Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/40540)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 Closure Under Flat Contexts

Using the flat contexts

{0(☐), 1(☐), 2(☐)}

We obtain the transformed TRS

There are 189 ruless (increase limit for explicit display).

1.1 Semantic Labeling

Root-labeling is applied.

We obtain the labeled TRS

There are 567 ruless (increase limit for explicit display).

1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[00(x1)] = 1 · x1
[01(x1)] = 1 · x1 + 1
[12(x1)] = 1 · x1
[21(x1)] = 1 · x1 + 5
[22(x1)] = 1 · x1 + 3
[11(x1)] = 1 · x1 + 7
[20(x1)] = 1 · x1
[02(x1)] = 1 · x1
[10(x1)] = 1 · x1 + 2
all of the following rules can be deleted.

There are 554 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[11(x1)] = 1 · x1
[12(x1)] = 1 · x1
[21(x1)] = 1 · x1
[10(x1)] = 1 · x1
[02(x1)] = 1 · x1
[22(x1)] = 1 · x1
[20(x1)] = 1 · x1 + 1
[00(x1)] = 1 · x1 + 1
[01(x1)] = 1 · x1
all of the following rules can be deleted.
11(12(21(11(11(10(02(22(20(00(00(02(21(12(20(00(02(20(02(20(x1)))))))))))))))))))) → 11(10(01(10(01(10(02(22(22(21(12(20(01(11(10(00(00(00(00(00(x1)))))))))))))))))))) (316)
20(02(21(12(21(11(12(20(00(02(22(20(00(00(02(22(22(21(11(10(x1)))))))))))))))))))) → 22(20(02(22(22(20(02(22(20(01(11(12(21(12(21(12(20(01(11(10(x1)))))))))))))))))))) (340)
20(02(21(12(21(11(12(20(00(02(22(20(00(00(02(22(22(21(11(11(x1)))))))))))))))))))) → 22(20(02(22(22(20(02(22(20(01(11(12(21(12(21(12(20(01(11(11(x1)))))))))))))))))))) (341)
20(02(21(12(21(11(12(20(00(02(22(20(00(00(02(22(22(21(11(12(x1)))))))))))))))))))) → 22(20(02(22(22(20(02(22(20(01(11(12(21(12(21(12(20(01(11(12(x1)))))))))))))))))))) (342)
22(20(01(11(11(12(20(02(21(12(20(02(21(12(20(02(21(10(02(20(x1)))))))))))))))))))) → 22(20(01(12(22(22(21(10(02(22(22(22(21(12(20(01(12(20(01(10(x1)))))))))))))))))))) (382)
22(20(01(11(11(12(20(02(21(12(20(02(21(12(20(02(21(10(02(21(x1)))))))))))))))))))) → 22(20(01(12(22(22(21(10(02(22(22(22(21(12(20(01(12(20(01(11(x1)))))))))))))))))))) (383)
22(20(02(20(00(01(10(01(11(11(10(02(22(21(10(00(02(20(01(12(x1)))))))))))))))))))) → 20(02(22(22(22(21(10(00(02(22(21(12(20(02(22(20(02(21(10(02(x1)))))))))))))))))))) (390)

1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[21(x1)] = 1 · x1
[11(x1)] = 1 · x1 + 1
[10(x1)] = 1 · x1
[02(x1)] = 1 · x1
[20(x1)] = 1 · x1
[00(x1)] = 1 · x1
[22(x1)] = 1 · x1
[12(x1)] = 1 · x1
[01(x1)] = 1 · x1 + 1
all of the following rules can be deleted.
21(11(10(02(20(00(02(20(02(22(21(12(21(12(22(20(01(12(20(00(x1)))))))))))))))))))) → 21(12(22(22(22(20(02(21(10(00(00(01(12(22(22(22(20(02(20(00(x1)))))))))))))))))))) (358)
21(11(10(02(20(00(02(20(02(22(21(12(21(12(22(20(01(12(20(01(x1)))))))))))))))))))) → 21(12(22(22(22(20(02(21(10(00(00(01(12(22(22(22(20(02(20(01(x1)))))))))))))))))))) (359)
21(11(10(02(20(00(02(20(02(22(21(12(21(12(22(20(01(12(20(02(x1)))))))))))))))))))) → 21(12(22(22(22(20(02(21(10(00(00(01(12(22(22(22(20(02(20(02(x1)))))))))))))))))))) (360)

1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[20(x1)] = 1 · x1
[02(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1 + 1
[10(x1)] = 1 · x1
[01(x1)] = 1 · x1
[11(x1)] = 1 · x1
[12(x1)] = 1 · x1
[00(x1)] = 1 · x1
all of the following rules can be deleted.
20(02(22(21(10(01(11(11(12(21(10(02(20(01(12(21(12(20(02(20(00(x1))))))))))))))))))))) → 22(22(20(02(21(12(22(22(21(10(00(00(01(12(20(01(11(10(01(10(00(x1))))))))))))))))))))) (493)
20(02(22(21(10(01(11(11(12(21(10(02(20(01(12(21(12(20(02(20(01(x1))))))))))))))))))))) → 22(22(20(02(21(12(22(22(21(10(00(00(01(12(20(01(11(10(01(10(01(x1))))))))))))))))))))) (494)
20(02(22(21(10(01(11(11(12(21(10(02(20(01(12(21(12(20(02(20(02(x1))))))))))))))))))))) → 22(22(20(02(21(12(22(22(21(10(00(00(01(12(20(01(11(10(01(10(02(x1))))))))))))))))))))) (495)

1.1.1.1.1.1.1 R is empty

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