Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/138142)

The rewrite relation of the following TRS is considered.

0(0(0(3(0(4(3(1(4(5(2(0(x1)))))))))))) → 1(0(2(3(5(5(1(0(3(2(2(3(3(4(2(4(x1)))))))))))))))) (1)
0(0(0(3(1(5(0(5(1(0(3(1(x1)))))))))))) → 3(3(1(2(5(5(1(2(4(4(4(1(2(3(3(x1))))))))))))))) (2)
0(0(1(1(4(3(4(0(5(1(4(3(x1)))))))))))) → 3(4(1(1(2(5(5(2(2(2(2(3(5(0(4(2(x1)))))))))))))))) (3)
0(0(1(3(4(3(4(4(4(0(3(0(x1)))))))))))) → 2(5(5(0(2(5(2(5(4(4(2(1(1(2(4(3(5(1(x1)))))))))))))))))) (4)
0(0(2(1(0(3(0(0(1(0(1(0(x1)))))))))))) → 2(1(2(4(3(4(2(5(5(3(5(1(0(0(3(x1))))))))))))))) (5)
0(0(4(3(0(0(1(4(0(1(3(5(x1)))))))))))) → 5(1(5(1(0(2(2(2(3(3(4(5(3(4(2(2(2(0(x1)))))))))))))))))) (6)
0(0(5(4(0(0(3(1(3(0(1(5(x1)))))))))))) → 3(1(0(5(5(5(5(4(1(1(2(2(2(4(5(2(1(2(x1)))))))))))))))))) (7)
0(0(5(4(5(0(5(0(0(3(0(3(x1)))))))))))) → 2(5(5(3(3(0(4(1(4(2(1(1(2(4(4(1(0(x1))))))))))))))))) (8)
0(1(0(0(1(3(1(0(3(2(5(0(x1)))))))))))) → 5(1(1(4(0(3(2(2(4(2(2(1(2(5(1(x1))))))))))))))) (9)
0(1(0(0(1(4(4(4(4(2(1(0(x1)))))))))))) → 5(5(2(4(1(5(3(1(2(2(2(4(2(3(2(1(3(4(x1)))))))))))))))))) (10)
0(1(1(3(4(4(0(2(0(1(1(1(x1)))))))))))) → 0(5(3(2(2(2(5(1(4(1(3(2(4(2(2(1(2(1(x1)))))))))))))))))) (11)
0(1(4(5(0(0(5(1(3(0(4(5(x1)))))))))))) → 2(3(3(1(2(5(4(1(2(5(3(4(1(2(5(5(3(5(x1)))))))))))))))))) (12)
0(2(0(4(4(1(2(1(0(4(3(3(x1)))))))))))) → 2(1(2(4(3(5(2(5(2(5(3(4(4(1(x1)))))))))))))) (13)
0(2(4(3(4(1(2(0(1(4(4(5(x1)))))))))))) → 4(2(5(1(2(1(2(3(0(2(2(2(2(2(3(3(x1)))))))))))))))) (14)
0(3(0(4(4(0(0(4(4(0(1(3(x1)))))))))))) → 5(2(1(2(4(2(2(4(0(4(3(1(0(2(3(2(5(3(x1)))))))))))))))))) (15)
0(3(4(1(3(4(1(0(1(4(3(1(x1)))))))))))) → 2(2(2(3(2(0(2(5(2(2(2(1(5(2(4(1(x1)))))))))))))))) (16)
0(3(4(3(5(0(0(4(4(3(1(1(x1)))))))))))) → 4(2(1(1(2(2(5(1(2(0(4(5(4(2(1(2(5(x1))))))))))))))))) (17)
0(3(5(4(0(1(1(4(0(5(5(0(x1)))))))))))) → 3(2(4(1(0(5(1(1(2(3(5(3(2(1(2(2(x1)))))))))))))))) (18)
0(4(0(3(1(4(0(4(1(4(5(5(x1)))))))))))) → 2(5(1(2(2(4(2(5(2(5(4(1(0(4(x1)))))))))))))) (19)
0(4(3(1(3(0(4(5(1(5(0(0(x1)))))))))))) → 3(5(1(2(1(3(2(2(2(2(0(3(2(2(2(2(4(5(x1)))))))))))))))))) (20)
0(4(3(5(3(1(4(4(0(0(0(4(x1)))))))))))) → 5(2(3(3(2(4(3(5(2(3(4(2(2(3(3(2(0(x1))))))))))))))))) (21)
0(4(5(0(0(2(0(3(3(5(5(5(x1)))))))))))) → 2(4(2(2(2(5(1(0(2(4(4(2(1(2(2(x1))))))))))))))) (22)
0(5(0(4(1(0(1(0(5(4(0(5(x1)))))))))))) → 5(3(1(5(3(2(5(3(1(0(2(3(5(2(0(4(x1)))))))))))))))) (23)
0(5(1(5(0(0(5(4(5(0(4(1(x1)))))))))))) → 5(5(2(4(2(5(5(0(4(0(1(1(2(5(5(5(5(x1))))))))))))))))) (24)
0(5(3(1(1(1(4(4(3(0(1(4(x1)))))))))))) → 2(0(2(4(5(5(2(2(3(3(5(0(5(2(3(2(x1)))))))))))))))) (25)
0(5(3(1(2(5(1(3(4(3(5(0(x1)))))))))))) → 5(2(2(5(2(0(5(5(2(5(5(5(3(5(4(2(x1)))))))))))))))) (26)
0(5(4(2(1(0(4(3(0(2(3(3(x1)))))))))))) → 3(3(3(2(3(2(0(5(4(2(3(4(1(2(3(x1))))))))))))))) (27)
0(5(4(5(0(3(3(0(4(0(5(4(x1)))))))))))) → 5(4(2(5(4(1(2(1(3(3(4(2(2(2(1(2(5(0(x1)))))))))))))))))) (28)
1(0(0(0(1(0(5(0(1(1(3(0(x1)))))))))))) → 3(5(5(2(1(2(5(5(5(0(2(3(3(1(0(2(x1)))))))))))))))) (29)
1(0(1(3(2(5(2(2(3(4(1(2(x1)))))))))))) → 3(2(1(2(0(2(3(5(4(1(2(2(2(2(x1)))))))))))))) (30)
1(0(4(3(0(0(5(4(4(1(0(5(x1)))))))))))) → 1(3(2(2(3(0(0(2(4(2(1(2(5(3(x1)))))))))))))) (31)
1(1(4(5(0(5(4(4(0(5(0(0(x1)))))))))))) → 5(4(4(1(1(4(1(2(2(5(0(2(1(2(0(5(x1)))))))))))))))) (32)
1(2(5(4(4(0(0(4(3(1(1(2(x1)))))))))))) → 5(2(2(2(3(0(4(1(5(4(2(3(2(2(x1)))))))))))))) (33)
1(3(1(3(3(4(4(4(3(0(4(4(x1)))))))))))) → 2(5(5(5(3(3(2(3(0(5(0(4(2(1(x1)))))))))))))) (34)
1(3(3(5(4(0(4(4(5(2(0(0(x1)))))))))))) → 4(2(2(1(2(5(3(3(3(5(4(5(1(5(5(x1))))))))))))))) (35)
1(4(1(0(4(3(1(0(0(5(4(0(x1)))))))))))) → 2(5(1(5(1(3(3(1(4(1(0(2(0(0(2(x1))))))))))))))) (36)
1(4(3(5(3(3(0(4(0(0(4(0(x1)))))))))))) → 1(5(3(2(2(2(2(1(5(2(5(1(0(1(5(0(x1)))))))))))))))) (37)
2(0(0(3(1(2(4(3(0(1(4(3(x1)))))))))))) → 1(1(2(2(5(0(2(1(1(5(0(5(5(2(2(3(x1)))))))))))))))) (38)
