Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/136280)

The rewrite relation of the following TRS is considered.

0(0(0(0(0(1(0(1(2(1(0(2(1(3(3(2(3(1(2(4(x1)))))))))))))))))))) → 4(0(1(3(0(4(2(1(3(0(1(3(2(0(4(4(1(1(1(4(x1)))))))))))))))))))) (1)
0(0(0(0(3(3(3(2(3(1(1(0(2(1(0(2(4(2(1(3(x1)))))))))))))))))))) → 1(0(0(3(4(1(1(0(4(0(2(4(1(0(2(4(0(0(1(1(x1)))))))))))))))))))) (2)
0(0(0(1(1(0(0(0(3(4(0(4(3(3(3(1(0(2(1(4(x1)))))))))))))))))))) → 2(2(0(1(1(1(1(3(0(4(2(2(4(3(1(2(4(0(3(1(x1)))))))))))))))))))) (3)
0(0(2(1(3(1(4(4(1(1(3(2(4(0(0(0(1(1(2(1(x1)))))))))))))))))))) → 0(2(0(2(4(1(2(2(1(1(1(1(1(0(0(0(1(4(1(4(x1)))))))))))))))))))) (4)
0(0(3(1(0(1(0(3(2(0(1(1(2(3(4(4(3(0(4(4(x1)))))))))))))))))))) → 3(2(0(0(0(4(4(1(1(1(3(1(1(1(0(2(1(3(0(4(x1)))))))))))))))))))) (5)
0(1(0(0(1(2(2(2(4(4(1(1(2(3(2(0(3(2(1(0(x1)))))))))))))))))))) → 4(2(1(0(4(2(2(2(4(4(0(1(1(4(3(1(3(3(2(2(x1)))))))))))))))))))) (6)
0(1(0(4(3(4(1(0(3(3(0(3(4(4(3(3(2(1(1(2(x1)))))))))))))))))))) → 4(2(3(1(1(1(2(1(0(0(4(1(4(2(4(2(4(3(1(4(x1)))))))))))))))))))) (7)
0(1(1(4(3(1(3(2(3(0(1(0(2(3(2(2(3(1(0(1(x1)))))))))))))))))))) → 0(1(0(4(0(1(4(2(3(1(4(4(0(3(1(1(2(3(1(1(x1)))))))))))))))))))) (8)
0(1(3(1(1(3(4(1(0(0(1(3(4(2(4(1(4(3(4(0(x1)))))))))))))))))))) → 4(1(4(1(3(1(2(1(2(2(1(4(4(1(4(0(3(1(4(0(x1)))))))))))))))))))) (9)
0(1(4(1(4(2(4(1(0(4(4(0(1(1(0(2(3(2(4(0(x1)))))))))))))))))))) → 0(1(1(3(4(1(2(2(2(1(3(4(0(0(1(4(1(4(2(1(x1)))))))))))))))))))) (10)
0(2(1(2(2(1(0(1(2(0(0(2(0(4(3(2(2(0(0(1(x1)))))))))))))))))))) → 3(4(1(0(1(0(4(4(3(1(0(3(3(2(1(0(1(4(1(1(x1)))))))))))))))))))) (11)
0(2(1(2(3(4(3(2(1(0(2(3(4(0(3(0(3(4(0(3(x1)))))))))))))))))))) → 3(2(1(4(3(0(2(3(1(2(2(3(1(2(2(1(0(3(4(0(x1)))))))))))))))))))) (12)
0(2(1(4(2(3(3(3(0(4(1(0(2(1(2(1(4(2(3(0(x1)))))))))))))))))))) → 2(4(1(1(0(2(2(1(1(3(1(1(4(1(3(4(0(1(3(4(x1)))))))))))))))))))) (13)
0(2(2(2(3(0(4(1(4(2(3(0(4(2(1(0(1(0(2(1(x1)))))))))))))))))))) → 1(1(1(2(1(4(1(4(1(2(3(4(1(0(2(4(1(4(3(4(x1)))))))))))))))))))) (14)
0(2(2(3(2(2(0(1(1(4(3(1(3(3(3(3(1(3(4(1(x1)))))))))))))))))))) → 0(1(0(3(2(0(1(4(1(1(3(4(4(0(0(1(2(0(4(2(x1)))))))))))))))))))) (15)
0(3(0(1(4(2(4(2(1(3(1(4(3(4(2(4(4(3(0(1(x1)))))))))))))))))))) → 0(1(3(4(3(4(4(0(1(3(2(2(2(4(4(1(3(2(2(4(x1)))))))))))))))))))) (16)
