Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/98623)

The rewrite relation of the following TRS is considered.

0(0(0(0(1(0(2(0(0(1(0(2(0(0(0(1(1(2(0(2(x1)))))))))))))))))))) → 1(1(2(1(0(0(1(2(0(1(0(1(2(0(0(0(1(1(0(0(x1)))))))))))))))))))) (1)
0(0(0(0(1(2(1(2(0(0(2(0(1(0(0(1(1(0(2(0(x1)))))))))))))))))))) → 0(0(1(2(0(0(1(1(1(0(1(0(1(0(2(0(1(0(0(0(x1)))))))))))))))))))) (2)
0(0(0(1(0(0(1(1(0(1(0(1(2(1(2(2(0(2(0(1(x1)))))))))))))))))))) → 0(0(0(0(2(2(0(1(0(1(0(0(1(2(0(1(0(0(1(1(x1)))))))))))))))))))) (3)
0(0(1(0(2(1(0(0(1(2(2(1(1(2(0(0(2(1(2(1(x1)))))))))))))))))))) → 2(1(0(0(1(2(1(1(0(1(0(1(2(0(1(0(1(1(1(0(x1)))))))))))))))))))) (4)
0(0(1(1(0(0(1(0(0(1(2(1(1(0(1(2(0(1(2(2(x1)))))))))))))))))))) → 1(2(0(0(1(1(1(1(0(0(1(2(0(1(1(2(2(1(1(2(x1)))))))))))))))))))) (5)
0(0(1(2(0(0(0(1(2(2(0(2(0(0(2(0(1(1(1(1(x1)))))))))))))))))))) → 1(0(1(1(0(2(0(1(1(1(0(0(0(0(1(0(0(0(1(2(x1)))))))))))))))))))) (6)
0(0(1(2(2(2(0(0(1(0(2(0(0(1(1(0(0(0(2(1(x1)))))))))))))))))))) → 1(1(0(1(0(0(1(0(2(0(1(2(1(1(2(2(0(0(0(1(x1)))))))))))))))))))) (7)
0(0(2(0(1(2(2(2(1(2(1(2(1(2(0(0(0(0(0(1(x1)))))))))))))))))))) → 0(1(0(0(2(1(2(1(1(1(0(2(0(1(0(1(2(2(0(1(x1)))))))))))))))))))) (8)
0(0(2(1(1(1(0(0(2(1(1(0(0(1(1(0(2(0(2(1(x1)))))))))))))))))))) → 0(1(1(2(0(0(0(1(1(1(2(1(1(0(1(2(0(1(2(1(x1)))))))))))))))))))) (9)
0(1(0(0(0(2(1(0(2(1(1(0(1(1(2(1(1(0(2(0(x1)))))))))))))))))))) → 0(2(0(1(1(0(2(1(1(1(0(1(1(2(2(1(1(2(1(1(x1)))))))))))))))))))) (10)
0(1(0(0(1(0(1(2(2(1(2(1(1(1(1(2(0(0(1(1(x1)))))))))))))))))))) → 2(0(0(2(1(1(1(1(2(0(1(0(0(1(0(1(1(0(0(0(x1)))))))))))))))))))) (11)
0(1(0(1(0(2(0(1(2(0(0(0(2(2(2(1(1(0(0(1(x1)))))))))))))))))))) → 1(2(1(1(0(1(0(0(0(0(1(0(1(1(1(0(0(1(0(1(x1)))))))))))))))))))) (12)
0(1(0(1(2(1(1(2(0(2(1(0(1(2(2(2(1(1(1(1(x1)))))))))))))))))))) → 0(1(0(2(0(0(2(0(2(1(2(0(0(1(0(0(1(1(1(2(x1)))))))))))))))))))) (13)
0(1(0(1(2(1(2(0(1(2(1(2(0(1(1(2(0(1(1(1(x1)))))))))))))))))))) → 2(2(0(2(0(1(0(1(2(1(1(1(1(1(1(1(0(1(1(1(x1)))))))))))))))))))) (14)
0(1(0(1(2(2(0(0(2(0(2(0(1(2(2(1(0(1(1(1(x1)))))))))))))))))))) → 0(2(0(0(1(1(2(1(1(2(1(2(1(2(0(1(1(1(0(2(x1)))))))))))))))))))) (15)
0(1(0(2(0(2(2(2(2(0(0(1(0(0(2(1(1(0(0(1(x1)))))))))))))))))))) → 1(1(1(0(0(0(2(2(2(1(0(2(0(0(2(0(0(0(0(1(x1)))))))))))))))))))) (16)