2(0(3(1(4(5(2(0(2(5(1(4(x1)))))))))))) → 1(2(5(3(2(0(1(2(4(1(3(2(5(3(5(x1))))))))))))))) (39)
2(1(0(1(5(3(1(3(1(0(3(5(x1)))))))))))) → 5(3(5(2(4(4(0(3(5(2(2(1(2(2(1(3(x1)))))))))))))))) (40)
2(2(4(0(4(0(0(5(5(4(3(5(x1)))))))))))) → 2(2(5(4(2(3(0(1(2(2(1(2(2(3(5(3(x1)))))))))))))))) (41)
2(4(0(4(4(4(0(4(1(3(2(0(x1)))))))))))) → 3(0(5(5(2(2(0(2(2(5(2(2(5(3(x1)))))))))))))) (42)
2(4(0(4(5(4(0(3(4(4(1(5(x1)))))))))))) → 2(4(1(1(5(2(3(2(1(4(0(2(2(5(5(2(3(3(x1)))))))))))))))))) (43)
2(5(1(4(0(0(5(4(0(0(4(1(x1)))))))))))) → 5(5(4(1(3(3(1(1(2(2(3(3(2(2(2(3(5(5(x1)))))))))))))))))) (44)
3(1(0(3(4(4(4(3(1(3(4(1(x1)))))))))))) → 1(2(2(4(4(1(2(0(5(2(4(1(5(4(x1)))))))))))))) (45)
3(3(4(0(4(2(2(3(4(3(0(0(x1)))))))))))) → 1(2(3(0(4(1(5(3(0(2(2(5(2(4(1(x1))))))))))))))) (46)
3(4(0(4(4(4(3(0(3(4(4(2(x1)))))))))))) → 1(2(4(5(3(2(2(2(1(2(4(0(5(3(2(0(0(1(x1)))))))))))))))))) (47)
3(4(4(4(0(4(0(0(2(3(1(4(x1)))))))))))) → 2(5(2(2(2(2(3(5(2(1(3(2(1(3(4(5(5(2(x1)))))))))))))))))) (48)
4(0(0(3(2(2(4(5(0(4(3(3(x1)))))))))))) → 5(2(2(5(2(1(3(2(2(3(3(5(5(2(2(2(4(3(x1)))))))))))))))))) (49)
4(0(1(0(1(0(0(3(3(4(0(4(x1)))))))))))) → 4(4(5(2(1(3(2(5(1(2(0(2(5(1(3(2(2(x1))))))))))))))))) (50)
4(0(1(1(4(1(3(4(5(4(3(5(x1)))))))))))) → 5(2(5(2(3(2(4(1(3(2(2(0(5(1(4(x1))))))))))))))) (51)
4(0(1(4(3(0(5(4(5(1(0(4(x1)))))))))))) → 2(1(1(5(2(1(5(5(0(3(2(4(3(2(5(x1))))))))))))))) (52)
4(0(3(1(5(1(3(1(4(0(1(2(x1)))))))))))) → 2(2(5(2(3(2(3(5(5(3(4(4(1(5(3(5(2(2(x1)))))))))))))))))) (53)
4(0(3(4(4(3(0(2(5(4(1(1(x1)))))))))))) → 0(5(3(5(5(2(2(1(2(2(3(2(5(5(4(3(x1)))))))))))))))) (54)
4(0(4(3(1(3(3(4(3(4(0(0(x1)))))))))))) → 5(3(2(2(2(5(2(2(1(0(4(2(2(4(3(2(3(x1))))))))))))))))) (55)
4(1(0(0(0(3(5(4(3(3(0(2(x1)))))))))))) → 2(2(5(3(3(5(2(3(3(1(2(2(0(2(5(3(3(x1))))))))))))))))) (56)
4(1(0(4(3(0(5(0(3(2(3(0(x1)))))))))))) → 2(3(3(2(1(4(4(5(2(0(1(5(2(5(1(1(x1)))))))))))))))) (57)
4(1(1(3(1(3(2(4(3(1(4(4(x1)))))))))))) → 4(0(1(2(3(2(2(2(3(2(3(1(4(1(2(5(3(2(x1)))))))))))))))))) (58)
4(1(1(3(2(3(1(5(0(4(0(0(x1)))))))))))) → 5(0(5(5(3(4(2(2(3(2(2(2(5(1(0(5(x1)))))))))))))))) (59)
4(1(5(2(3(0(1(5(4(3(3(0(x1)))))))))))) → 5(5(4(2(2(0(5(3(2(3(2(1(3(2(1(3(5(1(x1)))))))))))))))))) (60)
4(2(0(0(4(3(0(3(0(4(4(5(x1)))))))))))) → 2(0(5(3(2(2(3(3(5(3(5(0(1(1(2(3(0(2(x1)))))))))))))))))) (61)
4(2(2(0(4(1(4(4(0(0(3(4(x1)))))))))))) → 3(5(1(2(3(4(1(2(5(2(0(5(3(3(2(x1))))))))))))))) (62)
4(3(2(0(0(5(4(4(5(4(4(0(x1)))))))))))) → 4(1(2(3(1(2(2(0(3(5(2(0(5(2(5(1(5(0(x1)))))))))))))))))) (63)
4(3(2(1(4(4(5(0(3(0(0(4(x1)))))))))))) → 2(1(2(5(3(3(5(2(0(5(3(4(2(5(2(3(5(3(x1)))))))))))))))))) (64)
4(3(2(5(4(4(4(1(4(5(1(0(x1)))))))))))) → 2(1(5(5(2(3(3(1(2(3(2(2(3(0(1(5(x1)))))))))))))))) (65)
4(3(5(4(5(0(5(4(3(4(3(5(x1)))))))))))) → 5(3(4(2(2(0(2(2(5(5(4(3(4(0(1(5(5(x1))))))))))))))))) (66)
4(4(0(4(3(1(0(5(4(4(0(0(x1)))))))))))) → 0(4(5(5(4(3(4(5(5(3(5(1(1(3(2(5(x1)))))))))))))))) (67)
4(4(3(1(2(1(4(3(0(4(5(4(x1)))))))))))) → 3(3(5(4(4(1(2(3(0(0(1(1(2(1(2(x1))))))))))))))) (68)
4(4(3(4(3(1(4(3(4(5(0(4(x1)))))))))))) → 0(2(4(2(5(1(3(2(0(2(0(0(1(2(x1)))))))))))))) (69)
4(4(4(0(3(5(5(0(5(2(3(1(x1)))))))))))) → 5(2(2(2(2(0(2(4(1(3(0(0(1(5(3(x1))))))))))))))) (70)
4(4(4(4(4(0(3(5(1(0(2(0(x1)))))))))))) → 1(2(5(5(3(3(3(1(2(3(0(2(5(3(3(3(0(2(x1)))))))))))))))))) (71)
4(4(5(0(3(5(4(1(1(5(1(0(x1)))))))))))) → 2(2(5(5(2(3(2(2(5(3(1(2(0(2(x1)))))))))))))) (72)
4(5(0(0(1(0(2(5(4(4(0(4(x1)))))))))))) → 3(5(5(0(2(4(2(2(4(0(1(1(2(2(1(x1))))))))))))))) (73)
4(5(2(0(5(3(1(2(4(0(2(1(x1)))))))))))) → 4(2(5(3(5(5(3(5(2(2(4(3(3(2(4(x1))))))))))))))) (74)
4(5(2(1(4(2(0(3(0(0(4(0(x1)))))))))))) → 3(4(5(3(5(2(5(2(1(4(0(2(2(2(0(x1))))))))))))))) (75)
4(5(3(0(0(5(0(4(5(2(4(0(x1)))))))))))) → 5(2(2(4(3(2(2(3(3(2(3(4(1(1(2(2(0(x1))))))))))))))))) (76)
4(5(4(5(4(4(5(2(1(0(0(5(x1)))))))))))) → 5(3(5(5(5(3(3(1(2(3(4(5(2(2(3(3(5(x1))))))))))))))))) (77)
5(0(0(4(4(5(0(3(3(4(3(1(x1)))))))))))) → 5(1(1(0(4(0(2(2(0(2(5(2(2(5(5(1(1(2(x1)))))))))))))))))) (78)
