Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/25743)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[5(x1)] = x1 +
6
[4(x1)] = x1 +
7
[3(x1)] = x1 +
6
[2(x1)] = x1 +
6
[1(x1)] = x1 +
6
[0(x1)] = x1 +
7
all of the following rules can be deleted.
0(0(0(2(2(3(4(4(3(3(x1)))))))))) 0(2(3(0(3(2(1(5(1(3(x1)))))))))) (8)
0(4(5(0(0(4(2(4(5(0(x1)))))))))) 3(5(3(5(5(4(0(2(2(3(x1)))))))))) (9)
4(0(5(4(0(2(4(0(4(3(x1)))))))))) 2(3(1(3(5(3(1(2(4(5(x1)))))))))) (13)
0(0(5(2(2(4(4(3(3(4(0(x1))))))))))) 4(0(4(2(3(1(5(3(5(5(x1)))))))))) (14)
0(2(2(5(5(0(0(4(5(3(4(x1))))))))))) 4(0(5(1(3(5(5(4(5(0(x1)))))))))) (15)
0(4(0(4(5(3(3(0(5(5(2(x1))))))))))) 4(5(3(5(2(2(1(1(4(3(x1)))))))))) (16)
0(4(3(0(0(0(4(3(2(3(3(x1))))))))))) 2(5(1(5(2(4(5(4(3(2(x1)))))))))) (17)
0(5(2(0(0(2(1(4(2(4(5(x1))))))))))) 5(0(4(3(4(2(5(5(4(1(x1)))))))))) (19)
1(0(1(5(1(5(3(3(1(4(0(x1))))))))))) 3(1(2(1(5(2(4(5(1(1(x1)))))))))) (20)
1(1(1(2(2(5(2(1(3(1(0(x1))))))))))) 1(5(1(1(3(5(0(0(2(4(x1)))))))))) (21)
2(0(5(0(5(4(4(3(1(3(2(x1))))))))))) 2(1(0(3(1(2(1(3(4(0(x1)))))))))) (22)
2(2(0(2(2(5(0(3(2(0(5(x1))))))))))) 5(0(3(5(4(2(2(3(1(0(x1)))))))))) (23)
2(5(3(1(0(1(4(4(2(2(4(x1))))))))))) 0(5(1(0(0(2(0(5(5(1(x1)))))))))) (24)
3(1(3(2(1(0(5(3(4(0(1(x1))))))))))) 1(2(0(4(0(3(2(0(4(0(x1)))))))))) (25)
3(1(3(3(3(0(4(1(1(3(0(x1))))))))))) 1(0(2(1(2(1(0(1(1(3(x1)))))))))) (26)
3(2(2(2(1(1(2(0(0(2(0(x1))))))))))) 4(4(2(5(4(5(5(0(5(0(x1)))))))))) (27)
3(2(5(3(4(4(0(1(3(5(4(x1))))))))))) 5(0(1(3(5(5(1(3(4(2(x1)))))))))) (28)
3(3(3(4(0(2(5(4(5(0(0(x1))))))))))) 3(1(5(1(1(5(2(3(1(4(x1)))))))))) (29)
3(4(2(2(2(3(1(3(1(2(1(x1))))))))))) 3(4(5(5(4(3(2(1(5(4(x1)))))))))) (30)
3(5(4(4(5(1(1(5(0(2(0(x1))))))))))) 3(1(5(1(3(5(0(1(5(1(x1)))))))))) (31)
3(5(5(4(5(3(0(2(5(5(1(x1))))))))))) 3(1(1(2(4(2(3(0(2(5(x1)))))))))) (32)
4(0(3(0(0(3(0(5(1(4(3(x1))))))))))) 1(2(1(5(5(5(0(4(1(1(x1)))))))))) (33)
4(0(5(2(5(3(0(0(3(5(5(x1))))))))))) 0(0(5(2(3(0(3(1(5(5(x1)))))))))) (34)
4(0(5(4(5(5(3(4(3(4(1(x1))))))))))) 3(4(1(1(3(1(4(0(1(4(x1)))))))))) (35)