0(3(1(3(2(4(3(0(4(4(4(1(2(3(2(4(1(3(0(4(x1)))))))))))))))))))) → 3(1(1(4(3(1(1(4(1(0(2(0(2(4(4(3(2(2(0(1(x1)))))))))))))))))))) (17)
0(3(3(4(3(4(2(0(2(1(0(1(1(1(3(1(1(2(4(0(x1)))))))))))))))))))) → 0(1(4(2(1(1(1(4(1(4(0(2(3(0(2(3(4(4(4(2(x1)))))))))))))))))))) (18)
0(3(4(0(3(1(1(2(3(0(1(4(2(3(3(2(3(0(2(4(x1)))))))))))))))))))) → 0(3(4(2(4(2(1(0(0(1(0(3(4(1(0(3(1(2(0(1(x1)))))))))))))))))))) (19)
0(3(4(4(2(4(3(1(3(1(3(3(4(4(3(1(0(1(0(1(x1)))))))))))))))))))) → 3(2(2(0(1(4(0(1(4(0(3(1(4(1(4(1(4(1(2(1(x1)))))))))))))))))))) (20)
0(4(1(3(1(2(0(3(1(0(1(4(2(4(2(1(0(1(4(3(x1)))))))))))))))))))) → 1(2(2(2(4(4(0(1(1(0(0(0(1(1(4(0(1(4(3(1(x1)))))))))))))))))))) (21)
0(4(2(2(4(2(4(1(2(4(1(1(0(4(3(4(0(3(1(1(x1)))))))))))))))))))) → 2(1(1(2(4(0(0(0(1(2(0(2(1(1(1(1(0(0(1(2(x1)))))))))))))))))))) (22)
0(4(4(0(2(0(0(0(1(4(1(3(0(3(4(0(3(4(3(4(x1)))))))))))))))))))) → 3(2(0(2(2(1(4(3(3(4(1(4(3(4(1(3(1(1(2(1(x1)))))))))))))))))))) (23)
1(0(1(4(1(0(0(0(3(4(1(2(0(2(2(1(2(2(4(0(x1)))))))))))))))))))) → 0(1(3(1(0(4(3(3(4(4(1(2(2(1(1(0(4(1(3(1(x1)))))))))))))))))))) (24)
1(0(2(0(0(2(0(2(1(3(4(1(1(2(3(1(2(1(4(2(x1)))))))))))))))))))) → 1(2(1(1(1(1(2(0(2(0(3(2(1(4(3(0(2(1(2(1(x1)))))))))))))))))))) (25)
1(0(3(2(1(4(4(1(3(2(2(0(4(1(1(3(2(3(2(0(x1)))))))))))))))))))) → 2(2(0(1(2(3(1(2(0(1(1(0(1(3(0(4(2(0(3(4(x1)))))))))))))))))))) (26)
1(1(3(0(1(2(4(3(0(4(3(1(1(4(0(4(0(0(0(4(x1)))))))))))))))))))) → 3(4(3(3(4(0(0(1(2(2(1(1(2(2(0(4(1(3(1(2(x1)))))))))))))))))))) (27)
1(1(3(1(3(3(3(0(4(1(1(3(3(3(3(4(1(1(0(3(x1)))))))))))))))))))) → 1(4(2(2(1(1(4(0(0(4(2(1(0(4(1(1(4(0(1(0(x1)))))))))))))))))))) (28)
1(2(0(1(2(2(4(0(1(3(3(0(0(3(1(3(3(1(2(4(x1)))))))))))))))))))) → 3(1(0(1(2(0(2(4(3(3(4(4(1(1(2(1(0(4(2(4(x1)))))))))))))))))))) (29)
1(2(0(2(1(1(4(4(0(4(0(3(3(3(2(2(3(0(3(4(x1)))))))))))))))))))) → 1(2(2(0(2(4(3(1(1(1(4(1(4(2(1(3(3(0(1(0(x1)))))))))))))))))))) (30)
1(2(0(3(2(4(1(0(1(0(4(1(0(3(3(4(2(2(4(3(x1)))))))))))))))))))) → 1(1(2(0(4(4(1(3(0(0(2(2(1(2(2(2(3(2(3(0(x1)))))))))))))))))))) (31)
1(2(3(1(2(4(0(3(0(4(1(1(1(3(2(1(1(3(3(1(x1)))))))))))))))))))) → 0(4(2(0(1(0(0(4(2(1(0(1(1(2(1(1(4(4(1(2(x1)))))))))))))))))))) (32)
1(2(3(2(3(1(1(0(1(1(0(3(0(1(0(2(1(0(2(3(x1)))))))))))))))))))) → 4(4(0(0(1(0(4(2(1(1(4(1(1(3(1(1(3(0(1(0(x1)))))))))))))))))))) (33)