5(0(1(4(0(5(2(0(0(0(0(0(x1)))))))))))) → 1(0(1(1(1(2(3(3(2(2(5(5(3(0(4(5(x1)))))))))))))))) (79)
5(0(3(5(3(4(2(1(0(3(0(4(x1)))))))))))) → 2(1(2(5(3(2(0(2(1(2(5(4(3(5(2(1(x1)))))))))))))))) (80)
5(0(5(0(4(0(0(5(2(0(0(0(x1)))))))))))) → 0(3(2(2(3(5(4(2(0(2(5(2(2(1(3(4(x1)))))))))))))))) (81)
5(1(0(0(4(2(1(1(2(1(4(2(x1)))))))))))) → 2(2(2(2(3(3(2(3(3(2(5(5(2(2(1(0(2(x1))))))))))))))))) (82)
5(1(1(1(4(4(0(3(1(4(5(0(x1)))))))))))) → 4(1(2(3(1(5(3(5(2(0(4(2(2(4(2(2(x1)))))))))))))))) (83)
5(1(3(0(3(0(3(4(1(0(5(5(x1)))))))))))) → 4(3(2(5(5(2(5(5(4(1(1(5(5(2(x1)))))))))))))) (84)
5(1(5(0(0(3(5(2(1(4(4(5(x1)))))))))))) → 3(4(2(3(2(5(2(2(3(2(2(2(1(2(3(2(5(3(x1)))))))))))))))))) (85)
5(1(5(1(1(4(5(2(4(2(1(4(x1)))))))))))) → 5(1(2(2(1(2(3(1(1(4(1(4(2(2(2(2(2(5(x1)))))))))))))))))) (86)
5(3(0(3(5(1(0(0(0(0(5(4(x1)))))))))))) → 2(3(3(1(2(2(3(2(1(5(4(1(5(1(2(1(2(x1))))))))))))))))) (87)
5(4(0(3(4(0(0(2(3(0(0(2(x1)))))))))))) → 2(1(3(5(1(1(1(2(5(4(3(3(2(1(3(x1))))))))))))))) (88)
5(4(0(4(0(4(5(3(5(4(4(4(x1)))))))))))) → 2(4(1(5(5(2(0(2(0(3(5(4(2(3(1(x1))))))))))))))) (89)
5(4(3(4(4(3(4(2(4(3(2(0(x1)))))))))))) → 2(1(2(3(0(4(2(4(2(5(3(4(1(5(x1)))))))))))))) (90)
5(4(4(0(5(2(0(3(0(0(4(2(x1)))))))))))) → 3(1(2(4(0(1(5(1(4(4(1(2(5(4(x1)))))))))))))) (91)
5(4(4(4(0(2(0(4(5(4(3(4(x1)))))))))))) → 5(2(0(2(1(1(1(1(1(0(4(2(1(1(4(x1))))))))))))))) (92)
5(4(5(1(4(3(1(3(0(0(1(0(x1)))))))))))) → 5(5(3(0(1(3(5(2(0(2(1(1(1(2(3(4(x1)))))))))))))))) (93)
5(4(5(5(5(0(3(4(3(4(4(1(x1)))))))))))) → 1(0(5(5(1(2(2(1(3(5(2(0(5(3(5(4(1(x1))))))))))))))))) (94)
5(5(0(5(0(5(0(0(3(0(3(4(x1)))))))))))) → 3(4(2(2(1(4(0(1(5(1(2(1(2(5(4(5(3(1(x1)))))))))))))))))) (95)
5(5(2(2(1(0(4(0(0(5(5(0(x1)))))))))))) → 5(3(2(1(3(1(1(2(2(2(0(5(3(3(2(5(5(x1))))))))))))))))) (96)

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
0(2(5(4(1(3(4(0(3(0(0(0(x1)))))))))))) → 4(2(4(3(3(2(2(3(0(1(5(5(3(2(0(1(x1)))))))))))))))) (97)
1(3(0(1(5(0(5(1(3(0(0(0(x1)))))))))))) → 3(3(2(1(4(4(4(2(1(5(5(2(1(3(3(x1))))))))))))))) (98)
3(4(1(5(0(4(3(4(1(1(0(0(x1)))))))))))) → 2(4(0(5(3(2(2(2(2(5(5(2(1(1(4(3(x1)))))))))))))))) (99)
0(3(0(4(4(4(3(4(3(1(0(0(x1)))))))))))) → 1(5(3(4(2(1(1(2(4(4(5(2(5(2(0(5(5(2(x1)))))))))))))))))) (100)
0(1(0(1(0(0(3(0(1(2(0(0(x1)))))))))))) → 3(0(0(1(5(3(5(5(2(4(3(4(2(1(2(x1))))))))))))))) (101)
5(3(1(0(4(1(0(0(3(4(0(0(x1)))))))))))) → 0(2(2(2(4(3(5(4(3(3(2(2(2(0(1(5(1(5(x1)))))))))))))))))) (102)
5(1(0(3(1(3(0(0(4(5(0(0(x1)))))))))))) → 2(1(2(5(4(2(2(2(1(1(4(5(5(5(5(0(1(3(x1)))))))))))))))))) (103)
3(0(3(0(0(5(0(5(4(5(0(0(x1)))))))))))) → 0(1(4(4(2(1(1(2(4(1(4(0(3(3(5(5(2(x1))))))))))))))))) (104)
0(5(2(3(0(1(3(1(0(0(1(0(x1)))))))))))) → 1(5(2(1(2(2(4(2(2(3(0(4(1(1(5(x1))))))))))))))) (105)
0(1(2(4(4(4(4(1(0(0(1(0(x1)))))))))))) → 4(3(1(2(3(2(4(2(2(2(1(3(5(1(4(2(5(5(x1)))))))))))))))))) (106)
1(1(1(0(2(0(4(4(3(1(1(0(x1)))))))))))) → 1(2(1(2(2(4(2(3(1(4(1(5(2(2(2(3(5(0(x1)))))))))))))))))) (107)
5(4(0(3(1(5(0(0(5(4(1(0(x1)))))))))))) → 5(3(5(5(2(1(4(3(5(2(1(4(5(2(1(3(3(2(x1)))))))))))))))))) (108)
3(3(4(0(1(2(1(4(4(0(2(0(x1)))))))))))) → 1(4(4(3(5(2(5(2(5(3(4(2(1(2(x1)))))))))))))) (109)
5(4(4(1(0(2(1(4(3(4(2(0(x1)))))))))))) → 3(3(2(2(2(2(2(0(3(2(1(2(1(5(2(4(x1)))))))))))))))) (110)
3(1(0(4(4(0(0(4(4(0(3(0(x1)))))))))))) → 3(5(2(3(2(0(1(3(4(0(4(2(2(4(2(1(2(5(x1)))))))))))))))))) (111)
1(3(4(1(0(1(4(3(1(4(3(0(x1)))))))))))) → 1(4(2(5(1(2(2(2(5(2(0(2(3(2(2(2(x1)))))))))))))))) (112)
1(1(3(4(4(0(0(5(3(4(3(0(x1)))))))))))) → 5(2(1(2(4(5(4(0(2(1(5(2(2(1(1(2(4(x1))))))))))))))))) (113)
0(5(5(0(4(1(1(0(4(5(3(0(x1)))))))))))) → 2(2(1(2(3(5(3(2(1(1(5(0(1(4(2(3(x1)))))))))))))))) (114)
5(5(4(1(4(0(4(1(3(0(4(0(x1)))))))))))) → 4(0(1(4(5(2(5(2(4(2(2(1(5(2(x1)))))))))))))) (115)
0(0(5(1(5(4(0(3(1(3(4(0(x1)))))))))))) → 5(4(2(2(2(2(3(0(2(2(2(2(3(1(2(1(5(3(x1)))))))))))))))))) (116)