4(0(5(5(2(0(4(0(2(3(5(x1))))))))))) 5(5(0(4(3(5(4(1(5(1(x1)))))))))) (36)
4(1(2(0(5(5(4(0(0(0(2(x1))))))))))) 3(3(5(4(5(3(2(0(0(2(x1)))))))))) (37)
4(1(3(3(1(5(1(1(2(4(3(x1))))))))))) 0(1(2(3(3(2(1(3(3(2(x1)))))))))) (38)
4(1(3(5(2(3(5(5(0(0(3(x1))))))))))) 5(2(3(0(3(5(2(3(5(3(x1)))))))))) (39)
4(2(1(2(2(3(3(3(1(3(2(x1))))))))))) 5(5(2(3(4(2(5(4(0(3(x1)))))))))) (40)
4(4(3(3(3(2(4(2(5(1(4(x1))))))))))) 2(0(3(4(4(1(3(0(2(0(x1)))))))))) (41)
4(5(4(0(2(5(0(2(3(2(5(x1))))))))))) 3(3(4(4(5(2(3(5(3(0(x1)))))))))) (42)
5(0(5(0(0(4(0(1(3(4(1(x1))))))))))) 2(2(4(2(1(1(3(3(3(0(x1)))))))))) (43)
5(1(0(3(5(0(1(1(3(4(3(x1))))))))))) 1(0(3(0(0(4(2(4(5(3(x1)))))))))) (44)
5(5(0(5(3(4(1(2(3(2(2(x1))))))))))) 1(2(3(5(5(0(1(3(5(5(x1)))))))))) (45)
5(5(3(3(0(1(4(1(3(3(0(x1))))))))))) 2(3(3(4(5(4(2(2(0(1(x1)))))))))) (46)
0(0(0(5(1(5(3(5(1(3(2(3(x1)))))))))))) 1(3(3(0(1(4(1(0(5(5(x1)))))))))) (47)
0(5(5(1(1(1(2(5(2(3(5(5(x1)))))))))))) 1(3(5(2(3(4(3(3(4(3(x1)))))))))) (48)
2(1(2(0(5(0(3(5(1(2(3(5(x1)))))))))))) 1(0(0(4(5(4(1(4(1(0(x1)))))))))) (49)
2(3(2(1(1(1(0(2(1(3(5(1(x1)))))))))))) 5(4(3(0(1(2(3(3(2(5(x1)))))))))) (50)
2(3(4(3(5(1(2(4(2(0(2(1(x1)))))))))))) 2(4(1(3(2(2(5(5(1(0(x1)))))))))) (51)
4(3(1(3(5(1(5(1(5(0(2(1(x1)))))))))))) 0(1(3(1(0(4(0(0(5(3(x1)))))))))) (52)
4(3(3(0(5(2(0(4(4(5(1(2(x1)))))))))))) 2(0(1(1(5(1(1(4(0(0(x1)))))))))) (53)
5(1(2(1(0(2(3(1(3(1(0(0(x1)))))))))))) 5(2(0(4(2(1(4(1(1(3(x1)))))))))) (54)
5(2(3(3(1(0(1(1(1(4(1(4(x1)))))))))))) 0(2(4(0(4(0(4(0(0(1(x1)))))))))) (55)
0(1(1(1(2(0(1(3(0(4(2(3(3(x1))))))))))))) 0(4(1(2(4(2(5(0(0(0(x1)))))))))) (56)
0(1(1(4(1(3(2(4(3(5(5(0(1(x1))))))))))))) 4(3(2(0(5(0(4(0(4(4(x1)))))))))) (57)
0(1(1(5(1(1(4(4(5(0(4(2(1(x1))))))))))))) 0(3(2(0(0(4(3(1(0(4(x1)))))))))) (58)
4(1(1(3(1(3(2(1(2(2(2(0(5(x1))))))))))))) 0(3(5(4(0(1(4(0(5(0(x1)))))))))) (59)
4(3(1(1(2(1(2(0(5(2(0(3(2(x1))))))))))))) 4(4(4(4(4(0(0(3(4(1(x1)))))))))) (60)
5(1(4(4(3(1(5(4(3(5(1(2(0(x1))))))))))))) 2(2(1(3(0(0(4(3(2(5(x1)))))))))) (61)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 258 ruless (increase limit for explicit display).

