)
21(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(31(x1)))))))))))))))))))))) 24(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(31(x1)))))))))))))))))))))) (497)
21(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(30(x1)))))))))))))))))))))) 24(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(30(x1)))))))))))))))))))))) (498)
21(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(34(x1)))))))))))))))))))))) 24(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(34(x1)))))))))))))))))))))) (499)
21(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(35(x1)))))))))))))))))))))) 24(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(35(x1)))))))))))))))))))))) (500)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[11(x1)] = 1 · x1 + 1
[12(x1)] = 1 · x1
[23(x1)] = 1 · x1
[30(x1)] = 1 · x1
[04(x1)] = 1 · x1
[45(x1)] = 1 · x1
[54(x1)] = 1 · x1
[41(x1)] = 1 · x1
[14(x1)] = 1 · x1
[42(x1)] = 1 · x1
[25(x1)] = 1 · x1
[44(x1)] = 1 · x1
[50(x1)] = 1 · x1
[01(x1)] = 1 · x1
[10(x1)] = 1 · x1
[03(x1)] = 1 · x1
[33(x1)] = 1 · x1
[35(x1)] = 1 · x1
[55(x1)] = 1 · x1
[05(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
[22(x1)] = 1 · x1
[40(x1)] = 1 · x1
[02(x1)] = 1 · x1
[24(x1)] = 1 · x1
[43(x1)] = 1 · x1
[31(x1)] = 1 · x1
[34(x1)] = 1 · x1
[51(x1)] = 1 · x1
all of the following rules can be deleted.
11(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(33(x1)))))))))))))))))))))) 14(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(33(x1)))))))))))))))))))))) (501)
11(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(32(x1)))))))))))))))))))))) 14(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(32(x1)))))))))))))))))))))) (502)
11(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(31(x1)))))))))))))))))))))) 14(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(31(x1)))))))))))))))))))))) (503)
11(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(30(x1)))))))))))))))))))))) 14(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(30(x1)))))))))))))))))))))) (504)
11(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(34(x1)))))))))))))))))))))) 14(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(34(x1)))))))))))))))))))))) (505)
11(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(35(x1)))))))))))))))))))))) 14(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(35(x1)))))))))))))))))))))) (506)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[01(x1)] = 1 · x1 + 1
[12(x1)] = 1 · x1
[23(x1)] = 1 · x1
[30(x1)] = 1 · x1
[04(x1)] = 1 · x1
[45(x1)] = 1 · x1
[54(x1)] = 1 · x1
[41(x1)] = 1 · x1
[11(x1)] = 1 · x1
[14(x1)] = 1 · x1
[42(x1)] = 1 · x1
[25(x1)] = 1 · x1
[44(x1)] = 1 · x1
[50(x1)] = 1 · x1
[10(x1)] = 1 · x1
[03(x1)] = 1 · x1
[33(x1)] = 1 · x1
[35(x1)] = 1 · x1
[55(x1)] = 1 · x1
[05(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
[22(x1)] = 1 · x1
[40(x1)] = 1 · x1
[02(x1)] = 1 · x1 + 1
[24(x1)] = 1 · x1
[43(x1)] = 1 · x1
[31(x1)] = 1 · x1
[34(x1)] = 1 · x1
[51(x1)] = 1 · x1
all of the following rules can be deleted.