4(0(0(0(4(4(1(3(5(3(4(0(x1)))))))))))) → 0(2(3(3(2(2(4(3(2(5(3(4(2(3(3(2(5(x1))))))))))))))))) (117)
5(5(5(3(3(0(2(0(0(5(4(0(x1)))))))))))) → 2(2(1(2(4(4(2(0(1(5(2(2(2(4(2(x1))))))))))))))) (118)
5(0(4(5(0(1(0(1(4(0(5(0(x1)))))))))))) → 4(0(2(5(3(2(0(1(3(5(2(3(5(1(3(5(x1)))))))))))))))) (119)
1(4(0(5(4(5(0(0(5(1(5(0(x1)))))))))))) → 5(5(5(5(2(1(1(0(4(0(5(5(2(4(2(5(5(x1))))))))))))))))) (120)
4(1(0(3(4(4(1(1(1(3(5(0(x1)))))))))))) → 2(3(2(5(0(5(3(3(2(2(5(5(4(2(0(2(x1)))))))))))))))) (121)
0(5(3(4(3(1(5(2(1(3(5(0(x1)))))))))))) → 2(4(5(3(5(5(5(2(5(5(0(2(5(2(2(5(x1)))))))))))))))) (122)
3(3(2(0(3(4(0(1(2(4(5(0(x1)))))))))))) → 3(2(1(4(3(2(4(5(0(2(3(2(3(3(3(x1))))))))))))))) (123)
4(5(0(4(0(3(3(0(5(4(5(0(x1)))))))))))) → 0(5(2(1(2(2(2(4(3(3(1(2(1(4(5(2(4(5(x1)))))))))))))))))) (124)
0(3(1(1(0(5(0(1(0(0(0(1(x1)))))))))))) → 2(0(1(3(3(2(0(5(5(5(2(1(2(5(5(3(x1)))))))))))))))) (125)
2(1(4(3(2(2(5(2(3(1(0(1(x1)))))))))))) → 2(2(2(2(1(4(5(3(2(0(2(1(2(3(x1)))))))))))))) (126)
5(0(1(4(4(5(0(0(3(4(0(1(x1)))))))))))) → 3(5(2(1(2(4(2(0(0(3(2(2(3(1(x1)))))))))))))) (127)
0(0(5(0(4(4(5(0(5(4(1(1(x1)))))))))))) → 5(0(2(1(2(0(5(2(2(1(4(1(1(4(4(5(x1)))))))))))))))) (128)
2(1(1(3(4(0(0(4(4(5(2(1(x1)))))))))))) → 2(2(3(2(4(5(1(4(0(3(2(2(2(5(x1)))))))))))))) (129)
4(4(0(3(4(4(4(3(3(1(3(1(x1)))))))))))) → 1(2(4(0(5(0(3(2(3(3(5(5(5(2(x1)))))))))))))) (130)
0(0(2(5(4(4(0(4(5(3(3(1(x1)))))))))))) → 5(5(1(5(4(5(3(3(3(5(2(1(2(2(4(x1))))))))))))))) (131)
0(4(5(0(0(1(3(4(0(1(4(1(x1)))))))))))) → 2(0(0(2(0(1(4(1(3(3(1(5(1(5(2(x1))))))))))))))) (132)
0(4(0(0(4(0(3(3(5(3(4(1(x1)))))))))))) → 0(5(1(0(1(5(2(5(1(2(2(2(2(3(5(1(x1)))))))))))))))) (133)
3(4(1(0(3(4(2(1(3(0(0(2(x1)))))))))))) → 3(2(2(5(5(0(5(1(1(2(0(5(2(2(1(1(x1)))))))))))))))) (134)
4(1(5(2(0(2(5(4(1(3(0(2(x1)))))))))))) → 5(3(5(2(3(1(4(2(1(0(2(3(5(2(1(x1))))))))))))))) (135)
5(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) → 3(1(2(2(1(2(2(5(3(0(4(4(2(5(3(5(x1)))))))))))))))) (136)
5(3(4(5(5(0(0(4(0(4(2(2(x1)))))))))))) → 3(5(3(2(2(1(2(2(1(0(3(2(4(5(2(2(x1)))))))))))))))) (137)
0(2(3(1(4(0(4(4(4(0(4(2(x1)))))))))))) → 3(5(2(2(5(2(2(0(2(2(5(5(0(3(x1)))))))))))))) (138)
5(1(4(4(3(0(4(5(4(0(4(2(x1)))))))))))) → 3(3(2(5(5(2(2(0(4(1(2(3(2(5(1(1(4(2(x1)))))))))))))))))) (139)
1(4(0(0(4(5(0(0(4(1(5(2(x1)))))))))))) → 5(5(3(2(2(2(3(3(2(2(1(1(3(3(1(4(5(5(x1)))))))))))))))))) (140)
1(4(3(1(3(4(4(4(3(0(1(3(x1)))))))))))) → 4(5(1(4(2(5(0(2(1(4(4(2(2(1(x1)))))))))))))) (141)
0(0(3(4(3(2(2(4(0(4(3(3(x1)))))))))))) → 1(4(2(5(2(2(0(3(5(1(4(0(3(2(1(x1))))))))))))))) (142)
2(4(4(3(0(3(4(4(4(0(4(3(x1)))))))))))) → 1(0(0(2(3(5(0(4(2(1(2(2(2(3(5(4(2(1(x1)))))))))))))))))) (143)
4(1(3(2(0(0(4(0(4(4(4(3(x1)))))))))))) → 2(5(5(4(3(1(2(3(1(2(5(3(2(2(2(2(5(2(x1)))))))))))))))))) (144)
3(3(4(0(5(4(2(2(3(0(0(4(x1)))))))))))) → 3(4(2(2(2(5(5(3(3(2(2(3(1(2(5(2(2(5(x1)))))))))))))))))) (145)
4(0(4(3(3(0(0(1(0(1(0(4(x1)))))))))))) → 2(2(3(1(5(2(0(2(1(5(2(3(1(2(5(4(4(x1))))))))))))))))) (146)
5(3(4(5(4(3(1(4(1(1(0(4(x1)))))))))))) → 4(1(5(0(2(2(3(1(4(2(3(2(5(2(5(x1))))))))))))))) (147)
4(0(1(5(4(5(0(3(4(1(0(4(x1)))))))))))) → 5(2(3(4(2(3(0(5(5(1(2(5(1(1(2(x1))))))))))))))) (148)
2(1(0(4(1(3(1(5(1(3(0(4(x1)))))))))))) → 2(2(5(3(5(1(4(4(3(5(5(3(2(3(2(5(2(2(x1)))))))))))))))))) (149)
1(1(4(5(2(0(3(4(4(3(0(4(x1)))))))))))) → 3(4(5(5(2(3(2(2(1(2(2(5(5(3(5(0(x1)))))))))))))))) (150)
0(0(4(3(4(3(3(1(3(4(0(4(x1)))))))))))) → 3(2(3(4(2(2(4(0(1(2(2(5(2(2(2(3(5(x1))))))))))))))))) (151)
2(0(3(3(4(5(3(0(0(0(1(4(x1)))))))))))) → 3(3(5(2(0(2(2(1(3(3(2(5(3(3(5(2(2(x1))))))))))))))))) (152)
0(3(2(3(0(5(0(3(4(0(1(4(x1)))))))))))) → 1(1(5(2(5(1(0(2(5(4(4(1(2(3(3(2(x1)))))))))))))))) (153)
4(4(1(3(4(2(3(1(3(1(1(4(x1)))))))))))) → 2(3(5(2(1(4(1(3(2(3(2(2(2(3(2(1(0(4(x1)))))))))))))))))) (154)
0(0(4(0(5(1(3(2(3(1(1(4(x1)))))))))))) → 5(0(1(5(2(2(2(3(2(2(4(3(5(5(0(5(x1)))))))))))))))) (155)