1.1.1 Semantic Labeling

The following interpretations form a model of the rules.

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

We obtain the labeled TRS

There are 1548 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
30
[51(x1)] = x1 +
0
[52(x1)] = x1 +
30
[53(x1)] = x1 +
20
[54(x1)] = x1 +
1
[55(x1)] = x1 +
2
[40(x1)] = x1 +
0
[41(x1)] = x1 +
5
[42(x1)] = x1 +
30
[43(x1)] = x1 +
0
[44(x1)] = x1 +
10
[45(x1)] = x1 +
30
[30(x1)] = x1 +
10
[31(x1)] = x1 +
20
[32(x1)] = x1 +
40
[33(x1)] = x1 +
10
[34(x1)] = x1 +
0
[35(x1)] = x1 +
30
[20(x1)] = x1 +
30
[21(x1)] = x1 +
32
[22(x1)] = x1 +
0
[23(x1)] = x1 +
30
[24(x1)] = x1 +
30
[25(x1)] = x1 +
0
[10(x1)] = x1 +
2
[11(x1)] = x1 +
1
[12(x1)] = x1 +
74
[13(x1)] = x1 +
40
[14(x1)] = x1 +
0
[15(x1)] = x1 +
0
[00(x1)] = x1 +
5
[01(x1)] = x1 +
0
[02(x1)] = x1 +
30
[03(x1)] = x1 +
0
[04(x1)] = x1 +
30
[05(x1)] = x1 +
40
all of the following rules can be deleted.

There are 1512 ruless (increase limit for explicit display).

1.1.1.1.1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
25(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 25(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1900)
24(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 24(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1901)
23(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 23(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1902)
22(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 22(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1903)
21(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 21(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1904)
20(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 20(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1905)
25(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 25(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1906)
24(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 24(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1907)
23(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 23(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1908)
22(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 22(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1909)
21(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 21(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1910)
20(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 20(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1911)
25(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 25(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1912)
24(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 24(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1913)
23(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 23(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1914)
22(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 22(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1915)
21(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 21(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1916)
20(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 20(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1917)
25(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 25(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1918)
24(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 24(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1919)
23(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 23(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1920)
22(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 22(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1921)
21(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 21(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1922)
20(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 20(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1923)
25(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 25(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1924)
24(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 24(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1925)
23(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 23(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1926)
22(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 22(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1927)
21(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 21(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1928)
20(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 20(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1929)
25(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 25(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1930)
24(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 24(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1931)
23(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 23(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1932)
22(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 22(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1933)
21(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 21(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1934)
20(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 20(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1935)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 20#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1936)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1))))))))))))))))))))) (1937)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 20#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1938)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1))))))))))))))))))))) (1939)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 20#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1940)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1))))))))))))))))))))) (1941)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 20#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1942)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1))))))))))))))))))))) (1943)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 20#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1944)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1))))))))))))))))))))) (1945)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 20#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1946)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1))))))))))))))))))))) (1947)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 21#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1948)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1))))))))))))))))))))) (1949)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 21#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1950)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1))))))))))))))))))))) (1951)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 21#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1952)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1))))))))))))))))))))) (1953)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 21#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1954)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1))))))))))))))))))))) (1955)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 21#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1956)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1))))))))))))))))))))) (1957)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 21#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1958)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1))))))))))))))))))))) (1959)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 22#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1960)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1))))))))))))))))))))) (1961)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 22#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1962)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1))))))))))))))))))))) (1963)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 22#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1964)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1))))))))))))))))))))) (1965)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 22#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1966)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1))))))))))))))))))))) (1967)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 22#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1968)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1))))))))))))))))))))) (1969)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 22#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1970)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1))))))))))))))))))))) (1971)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 23#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1972)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1))))))))))))))))))))) (1973)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 23#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1974)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1))))))))))))))))))))) (1975)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 23#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1976)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1))))))))))))))))))))) (1977)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 23#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1978)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1))))))))))))))))))))) (1979)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 23#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1980)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1))))))))))))))))))))) (1981)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 23#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1982)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1))))))))))))))))))))) (1983)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1))))))))))))))))))))) (1984)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 24#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1985)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1))))))))))))))))))))) (1986)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 24#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1987)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1))))))))))))))))))))) (1988)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 24#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1989)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1))))))))))))))))))))) (1990)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 24#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1991)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1))))))))))))))))))))) (1992)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 24#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1993)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1))))))))))))))))))))) (1994)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 24#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1995)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1))))))))))))))))))))) (1996)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 25#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1997)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1))))))))))))))))))))) (1998)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 25#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1999)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1))))))))))))))))))))) (2000)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 25#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (2001)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1))))))))))))))))))))) (2002)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 25#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (2003)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1))))))))))))))))))))) (2004)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 25#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (2005)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1))))))))))))))))))))) (2006)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 25#(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (2007)

