Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/133236)

The rewrite relation of the following TRS is considered.

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

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

We obtain the transformed TRS

There are 594 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,...,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 3564 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
[50(x1)] = x1 +
0
[51(x1)] = x1 +
0
[52(x1)] = x1 +
0
[53(x1)] = x1 +
0
[54(x1)] = x1 +
375/13
[55(x1)] = x1 +
0
[40(x1)] = x1 +
1557/13
[41(x1)] = x1 +
397/13
[42(x1)] = x1 +
3061/13
[43(x1)] = x1 +
0
[44(x1)] = x1 +
3048/13
[45(x1)] = x1 +
0
[30(x1)] = x1 +
0
[31(x1)] = x1 +
2976/13
[32(x1)] = x1 +
2043/13
[33(x1)] = x1 +
1275/13
[34(x1)] = x1 +
3048/13
[35(x1)] = x1 +
0
[20(x1)] = x1 +
0
[21(x1)] = x1 +
2361/13
[22(x1)] = x1 +
2061/13
[23(x1)] = x1 +
2094/13
[24(x1)] = x1 +
3048/13
[25(x1)] = x1 +
0
[10(x1)] = x1 +
570/13
[11(x1)] = x1 +
3048/13
[12(x1)] = x1 +
3074/13
[13(x1)] = x1 +
2664/13
[14(x1)] = x1 +
3061/13
[15(x1)] = x1 +
2166/13
[00(x1)] = x1 +
0
[01(x1)] = x1 +
1341/13
[02(x1)] = x1 +
0
[03(x1)] = x1 +
36/13
[04(x1)] = x1 +
375/13
[05(x1)] = x1 +
1
all of the following rules can be deleted.

There are 3564 ruless (increase limit for explicit display).

1.1.1.1 R is empty

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