1(2(4(2(1(0(2(4(0(1(1(3(0(2(3(0(4(2(4(0(x1)))))))))))))))))))) → 3(1(3(2(3(4(3(1(2(1(1(0(0(4(0(1(2(4(4(1(x1)))))))))))))))))))) (34)
1(3(1(1(3(1(2(0(0(4(0(1(1(3(1(4(1(2(2(1(x1)))))))))))))))))))) → 3(3(2(2(1(1(3(1(3(1(2(1(1(2(1(2(3(0(4(1(x1)))))))))))))))))))) (35)
1(3(2(1(3(4(4(3(0(4(2(2(2(1(2(0(1(3(1(4(x1)))))))))))))))))))) → 1(2(3(0(1(2(2(0(3(4(1(4(1(0(1(0(4(1(2(1(x1)))))))))))))))))))) (36)
1(4(1(0(2(3(3(1(1(0(4(4(3(4(1(3(1(1(2(3(x1)))))))))))))))))))) → 2(2(2(2(1(0(2(1(4(4(1(2(1(4(3(3(3(1(1(3(x1)))))))))))))))))))) (37)
1(4(1(3(2(1(3(4(3(0(2(1(1(1(4(3(3(4(4(2(x1)))))))))))))))))))) → 2(1(3(1(1(1(1(3(3(0(2(1(4(1(1(0(1(1(3(4(x1)))))))))))))))))))) (38)
1(4(1(4(4(0(3(2(2(2(0(4(2(1(4(1(2(0(0(4(x1)))))))))))))))))))) → 3(1(3(2(2(0(3(4(4(4(4(2(2(1(2(1(4(3(2(1(x1)))))))))))))))))))) (39)
1(4(2(0(1(2(3(2(2(2(2(1(4(4(3(0(2(4(0(1(x1)))))))))))))))))))) → 1(0(1(0(1(1(3(4(2(1(0(2(4(0(4(4(4(2(0(4(x1)))))))))))))))))))) (40)
1(4(2(0(4(0(2(1(2(2(1(3(3(1(1(1(4(3(1(3(x1)))))))))))))))))))) → 0(1(2(1(0(1(0(3(1(1(2(2(1(2(1(1(3(2(3(0(x1)))))))))))))))))))) (41)
2(0(0(2(4(0(3(3(3(2(4(2(0(2(2(1(1(3(4(0(x1)))))))))))))))))))) → 4(1(0(3(1(3(3(2(4(4(1(0(3(1(4(4(4(4(1(0(x1)))))))))))))))))))) (42)
2(0(2(3(0(0(4(3(2(2(1(2(1(3(3(1(1(1(4(0(x1)))))))))))))))))))) → 0(0(1(4(3(3(1(1(2(1(1(4(4(1(1(1(1(2(4(4(x1)))))))))))))))))))) (43)
2(0(3(4(3(3(2(0(1(2(2(1(1(4(4(4(2(2(2(2(x1)))))))))))))))))))) → 2(3(1(1(2(1(4(1(0(2(3(2(1(4(0(2(3(0(2(1(x1)))))))))))))))))))) (44)
2(1(1(3(0(1(3(0(3(3(0(0(4(4(3(3(4(4(1(4(x1)))))))))))))))))))) → 4(1(3(0(0(1(2(3(1(1(1(1(1(0(1(0(1(3(3(1(x1)))))))))))))))))))) (45)
2(1(2(2(1(2(1(3(0(3(1(4(1(3(4(2(0(3(1(1(x1)))))))))))))))))))) → 1(0(0(1(0(4(2(1(3(1(4(4(4(4(4(4(3(1(1(2(x1)))))))))))))))))))) (46)
2(1(3(4(1(2(4(1(4(3(2(1(2(0(3(4(2(1(0(4(x1)))))))))))))))))))) → 4(1(1(1(3(0(4(1(2(2(2(2(4(4(4(4(2(1(2(1(x1)))))))))))))))))))) (47)
2(1(4(3(3(3(1(1(0(0(2(1(0(1(0(1(2(0(4(4(x1)))))))))))))))))))) → 1(1(2(2(4(1(2(0(1(1(1(1(4(0(0(2(2(0(1(4(x1)))))))))))))))))))) (48)
2(2(2(4(2(4(3(0(4(4(4(4(1(0(4(4(3(0(2(4(x1)))))))))))))))))))) → 2(0(1(1(1(4(0(3(1(2(1(2(4(1(0(1(1(3(0(2(x1)))))))))))))))))))) (49)