01(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(33(x1)))))))))))))))))))))) 04(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(33(x1)))))))))))))))))))))) (507)
01(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(32(x1)))))))))))))))))))))) 04(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(32(x1)))))))))))))))))))))) (508)
01(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(31(x1)))))))))))))))))))))) 04(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(31(x1)))))))))))))))))))))) (509)
01(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(30(x1)))))))))))))))))))))) 04(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(30(x1)))))))))))))))))))))) (510)
01(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(34(x1)))))))))))))))))))))) 04(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(34(x1)))))))))))))))))))))) (511)
01(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(35(x1)))))))))))))))))))))) 04(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(35(x1)))))))))))))))))))))) (512)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[41(x1)] = 1 · x1
[12(x1)] = 1 · x1
[23(x1)] = 1 · x1
[30(x1)] = 1 · x1
[04(x1)] = 1 · x1
[45(x1)] = 1 · x1
[54(x1)] = 1 · x1 + 1
[11(x1)] = 1 · x1
[14(x1)] = 1 · x1
[42(x1)] = 1 · x1
[25(x1)] = 1 · x1
[44(x1)] = 1 · x1
[50(x1)] = 1 · x1
[01(x1)] = 1 · x1
[10(x1)] = 1 · x1
[03(x1)] = 1 · x1
[33(x1)] = 1 · x1
[35(x1)] = 1 · x1
[55(x1)] = 1 · x1
[05(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
[22(x1)] = 1 · x1
[40(x1)] = 1 · x1
[02(x1)] = 1 · x1
[24(x1)] = 1 · x1
[43(x1)] = 1 · x1
[31(x1)] = 1 · x1
[34(x1)] = 1 · x1
[51(x1)] = 1 · x1
all of the following rules can be deleted.
41(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(33(x1)))))))))))))))))))))) 44(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(33(x1)))))))))))))))))))))) (513)
41(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(32(x1)))))))))))))))))))))) 44(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(32(x1)))))))))))))))))))))) (514)
41(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(31(x1)))))))))))))))))))))) 44(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(31(x1)))))))))))))))))))))) (515)
41(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(30(x1)))))))))))))))))))))) 44(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(30(x1)))))))))))))))))))))) (516)
41(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(34(x1)))))))))))))))))))))) 44(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(34(x1)))))))))))))))))))))) (517)
41(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(35(x1)))))))))))))))))))))) 44(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(35(x1)))))))))))))))))))))) (518)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[51(x1)] = 1 · x1
[12(x1)] = 1 · x1
[23(x1)] = 1 · x1
[30(x1)] = 1 · x1
[04(x1)] = 1 · x1
[45(x1)] = 1 · x1
[54(x1)] = 1 · x1
[41(x1)] = 1 · x1
[11(x1)] = 1 · x1
[14(x1)] = 1 · x1
[42(x1)] = 1 · x1
[25(x1)] = 1 · x1
[44(x1)] = 1 · x1
[50(x1)] = 1 · x1
[01(x1)] = 1 · x1
[10(x1)] = 1 · x1 + 1
[03(x1)] = 1 · x1
[33(x1)] = 1 · x1
[35(x1)] = 1 · x1
[55(x1)] = 1 · x1
[05(x1)] = 1 · x1
[53(x1)] = 1 · x1
[32(x1)] = 1 · x1
[22(x1)] = 1 · x1
[40(x1)] = 1 · x1
[02(x1)] = 1 · x1
[24(x1)] = 1 · x1
[43(x1)] = 1 · x1
[31(x1)] = 1 · x1
[34(x1)] = 1 · x1
all of the following rules can be deleted.
51(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(33(x1)))))))))))))))))))))) 54(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(33(x1)))))))))))))))))))))) (519)
51(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(32(x1)))))))))))))))))))))) 54(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(32(x1)))))))))))))))))))))) (520)
51(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(31(x1)))))))))))))))))))))) 54(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(31(x1)))))))))))))))))))))) (521)
51(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(30(x1)))))))))))))))))))))) 54(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(30(x1)))))))))))))))))))))) (522)
51(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(34(x1)))))))))))))))))))))) 54(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(34(x1)))))))))))))))))))))) (523)
51(12(23(30(04(45(54(41(11(14(42(25(54(44(44(42(25(50(01(10(03(35(x1)))))))))))))))))))))) 54(41(11(12(23(35(55(50(05(53(33(33(32(22(22(25(54(40(02(24(43(35(x1)))))))))))))))))))))) (524)

1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1 R is empty

There are no rules in the TRS. Hence, it is terminating.