0(3(3(4(5(1(0(3(2(5(1(4(x1)))))))))))) → 1(5(3(1(2(3(1(2(3(2(3(5(0(2(2(4(5(5(x1)))))))))))))))))) (156)
5(4(4(0(3(0(3(4(0(0(2(4(x1)))))))))))) → 2(0(3(2(1(1(0(5(3(5(3(3(2(2(3(5(0(2(x1)))))))))))))))))) (157)
4(3(0(0(4(4(1(4(0(2(2(4(x1)))))))))))) → 2(3(3(5(0(2(5(2(1(4(3(2(1(5(3(x1))))))))))))))) (158)
0(4(4(5(4(4(5(0(0(2(3(4(x1)))))))))))) → 0(5(1(5(2(5(0(2(5(3(0(2(2(1(3(2(1(4(x1)))))))))))))))))) (159)
4(0(0(3(0(5(4(4(1(2(3(4(x1)))))))))))) → 3(5(3(2(5(2(4(3(5(0(2(5(3(3(5(2(1(2(x1)))))))))))))))))) (160)
0(1(5(4(1(4(4(4(5(2(3(4(x1)))))))))))) → 5(1(0(3(2(2(3(2(1(3(3(2(5(5(1(2(x1)))))))))))))))) (161)
5(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) → 5(5(1(0(4(3(4(5(5(2(2(0(2(2(4(3(5(x1))))))))))))))))) (162)
0(0(4(4(5(0(1(3(4(0(4(4(x1)))))))))))) → 5(2(3(1(1(5(3(5(5(4(3(4(5(5(4(0(x1)))))))))))))))) (163)
4(5(4(0(3(4(1(2(1(3(4(4(x1)))))))))))) → 2(1(2(1(1(0(0(3(2(1(4(4(5(3(3(x1))))))))))))))) (164)
4(0(5(4(3(4(1(3(4(3(4(4(x1)))))))))))) → 2(1(0(0(2(0(2(3(1(5(2(4(2(0(x1)))))))))))))) (165)
1(3(2(5(0(5(5(3(0(4(4(4(x1)))))))))))) → 3(5(1(0(0(3(1(4(2(0(2(2(2(2(5(x1))))))))))))))) (166)
0(2(0(1(5(3(0(4(4(4(4(4(x1)))))))))))) → 2(0(3(3(3(5(2(0(3(2(1(3(3(3(5(5(2(1(x1)))))))))))))))))) (167)
0(1(5(1(1(4(5(3(0(5(4(4(x1)))))))))))) → 2(0(2(1(3(5(2(2(3(2(5(5(2(2(x1)))))))))))))) (168)
4(0(4(4(5(2(0(1(0(0(5(4(x1)))))))))))) → 1(2(2(1(1(0(4(2(2(4(2(0(5(5(3(x1))))))))))))))) (169)
1(2(0(4(2(1(3(5(0(2(5(4(x1)))))))))))) → 4(2(3(3(4(2(2(5(3(5(5(3(5(2(4(x1))))))))))))))) (170)
0(4(0(0(3(0(2(4(1(2(5(4(x1)))))))))))) → 0(2(2(2(0(4(1(2(5(2(5(3(5(4(3(x1))))))))))))))) (171)
0(4(2(5(4(0(5(0(0(3(5(4(x1)))))))))))) → 0(2(2(1(1(4(3(2(3(3(2(2(3(4(2(2(5(x1))))))))))))))))) (172)
5(0(0(1(2(5(4(4(5(4(5(4(x1)))))))))))) → 5(3(3(2(2(5(4(3(2(1(3(3(5(5(5(3(5(x1))))))))))))))))) (173)
1(3(4(3(3(0(5(4(4(0(0(5(x1)))))))))))) → 2(1(1(5(5(2(2(5(2(0(2(2(0(4(0(1(1(5(x1)))))))))))))))))) (174)
0(0(0(0(0(2(5(0(4(1(0(5(x1)))))))))))) → 5(4(0(3(5(5(2(2(3(3(2(1(1(1(0(1(x1)))))))))))))))) (175)
4(0(3(0(1(2(4(3(5(3(0(5(x1)))))))))))) → 1(2(5(3(4(5(2(1(2(0(2(3(5(2(1(2(x1)))))))))))))))) (176)
0(0(0(2(5(0(0(4(0(5(0(5(x1)))))))))))) → 4(3(1(2(2(5(2(0(2(4(5(3(2(2(3(0(x1)))))))))))))))) (177)
2(4(1(2(1(1(2(4(0(0(1(5(x1)))))))))))) → 2(0(1(2(2(5(5(2(3(3(2(3(3(2(2(2(2(x1))))))))))))))))) (178)
0(5(4(1(3(0(4(4(1(1(1(5(x1)))))))))))) → 2(2(4(2(2(4(0(2(5(3(5(1(3(2(1(4(x1)))))))))))))))) (179)
5(5(0(1(4(3(0(3(0(3(1(5(x1)))))))))))) → 2(5(5(1(1(4(5(5(2(5(5(2(3(4(x1)))))))))))))) (180)
5(4(4(1(2(5(3(0(0(5(1(5(x1)))))))))))) → 3(5(2(3(2(1(2(2(2(3(2(2(5(2(3(2(4(3(x1)))))))))))))))))) (181)
4(1(2(4(2(5(4(1(1(5(1(5(x1)))))))))))) → 5(2(2(2(2(2(4(1(4(1(1(3(2(1(2(2(1(5(x1)))))))))))))))))) (182)
4(5(0(0(0(0(1(5(3(0(3(5(x1)))))))))))) → 2(1(2(1(5(1(4(5(1(2(3(2(2(1(3(3(2(x1))))))))))))))))) (183)
2(0(0(3(2(0(0(4(3(0(4(5(x1)))))))))))) → 3(1(2(3(3(4(5(2(1(1(1(5(3(1(2(x1))))))))))))))) (184)
4(4(4(5(3(5(4(0(4(0(4(5(x1)))))))))))) → 1(3(2(4(5(3(0(2(0(2(5(5(1(4(2(x1))))))))))))))) (185)
0(2(3(4(2(4(3(4(4(3(4(5(x1)))))))))))) → 5(1(4(3(5(2(4(2(4(0(3(2(1(2(x1)))))))))))))) (186)
2(4(0(0(3(0(2(5(0(4(4(5(x1)))))))))))) → 4(5(2(1(4(4(1(5(1(0(4(2(1(3(x1)))))))))))))) (187)
4(3(4(5(4(0(2(0(4(4(4(5(x1)))))))))))) → 4(1(1(2(4(0(1(1(1(1(1(2(0(2(5(x1))))))))))))))) (188)
0(1(0(0(3(1(3(4(1(5(4(5(x1)))))))))))) → 4(3(2(1(1(1(2(0(2(5(3(1(0(3(5(5(x1)))))))))))))))) (189)
1(4(4(3(4(3(0(5(5(5(4(5(x1)))))))))))) → 1(4(5(3(5(0(2(5(3(1(2(2(1(5(5(0(1(x1))))))))))))))))) (190)
4(3(0(3(0(0(5(0(5(0(5(5(x1)))))))))))) → 1(3(5(4(5(2(1(2(1(5(1(0(4(1(2(2(4(3(x1)))))))))))))))))) (191)
0(5(5(0(0(4(0(1(2(2(5(5(x1)))))))))))) → 5(5(2(3(3(5(0(2(2(2(1(1(3(1(2(3(5(x1))))))))))))))))) (192)

1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[0(x1)] = 1 · x1 + 4
[2(x1)] = 1 · x1
[5(x1)] = 1 · x1
[4(x1)] = 1 · x1 + 3
[1(x1)] = 1 · x1 + 1
[3(x1)] = 1 · x1 + 2
all of the following rules can be deleted.