2(3(0(3(0(0(3(3(1(4(3(1(0(3(2(0(0(4(1(4(x1)))))))))))))))))))) → 2(2(1(3(2(3(4(0(3(2(2(0(2(4(3(2(1(0(2(0(x1)))))))))))))))))))) (50)
2(3(1(0(4(1(2(3(0(2(3(0(4(0(2(3(4(4(2(4(x1)))))))))))))))))))) → 2(4(4(4(4(1(3(4(4(4(0(1(0(0(2(3(2(0(0(0(x1)))))))))))))))))))) (51)
2(3(1(3(2(2(2(4(0(2(3(2(2(1(1(0(0(4(3(4(x1)))))))))))))))))))) → 3(1(0(1(2(1(3(1(1(4(3(2(1(4(0(4(3(1(3(0(x1)))))))))))))))))))) (52)
2(3(2(4(0(2(3(1(3(0(2(4(3(2(2(3(2(3(0(2(x1)))))))))))))))))))) → 0(3(2(3(4(4(0(2(2(0(2(1(2(3(2(4(1(0(3(0(x1)))))))))))))))))))) (53)
2(3(4(1(0(3(4(3(1(4(0(4(4(4(0(4(2(0(2(1(x1)))))))))))))))))))) → 1(3(2(0(1(1(1(4(1(4(1(2(0(3(3(1(0(4(3(2(x1)))))))))))))))))))) (54)
2(3(4(3(0(3(3(2(4(0(4(4(1(4(4(4(2(3(0(4(x1)))))))))))))))))))) → 0(4(2(2(2(2(2(0(3(4(3(2(2(0(1(0(3(1(1(0(x1)))))))))))))))))))) (55)
2(4(1(3(2(4(3(4(1(1(1(3(2(3(0(4(1(3(4(4(x1)))))))))))))))))))) → 2(3(3(1(1(0(1(0(4(1(1(0(1(0(2(2(4(1(0(4(x1)))))))))))))))))))) (56)
2(4(3(0(0(4(2(1(0(1(0(1(0(2(0(2(0(0(1(0(x1)))))))))))))))))))) → 1(0(2(4(4(3(1(4(4(3(2(1(1(3(4(2(3(1(2(4(x1)))))))))))))))))))) (57)
2(4(3(1(1(3(4(0(4(4(0(4(4(2(2(1(1(2(0(3(x1)))))))))))))))))))) → 2(1(1(4(4(1(1(2(2(1(4(4(0(2(2(1(1(0(3(2(x1)))))))))))))))))))) (58)
2(4(3(3(4(3(0(0(0(1(4(1(3(0(3(0(2(1(3(0(x1)))))))))))))))))))) → 1(1(4(4(3(1(0(1(1(3(4(1(2(0(0(2(3(0(2(3(x1)))))))))))))))))))) (59)
2(4(4(0(3(3(3(0(0(0(1(4(4(2(4(1(1(4(4(2(x1)))))))))))))))))))) → 1(0(1(1(3(2(2(0(2(1(2(2(1(0(3(3(1(4(4(1(x1)))))))))))))))))))) (60)
3(1(0(2(1(3(0(2(0(1(0(2(4(1(2(1(1(3(3(2(x1)))))))))))))))))))) → 0(2(1(1(2(4(4(0(2(2(2(2(3(3(0(1(4(4(0(1(x1)))))))))))))))))))) (61)
3(1(3(4(2(2(1(2(0(0(2(3(4(4(0(2(1(0(2(0(x1)))))))))))))))))))) → 1(3(4(1(4(2(2(0(1(2(2(0(4(2(4(4(4(1(4(2(x1)))))))))))))))))))) (62)
3(1(4(0(3(0(1(1(1(2(1(0(2(4(1(4(3(1(4(2(x1)))))))))))))))))))) → 1(4(1(3(4(0(2(2(2(1(1(1(4(1(0(2(2(1(0(2(x1)))))))))))))))))))) (63)
3(2(2(4(0(1(0(4(2(4(4(1(1(4(0(4(2(4(2(0(x1)))))))))))))))))))) → 0(4(3(0(2(2(0(1(1(0(1(0(2(3(4(2(0(2(2(4(x1)))))))))))))))))))) (64)
3(2(4(0(2(2(1(4(1(0(2(0(1(2(4(4(4(0(2(0(x1)))))))))))))))))))) → 0(1(4(3(4(3(0(3(2(3(2(0(1(4(2(1(1(1(1(1(x1)))))))))))))))))))) (65)
3(3(0(1(0(2(2(0(2(2(0(1(0(0(2(3(2(0(2(4(x1)))))))))))))))))))) → 1(4(4(3(3(1(2(1(3(0(2(1(2(4(0(3(4(2(2(2(x1)))))))))))))))))))) (66)