1.1.1.1.1.1.1 Monotonic Reduction Pair Processor with Usable Rules

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[50(x1)] = x1 +
0
[52(x1)] = x1 +
0
[53(x1)] = x1 +
0
[54(x1)] = x1 +
0
[40(x1)] = x1 +
0
[30(x1)] = x1 +
0
[33(x1)] = x1 +
0
[20(x1)] = x1 +
0
[21(x1)] = x1 +
0
[22(x1)] = x1 +
0
[23(x1)] = x1 +
1
[24(x1)] = x1 +
0
[25(x1)] = x1 +
0
[10(x1)] = x1 +
0
[13(x1)] = x1 +
0
[00(x1)] = x1 +
0
[02(x1)] = x1 +
0
[20#(x1)] = x1 +
1
[21#(x1)] = x1 +
1
[22#(x1)] = x1 +
1
[23#(x1)] = x1 +
0
[24#(x1)] = x1 +
1
[25#(x1)] = x1 +
1
together with the usable rules
25(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 25(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1900)
24(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 24(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1901)
23(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 23(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1902)
22(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 22(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1903)
21(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 21(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1904)
20(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 20(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) (1905)
25(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 25(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1906)
24(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 24(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1907)
23(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 23(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1908)
22(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 22(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1909)
21(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 21(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1910)
20(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 20(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) (1911)
25(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 25(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1912)
24(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 24(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1913)
23(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 23(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1914)
22(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 22(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1915)
21(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 21(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1916)
20(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 20(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) (1917)
25(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 25(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1918)
24(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 24(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1919)
23(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 23(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1920)
22(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 22(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1921)
21(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 21(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1922)
20(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 20(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) (1923)
25(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 25(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1924)
24(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 24(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1925)
23(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 23(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1926)
22(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 22(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1927)
21(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 21(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1928)
20(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 20(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) (1929)
25(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 25(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1930)
24(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 24(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1931)
23(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 23(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1932)
22(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 22(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1933)
21(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 21(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1934)
20(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 20(23(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) (1935)
(w.r.t. the implicit argument filter of the reduction pair), the pairs
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1))))))))))))))))))))) (1937)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1))))))))))))))))))))) (1939)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1))))))))))))))))))))) (1941)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1))))))))))))))))))))) (1943)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1))))))))))))))))))))) (1945)
20#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1))))))))))))))))))))) (1947)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1))))))))))))))))))))) (1949)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1))))))))))))))))))))) (1951)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1))))))))))))))))))))) (1953)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1))))))))))))))))))))) (1955)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1))))))))))))))))))))) (1957)
21#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1))))))))))))))))))))) (1959)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1))))))))))))))))))))) (1961)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1))))))))))))))))))))) (1963)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1))))))))))))))))))))) (1965)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1))))))))))))))))))))) (1967)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1))))))))))))))))))))) (1969)
22#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1))))))))))))))))))))) (1971)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1))))))))))))))))))))) (1973)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1))))))))))))))))))))) (1975)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1))))))))))))))))))))) (1977)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1))))))))))))))))))))) (1979)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1))))))))))))))))))))) (1981)
23#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1))))))))))))))))))))) (1983)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1))))))))))))))))))))) (1984)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1))))))))))))))))))))) (1986)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1))))))))))))))))))))) (1988)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1))))))))))))))))))))) (1990)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1))))))))))))))))))))) (1992)
24#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1))))))))))))))))))))) (1994)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(50(x1))))))))))))))))))))) (1996)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(40(x1))))))))))))))))))))) (1998)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(30(x1))))))))))))))))))))) (2000)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(20(x1))))))))))))))))))))) (2002)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(10(x1))))))))))))))))))))) (2004)
25#(23(13(54(50(10(54(50(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1)))))))))))))))))))))) 23#(13(54(50(50(10(54(50(50(20(33(52(20(33(02(25(33(22(53(50(00(x1))))))))))))))))))))) (2006)
and no rules could be deleted.

1.1.1.1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.