0(2(5(4(1(3(4(0(3(0(0(0(x1)))))))))))) → 4(2(4(3(3(2(2(3(0(1(5(5(3(2(0(1(x1)))))))))))))))) (97)
1(3(0(1(5(0(5(1(3(0(0(0(x1)))))))))))) → 3(3(2(1(4(4(4(2(1(5(5(2(1(3(3(x1))))))))))))))) (98)
3(4(1(5(0(4(3(4(1(1(0(0(x1)))))))))))) → 2(4(0(5(3(2(2(2(2(5(5(2(1(1(4(3(x1)))))))))))))))) (99)
0(3(0(4(4(4(3(4(3(1(0(0(x1)))))))))))) → 1(5(3(4(2(1(1(2(4(4(5(2(5(2(0(5(5(2(x1)))))))))))))))))) (100)
0(1(0(1(0(0(3(0(1(2(0(0(x1)))))))))))) → 3(0(0(1(5(3(5(5(2(4(3(4(2(1(2(x1))))))))))))))) (101)
5(3(1(0(4(1(0(0(3(4(0(0(x1)))))))))))) → 0(2(2(2(4(3(5(4(3(3(2(2(2(0(1(5(1(5(x1)))))))))))))))))) (102)
5(1(0(3(1(3(0(0(4(5(0(0(x1)))))))))))) → 2(1(2(5(4(2(2(2(1(1(4(5(5(5(5(0(1(3(x1)))))))))))))))))) (103)
3(0(3(0(0(5(0(5(4(5(0(0(x1)))))))))))) → 0(1(4(4(2(1(1(2(4(1(4(0(3(3(5(5(2(x1))))))))))))))))) (104)
0(5(2(3(0(1(3(1(0(0(1(0(x1)))))))))))) → 1(5(2(1(2(2(4(2(2(3(0(4(1(1(5(x1))))))))))))))) (105)
0(1(2(4(4(4(4(1(0(0(1(0(x1)))))))))))) → 4(3(1(2(3(2(4(2(2(2(1(3(5(1(4(2(5(5(x1)))))))))))))))))) (106)
1(1(1(0(2(0(4(4(3(1(1(0(x1)))))))))))) → 1(2(1(2(2(4(2(3(1(4(1(5(2(2(2(3(5(0(x1)))))))))))))))))) (107)
5(4(0(3(1(5(0(0(5(4(1(0(x1)))))))))))) → 5(3(5(5(2(1(4(3(5(2(1(4(5(2(1(3(3(2(x1)))))))))))))))))) (108)
3(3(4(0(1(2(1(4(4(0(2(0(x1)))))))))))) → 1(4(4(3(5(2(5(2(5(3(4(2(1(2(x1)))))))))))))) (109)
5(4(4(1(0(2(1(4(3(4(2(0(x1)))))))))))) → 3(3(2(2(2(2(2(0(3(2(1(2(1(5(2(4(x1)))))))))))))))) (110)
3(1(0(4(4(0(0(4(4(0(3(0(x1)))))))))))) → 3(5(2(3(2(0(1(3(4(0(4(2(2(4(2(1(2(5(x1)))))))))))))))))) (111)
1(3(4(1(0(1(4(3(1(4(3(0(x1)))))))))))) → 1(4(2(5(1(2(2(2(5(2(0(2(3(2(2(2(x1)))))))))))))))) (112)
1(1(3(4(4(0(0(5(3(4(3(0(x1)))))))))))) → 5(2(1(2(4(5(4(0(2(1(5(2(2(1(1(2(4(x1))))))))))))))))) (113)
0(5(5(0(4(1(1(0(4(5(3(0(x1)))))))))))) → 2(2(1(2(3(5(3(2(1(1(5(0(1(4(2(3(x1)))))))))))))))) (114)
5(5(4(1(4(0(4(1(3(0(4(0(x1)))))))))))) → 4(0(1(4(5(2(5(2(4(2(2(1(5(2(x1)))))))))))))) (115)
0(0(5(1(5(4(0(3(1(3(4(0(x1)))))))))))) → 5(4(2(2(2(2(3(0(2(2(2(2(3(1(2(1(5(3(x1)))))))))))))))))) (116)
4(0(0(0(4(4(1(3(5(3(4(0(x1)))))))))))) → 0(2(3(3(2(2(4(3(2(5(3(4(2(3(3(2(5(x1))))))))))))))))) (117)
5(5(5(3(3(0(2(0(0(5(4(0(x1)))))))))))) → 2(2(1(2(4(4(2(0(1(5(2(2(2(4(2(x1))))))))))))))) (118)
5(0(4(5(0(1(0(1(4(0(5(0(x1)))))))))))) → 4(0(2(5(3(2(0(1(3(5(2(3(5(1(3(5(x1)))))))))))))))) (119)
1(4(0(5(4(5(0(0(5(1(5(0(x1)))))))))))) → 5(5(5(5(2(1(1(0(4(0(5(5(2(4(2(5(5(x1))))))))))))))))) (120)
4(1(0(3(4(4(1(1(1(3(5(0(x1)))))))))))) → 2(3(2(5(0(5(3(3(2(2(5(5(4(2(0(2(x1)))))))))))))))) (121)
0(5(3(4(3(1(5(2(1(3(5(0(x1)))))))))))) → 2(4(5(3(5(5(5(2(5(5(0(2(5(2(2(5(x1)))))))))))))))) (122)
3(3(2(0(3(4(0(1(2(4(5(0(x1)))))))))))) → 3(2(1(4(3(2(4(5(0(2(3(2(3(3(3(x1))))))))))))))) (123)
4(5(0(4(0(3(3(0(5(4(5(0(x1)))))))))))) → 0(5(2(1(2(2(2(4(3(3(1(2(1(4(5(2(4(5(x1)))))))))))))))))) (124)
0(3(1(1(0(5(0(1(0(0(0(1(x1)))))))))))) → 2(0(1(3(3(2(0(5(5(5(2(1(2(5(5(3(x1)))))))))))))))) (125)
2(1(4(3(2(2(5(2(3(1(0(1(x1)))))))))))) → 2(2(2(2(1(4(5(3(2(0(2(1(2(3(x1)))))))))))))) (126)
5(0(1(4(4(5(0(0(3(4(0(1(x1)))))))))))) → 3(5(2(1(2(4(2(0(0(3(2(2(3(1(x1)))))))))))))) (127)
0(0(5(0(4(4(5(0(5(4(1(1(x1)))))))))))) → 5(0(2(1(2(0(5(2(2(1(4(1(1(4(4(5(x1)))))))))))))))) (128)
2(1(1(3(4(0(0(4(4(5(2(1(x1)))))))))))) → 2(2(3(2(4(5(1(4(0(3(2(2(2(5(x1)))))))))))))) (129)
4(4(0(3(4(4(4(3(3(1(3(1(x1)))))))))))) → 1(2(4(0(5(0(3(2(3(3(5(5(5(2(x1)))))))))))))) (130)
0(0(2(5(4(4(0(4(5(3(3(1(x1)))))))))))) → 5(5(1(5(4(5(3(3(3(5(2(1(2(2(4(x1))))))))))))))) (131)
0(4(5(0(0(1(3(4(0(1(4(1(x1)))))))))))) → 2(0(0(2(0(1(4(1(3(3(1(5(1(5(2(x1))))))))))))))) (132)