3(3(0(3(1(0(1(0(3(3(3(0(0(0(1(1(2(2(1(2(x1)))))))))))))))))))) → 3(2(4(4(0(1(3(1(1(4(2(1(3(2(2(3(0(2(1(3(x1)))))))))))))))))))) (67)
3(3(3(4(1(2(1(1(2(0(2(3(1(4(1(1(3(1(2(2(x1)))))))))))))))))))) → 3(4(2(1(2(1(2(2(1(0(2(1(1(1(2(2(0(2(2(3(x1)))))))))))))))))))) (68)
3(3(4(4(0(2(2(2(1(3(1(2(1(0(3(3(3(4(1(1(x1)))))))))))))))))))) → 2(0(3(2(1(1(1(4(0(1(1(4(4(4(4(2(2(1(4(0(x1)))))))))))))))))))) (69)
3(4(2(4(3(2(2(3(3(3(1(1(1(3(2(0(0(1(3(4(x1)))))))))))))))))))) → 0(3(4(4(3(0(2(2(2(1(2(2(4(3(1(1(1(3(2(0(x1)))))))))))))))))))) (70)
3(4(4(0(1(3(2(0(3(2(2(4(1(4(1(0(3(0(1(1(x1)))))))))))))))))))) → 3(4(4(0(1(2(4(3(0(2(0(3(1(1(1(2(2(2(4(1(x1)))))))))))))))))))) (71)
3(4(4(1(1(3(1(2(0(4(3(0(1(2(0(4(1(3(3(1(x1)))))))))))))))))))) → 4(3(1(1(2(1(2(2(1(1(1(1(2(4(2(4(1(0(1(4(x1)))))))))))))))))))) (72)
4(0(1(4(2(0(1(1(1(4(1(3(4(1(2(1(2(0(2(3(x1)))))))))))))))))))) → 4(0(1(0(4(2(2(4(1(4(1(1(4(4(1(2(1(4(4(3(x1)))))))))))))))))))) (73)
4(0(2(0(3(4(4(3(4(0(2(2(0(0(4(4(1(4(0(4(x1)))))))))))))))))))) → 3(1(4(2(1(1(4(3(3(4(3(3(2(1(1(0(3(1(4(1(x1)))))))))))))))))))) (74)
4(0(2(4(0(0(1(3(4(1(2(0(1(0(3(2(3(1(1(2(x1)))))))))))))))))))) → 3(2(4(4(4(1(1(4(3(0(1(3(0(4(1(3(0(2(2(1(x1)))))))))))))))))))) (75)
4(0(3(2(2(2(1(4(3(0(2(4(4(2(4(1(2(4(4(4(x1)))))))))))))))))))) → 4(4(0(4(1(4(0(3(1(4(1(4(3(4(2(1(1(1(4(1(x1)))))))))))))))))))) (76)
4(1(0(2(4(1(1(4(2(4(3(2(1(4(2(3(4(4(1(2(x1)))))))))))))))))))) → 1(3(4(1(0(1(4(2(0(1(3(0(1(1(1(1(3(4(1(4(x1)))))))))))))))))))) (77)
4(1(1(1(1(3(2(3(3(4(4(2(2(3(2(1(4(3(0(1(x1)))))))))))))))))))) → 4(3(1(1(2(2(2(0(3(2(3(4(4(4(4(3(1(2(2(1(x1)))))))))))))))))))) (78)
4(1(2(2(1(1(2(3(4(2(2(2(2(4(0(2(4(2(2(3(x1)))))))))))))))))))) → 4(2(0(1(4(1(1(0(1(1(1(2(2(1(1(2(3(4(0(0(x1)))))))))))))))))))) (79)
4(2(1(0(1(1(0(0(0(3(1(1(3(3(4(2(2(2(3(0(x1)))))))))))))))))))) → 3(2(1(4(4(4(1(3(1(2(1(3(3(2(2(2(3(4(2(2(x1)))))))))))))))))))) (80)
4(2(1(0(2(4(3(4(0(1(1(1(0(2(4(1(4(1(3(0(x1)))))))))))))))))))) → 1(2(0(2(1(1(2(3(1(1(1(2(1(3(3(1(4(0(0(3(x1)))))))))))))))))))) (81)
4(2(1(1(2(2(3(4(2(4(4(0(4(4(3(1(4(0(3(1(x1)))))))))))))))))))) → 4(1(4(3(1(0(2(4(2(1(2(1(4(1(3(2(4(4(4(0(x1)))))))))))))))))))) (82)
4(2(3(4(2(4(4(1(3(1(4(4(1(0(0(0(1(0(2(4(x1)))))))))))))))))))) → 4(4(3(3(0(1(2(1(0(4(1(0(4(3(4(1(1(2(2(2(x1)))))))))))))))))))) (83)