0(4(0(0(4(0(3(3(5(3(4(1(x1)))))))))))) → 0(5(1(0(1(5(2(5(1(2(2(2(2(3(5(1(x1)))))))))))))))) (133)
3(4(1(0(3(4(2(1(3(0(0(2(x1)))))))))))) → 3(2(2(5(5(0(5(1(1(2(0(5(2(2(1(1(x1)))))))))))))))) (134)
4(1(5(2(0(2(5(4(1(3(0(2(x1)))))))))))) → 5(3(5(2(3(1(4(2(1(0(2(3(5(2(1(x1))))))))))))))) (135)
5(3(4(5(5(0(0(4(0(4(2(2(x1)))))))))))) → 3(5(3(2(2(1(2(2(1(0(3(2(4(5(2(2(x1)))))))))))))))) (137)
0(2(3(1(4(0(4(4(4(0(4(2(x1)))))))))))) → 3(5(2(2(5(2(2(0(2(2(5(5(0(3(x1)))))))))))))) (138)
5(1(4(4(3(0(4(5(4(0(4(2(x1)))))))))))) → 3(3(2(5(5(2(2(0(4(1(2(3(2(5(1(1(4(2(x1)))))))))))))))))) (139)
1(4(0(0(4(5(0(0(4(1(5(2(x1)))))))))))) → 5(5(3(2(2(2(3(3(2(2(1(1(3(3(1(4(5(5(x1)))))))))))))))))) (140)
1(4(3(1(3(4(4(4(3(0(1(3(x1)))))))))))) → 4(5(1(4(2(5(0(2(1(4(4(2(2(1(x1)))))))))))))) (141)
0(0(3(4(3(2(2(4(0(4(3(3(x1)))))))))))) → 1(4(2(5(2(2(0(3(5(1(4(0(3(2(1(x1))))))))))))))) (142)
2(4(4(3(0(3(4(4(4(0(4(3(x1)))))))))))) → 1(0(0(2(3(5(0(4(2(1(2(2(2(3(5(4(2(1(x1)))))))))))))))))) (143)
4(1(3(2(0(0(4(0(4(4(4(3(x1)))))))))))) → 2(5(5(4(3(1(2(3(1(2(5(3(2(2(2(2(5(2(x1)))))))))))))))))) (144)
3(3(4(0(5(4(2(2(3(0(0(4(x1)))))))))))) → 3(4(2(2(2(5(5(3(3(2(2(3(1(2(5(2(2(5(x1)))))))))))))))))) (145)
4(0(4(3(3(0(0(1(0(1(0(4(x1)))))))))))) → 2(2(3(1(5(2(0(2(1(5(2(3(1(2(5(4(4(x1))))))))))))))))) (146)
5(3(4(5(4(3(1(4(1(1(0(4(x1)))))))))))) → 4(1(5(0(2(2(3(1(4(2(3(2(5(2(5(x1))))))))))))))) (147)
4(0(1(5(4(5(0(3(4(1(0(4(x1)))))))))))) → 5(2(3(4(2(3(0(5(5(1(2(5(1(1(2(x1))))))))))))))) (148)
2(1(0(4(1(3(1(5(1(3(0(4(x1)))))))))))) → 2(2(5(3(5(1(4(4(3(5(5(3(2(3(2(5(2(2(x1)))))))))))))))))) (149)
1(1(4(5(2(0(3(4(4(3(0(4(x1)))))))))))) → 3(4(5(5(2(3(2(2(1(2(2(5(5(3(5(0(x1)))))))))))))))) (150)
0(0(4(3(4(3(3(1(3(4(0(4(x1)))))))))))) → 3(2(3(4(2(2(4(0(1(2(2(5(2(2(2(3(5(x1))))))))))))))))) (151)
2(0(3(3(4(5(3(0(0(0(1(4(x1)))))))))))) → 3(3(5(2(0(2(2(1(3(3(2(5(3(3(5(2(2(x1))))))))))))))))) (152)
0(3(2(3(0(5(0(3(4(0(1(4(x1)))))))))))) → 1(1(5(2(5(1(0(2(5(4(4(1(2(3(3(2(x1)))))))))))))))) (153)
4(4(1(3(4(2(3(1(3(1(1(4(x1)))))))))))) → 2(3(5(2(1(4(1(3(2(3(2(2(2(3(2(1(0(4(x1)))))))))))))))))) (154)
0(0(4(0(5(1(3(2(3(1(1(4(x1)))))))))))) → 5(0(1(5(2(2(2(3(2(2(4(3(5(5(0(5(x1)))))))))))))))) (155)
0(3(3(4(5(1(0(3(2(5(1(4(x1)))))))))))) → 1(5(3(1(2(3(1(2(3(2(3(5(0(2(2(4(5(5(x1)))))))))))))))))) (156)
5(4(4(0(3(0(3(4(0(0(2(4(x1)))))))))))) → 2(0(3(2(1(1(0(5(3(5(3(3(2(2(3(5(0(2(x1)))))))))))))))))) (157)
4(3(0(0(4(4(1(4(0(2(2(4(x1)))))))))))) → 2(3(3(5(0(2(5(2(1(4(3(2(1(5(3(x1))))))))))))))) (158)
0(4(4(5(4(4(5(0(0(2(3(4(x1)))))))))))) → 0(5(1(5(2(5(0(2(5(3(0(2(2(1(3(2(1(4(x1)))))))))))))))))) (159)
4(0(0(3(0(5(4(4(1(2(3(4(x1)))))))))))) → 3(5(3(2(5(2(4(3(5(0(2(5(3(3(5(2(1(2(x1)))))))))))))))))) (160)
0(1(5(4(1(4(4(4(5(2(3(4(x1)))))))))))) → 5(1(0(3(2(2(3(2(1(3(3(2(5(5(1(2(x1)))))))))))))))) (161)
0(0(4(4(5(0(1(3(4(0(4(4(x1)))))))))))) → 5(2(3(1(1(5(3(5(5(4(3(4(5(5(4(0(x1)))))))))))))))) (163)
4(5(4(0(3(4(1(2(1(3(4(4(x1)))))))))))) → 2(1(2(1(1(0(0(3(2(1(4(4(5(3(3(x1))))))))))))))) (164)
4(0(5(4(3(4(1(3(4(3(4(4(x1)))))))))))) → 2(1(0(0(2(0(2(3(1(5(2(4(2(0(x1)))))))))))))) (165)
1(3(2(5(0(5(5(3(0(4(4(4(x1)))))))))))) → 3(5(1(0(0(3(1(4(2(0(2(2(2(2(5(x1))))))))))))))) (166)
0(2(0(1(5(3(0(4(4(4(4(4(x1)))))))))))) → 2(0(3(3(3(5(2(0(3(2(1(3(3(3(5(5(2(1(x1)))))))))))))))))) (167)
0(1(5(1(1(4(5(3(0(5(4(4(x1)))))))))))) → 2(0(2(1(3(5(2(2(3(2(5(5(2(2(x1)))))))))))))) (168)
4(0(4(4(5(2(0(1(0(0(5(4(x1)))))))))))) → 1(2(2(1(1(0(4(2(2(4(2(0(5(5(3(x1))))))))))))))) (169)
1(2(0(4(2(1(3(5(0(2(5(4(x1)))))))))))) → 4(2(3(3(4(2(2(5(3(5(5(3(5(2(4(x1))))))))))))))) (170)
0(4(0(0(3(0(2(4(1(2(5(4(x1)))))))))))) → 0(2(2(2(0(4(1(2(5(2(5(3(5(4(3(x1))))))))))))))) (171)
0(4(2(5(4(0(5(0(0(3(5(4(x1)))))))))))) → 0(2(2(1(1(4(3(2(3(3(2(2(3(4(2(2(5(x1))))))))))))))))) (172)
5(0(0(1(2(5(4(4(5(4(5(4(x1)))))))))))) → 5(3(3(2(2(5(4(3(2(1(3(3(5(5(5(3(5(x1))))))))))))))))) (173)
1(3(4(3(3(0(5(4(4(0(0(5(x1)))))))))))) → 2(1(1(5(5(2(2(5(2(0(2(2(0(4(0(1(1(5(x1)))))))))))))))))) (174)
0(0(0(0(0(2(5(0(4(1(0(5(x1)))))))))))) → 5(4(0(3(5(5(2(2(3(3(2(1(1(1(0(1(x1)))))))))))))))) (175)
4(0(3(0(1(2(4(3(5(3(0(5(x1)))))))))))) → 1(2(5(3(4(5(2(1(2(0(2(3(5(2(1(2(x1)))))))))))))))) (176)
0(0(0(2(5(0(0(4(0(5(0(5(x1)))))))))))) → 4(3(1(2(2(5(2(0(2(4(5(3(2(2(3(0(x1)))))))))))))))) (177)
2(4(1(2(1(1(2(4(0(0(1(5(x1)))))))))))) → 2(0(1(2(2(5(5(2(3(3(2(3(3(2(2(2(2(x1))))))))))))))))) (178)
0(5(4(1(3(0(4(4(1(1(1(5(x1)))))))))))) → 2(2(4(2(2(4(0(2(5(3(5(1(3(2(1(4(x1)))))))))))))))) (179)
5(5(0(1(4(3(0(3(0(3(1(5(x1)))))))))))) → 2(5(5(1(1(4(5(5(2(5(5(2(3(4(x1)))))))))))))) (180)
5(4(4(1(2(5(3(0(0(5(1(5(x1)))))))))))) → 3(5(2(3(2(1(2(2(2(3(2(2(5(2(3(2(4(3(x1)))))))))))))))))) (181)
4(5(0(0(0(0(1(5(3(0(3(5(x1)))))))))))) → 2(1(2(1(5(1(4(5(1(2(3(2(2(1(3(3(2(x1))))))))))))))))) (183)
2(0(0(3(2(0(0(4(3(0(4(5(x1)))))))))))) → 3(1(2(3(3(4(5(2(1(1(1(5(3(1(2(x1))))))))))))))) (184)
4(4(4(5(3(5(4(0(4(0(4(5(x1)))))))))))) → 1(3(2(4(5(3(0(2(0(2(5(5(1(4(2(x1))))))))))))))) (185)
0(2(3(4(2(4(3(4(4(3(4(5(x1)))))))))))) → 5(1(4(3(5(2(4(2(4(0(3(2(1(2(x1)))))))))))))) (186)
2(4(0(0(3(0(2(5(0(4(4(5(x1)))))))))))) → 4(5(2(1(4(4(1(5(1(0(4(2(1(3(x1)))))))))))))) (187)
4(3(4(5(4(0(2(0(4(4(4(5(x1)))))))))))) → 4(1(1(2(4(0(1(1(1(1(1(2(0(2(5(x1))))))))))))))) (188)
0(1(0(0(3(1(3(4(1(5(4(5(x1)))))))))))) → 4(3(2(1(1(1(2(0(2(5(3(1(0(3(5(5(x1)))))))))))))))) (189)
1(4(4(3(4(3(0(5(5(5(4(5(x1)))))))))))) → 1(4(5(3(5(0(2(5(3(1(2(2(1(5(5(0(1(x1))))))))))))))))) (190)
4(3(0(3(0(0(5(0(5(0(5(5(x1)))))))))))) → 1(3(5(4(5(2(1(2(1(5(1(0(4(1(2(2(4(3(x1)))))))))))))))))) (191)
0(5(5(0(0(4(0(1(2(2(5(5(x1)))))))))))) → 5(5(2(3(3(5(0(2(2(2(1(1(3(1(2(3(5(x1))))))))))))))))) (192)

1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
5#(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) → 5#(3(0(4(4(2(5(3(5(x1))))))))) (193)
5#(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) → 4#(4(2(5(3(5(x1)))))) (194)
5#(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) → 4#(2(5(3(5(x1))))) (195)
5#(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) → 5#(3(5(x1))) (196)
5#(3(0(1(3(1(3(5(1(0(1(2(x1)))))))))))) → 5#(x1) (197)
5#(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) → 5#(5(1(0(4(3(4(5(5(2(2(0(2(2(4(3(5(x1))))))))))))))))) (198)
5#(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) → 5#(1(0(4(3(4(5(5(2(2(0(2(2(4(3(5(x1)))))))))))))))) (199)
5#(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) → 4#(3(4(5(5(2(2(0(2(2(4(3(5(x1))))))))))))) (200)
5#(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) → 4#(5(5(2(2(0(2(2(4(3(5(x1))))))))))) (201)
5#(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) → 5#(5(2(2(0(2(2(4(3(5(x1)))))))))) (202)
5#(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) → 5#(2(2(0(2(2(4(3(5(x1))))))))) (203)
5#(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) → 4#(3(5(x1))) (204)
5#(3(4(3(4(5(0(5(4(5(3(4(x1)))))))))))) → 5#(x1) (205)
4#(1(2(4(2(5(4(1(1(5(1(5(x1)))))))))))) → 5#(2(2(2(2(2(4(1(4(1(1(3(2(1(2(2(1(5(x1)))))))))))))))))) (206)
4#(1(2(4(2(5(4(1(1(5(1(5(x1)))))))))))) → 4#(1(4(1(1(3(2(1(2(2(1(5(x1)))))))))))) (207)
4#(1(2(4(2(5(4(1(1(5(1(5(x1)))))))))))) → 4#(1(1(3(2(1(2(2(1(5(x1)))))))))) (208)

1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.