4(2(4(0(1(3(2(4(4(4(1(4(1(0(3(4(1(2(2(0(x1)))))))))))))))))))) → 2(2(1(1(4(2(4(4(1(1(2(4(1(4(3(1(2(3(0(3(x1)))))))))))))))))))) (84)
4(2(4(1(1(4(3(1(0(4(2(0(4(0(3(1(0(2(0(4(x1)))))))))))))))))))) → 4(2(0(0(0(1(4(1(4(4(1(0(3(3(4(1(2(1(0(3(x1)))))))))))))))))))) (85)
4(3(0(1(0(3(2(3(0(4(0(3(0(0(1(2(3(0(4(3(x1)))))))))))))))))))) → 1(0(0(4(4(3(4(0(0(2(2(1(0(0(4(2(1(4(3(1(x1)))))))))))))))))))) (86)
4(3(0(3(0(1(0(2(4(1(4(2(4(2(1(3(1(1(3(4(x1)))))))))))))))))))) → 1(4(2(1(1(1(4(2(1(1(4(2(1(1(3(0(3(1(1(4(x1)))))))))))))))))))) (87)
4(3(0(4(2(3(1(4(1(4(3(3(1(1(4(2(1(2(3(0(x1)))))))))))))))))))) → 3(1(0(4(0(1(1(0(1(2(1(0(0(3(1(0(0(1(0(1(x1)))))))))))))))))))) (88)
4(3(2(1(1(3(1(0(0(3(2(1(2(4(3(4(0(0(1(4(x1)))))))))))))))))))) → 4(3(4(1(0(2(0(3(1(3(3(1(3(0(0(0(1(2(1(4(x1)))))))))))))))))))) (89)
4(3(2(1(2(1(4(2(3(3(3(0(1(1(3(4(3(1(1(3(x1)))))))))))))))))))) → 0(4(1(1(1(0(3(4(3(0(4(4(4(1(1(1(1(2(3(4(x1)))))))))))))))))))) (90)
4(3(2(1(3(0(0(0(2(2(2(2(1(4(1(3(1(3(4(3(x1)))))))))))))))))))) → 1(0(2(2(3(1(1(2(3(1(0(4(4(4(1(0(1(0(4(3(x1)))))))))))))))))))) (91)
4(3(2(1(3(0(3(0(2(4(1(1(3(0(0(4(2(1(3(2(x1)))))))))))))))))))) → 4(2(2(4(1(3(1(0(1(3(1(4(3(3(0(0(4(4(0(2(x1)))))))))))))))))))) (92)
4(3(3(0(3(1(0(4(1(1(4(1(3(3(2(0(4(1(1(0(x1)))))))))))))))))))) → 4(3(0(1(4(1(0(3(4(4(1(4(4(2(2(4(2(2(3(0(x1)))))))))))))))))))) (93)
4(4(0(4(4(2(0(3(1(1(4(1(2(2(0(3(0(0(4(2(x1)))))))))))))))))))) → 4(4(4(1(1(4(2(2(0(3(4(4(3(3(1(2(3(1(2(4(x1)))))))))))))))))))) (94)
4(4(1(1(0(1(0(0(3(0(1(2(2(1(2(4(3(3(2(3(x1)))))))))))))))))))) → 0(4(4(1(0(0(2(4(2(1(1(3(0(1(1(3(1(1(1(3(x1)))))))))))))))))))) (95)
4(4(2(2(2(1(2(1(1(1(4(3(2(3(0(3(3(1(3(3(x1)))))))))))))))))))) → 4(0(4(2(1(1(1(0(4(0(0(1(0(2(1(2(1(1(0(0(x1)))))))))))))))))))) (96)
4(4(2(3(3(2(3(4(1(3(1(0(2(2(2(1(1(0(2(4(x1)))))))))))))))))))) → 1(2(2(0(2(1(3(2(1(1(3(0(4(4(1(0(1(1(4(4(x1)))))))))))))))))))) (97)
4(4(3(4(4(3(4(0(2(3(1(0(2(0(2(3(0(2(2(0(x1)))))))))))))))))))) → 4(4(2(2(1(3(2(4(0(1(0(0(4(1(2(4(4(2(3(4(x1)))))))))))))))))))) (98)
4(4(4(4(3(3(4(2(2(4(1(3(1(4(0(1(3(2(2(3(x1)))))))))))))))))))) → 1(4(1(1(2(1(3(1(1(2(1(0(1(2(4(4(4(1(1(3(x1)))))))))))))))))))) (99)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Closure Under Flat Contexts

Using the flat contexts

{4(☐), 3(☐), 2(☐), 1(☐), 0(☐)}

We obtain the transformed TRS

There are 495 ruless (increase limit for explicit display).

1.1 Semantic Labeling

The following interpretations form a model of the rules.

As carrier we take the set {0,...,4}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 5):

[4(x1)] = 5x1 + 0
[3(x1)] = 5x1 + 1
[2(x1)] = 5x1 + 2
[1(x1)] = 5x1 + 3
[0(x1)] = 5x1 + 4

We obtain the labeled TRS

There are 2475 ruless (increase limit for explicit display).

1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[40(x1)] = x1 +
2413399/17880
[41(x1)] = x1 +
20688811/17880
[42(x1)] = x1 +
238972/745
[43(x1)] = x1 +
1508429/2980
[44(x1)] = x1 +
5396573/4470
[30(x1)] = x1 +
133714/149
[31(x1)] = x1 +
2700298/2235
[32(x1)] = x1 +
5420711/4470
[33(x1)] = x1 +
3206315/3576
[34(x1)] = x1 +
5401043/4470
[20(x1)] = x1 +
5396573/4470
[21(x1)] = x1 +
1398005/1788
[22(x1)] = x1 +
2436829/17880
[23(x1)] = x1 +
19/10
[24(x1)] = x1 +
5396573/4470
[10(x1)] = x1 +
111139/894
[11(x1)] = x1 +
2045863/17880
[12(x1)] = x1 +
0
[13(x1)] = x1 +
0
[14(x1)] = x1 +
111139/894
[00(x1)] = x1 +
6234007/5960
[01(x1)] = x1 +
2708344/2235
[02(x1)] = x1 +
1014229/1490
[03(x1)] = x1 +
1302871/2980
[04(x1)] = x1 +
5420711/4470
all of the following rules can be deleted.

There are 2475 ruless (increase limit for explicit display).

1.1.1.1 R is empty

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