0(1(0(2(1(0(0(2(1(2(0(2(0(0(0(1(0(1(1(0(x1)))))))))))))))))))) → 1(1(0(0(0(0(0(2(0(0(0(1(0(2(0(1(0(2(1(1(x1)))))))))))))))))))) (17)
0(1(1(0(0(1(0(1(0(0(2(2(1(0(1(0(0(2(0(1(x1)))))))))))))))))))) → 0(1(1(0(1(1(1(2(0(0(2(2(1(1(0(1(2(1(1(0(x1)))))))))))))))))))) (18)
0(1(1(0(0(2(2(1(0(1(2(0(2(0(2(0(2(0(0(1(x1)))))))))))))))))))) → 1(2(0(0(0(1(2(2(1(1(1(2(1(1(0(1(1(2(2(1(x1)))))))))))))))))))) (19)
0(1(1(0(1(0(2(2(0(0(1(0(2(1(1(0(2(2(0(1(x1)))))))))))))))))))) → 2(1(0(0(1(1(1(0(0(2(0(1(2(2(0(0(1(2(0(1(x1)))))))))))))))))))) (20)
0(1(1(0(1(2(2(1(1(0(0(2(0(0(2(2(1(1(2(1(x1)))))))))))))))))))) → 0(1(0(0(0(0(0(1(2(1(1(0(2(1(0(0(0(0(0(0(x1)))))))))))))))))))) (21)
0(1(1(0(2(0(2(0(0(1(0(2(0(0(1(1(0(0(1(2(x1)))))))))))))))))))) → 0(1(2(1(1(2(0(1(1(0(0(1(1(1(1(1(1(0(0(1(x1)))))))))))))))))))) (22)
0(1(1(0(2(1(2(0(0(1(1(0(0(2(0(0(2(2(1(1(x1)))))))))))))))))))) → 0(2(0(0(0(0(0(1(2(1(0(1(1(1(1(1(1(0(0(0(x1)))))))))))))))))))) (23)
0(1(1(1(0(2(2(0(1(0(2(2(2(1(1(2(1(1(2(1(x1)))))))))))))))))))) → 0(1(0(1(1(0(0(1(0(1(2(1(1(2(2(0(0(0(2(1(x1)))))))))))))))))))) (24)
0(1(1(1(2(0(1(2(0(1(2(1(0(2(0(1(1(2(2(1(x1)))))))))))))))))))) → 0(1(2(1(0(1(1(2(1(0(0(2(0(0(1(2(0(1(1(1(x1)))))))))))))))))))) (25)
0(1(1(2(1(2(0(1(1(1(0(2(0(1(1(0(2(1(1(2(x1)))))))))))))))))))) → 0(1(1(2(0(2(1(1(1(1(1(0(2(0(2(0(1(1(1(2(x1)))))))))))))))))))) (26)
0(1(2(0(1(2(2(0(1(0(1(1(0(1(1(0(1(2(1(0(x1)))))))))))))))))))) → 1(2(1(1(2(1(1(0(1(0(2(0(0(0(0(1(1(1(1(2(x1)))))))))))))))))))) (27)
0(1(2(1(0(0(2(2(0(0(0(0(2(0(1(0(1(1(1(2(x1)))))))))))))))))))) → 0(1(2(2(0(0(1(0(1(0(1(0(0(1(1(0(1(0(1(2(x1)))))))))))))))))))) (28)
0(1(2(1(0(1(1(0(0(0(0(2(2(2(0(1(1(2(2(1(x1)))))))))))))))))))) → 1(1(2(0(1(1(1(0(1(0(1(2(0(2(1(2(0(0(1(1(x1)))))))))))))))))))) (29)
0(1(2(1(0(1(2(0(1(0(2(2(0(2(0(1(2(0(0(1(x1)))))))))))))))))))) → 0(1(2(1(2(1(0(0(2(0(1(2(0(2(0(0(0(2(0(1(x1)))))))))))))))))))) (30)
0(2(0(1(0(1(1(0(0(0(2(1(1(0(0(1(0(2(2(0(x1)))))))))))))))))))) → 1(1(0(0(0(2(0(2(0(0(2(0(1(1(1(1(1(2(0(1(x1)))))))))))))))))))) (31)
0(2(0(1(2(1(0(0(1(2(0(0(1(2(1(1(0(1(0(2(x1)))))))))))))))))))) → 0(1(1(1(1(0(2(0(1(2(1(0(2(1(0(0(2(1(2(0(x1)))))))))))))))))))) (32)
0(2(0(2(0(1(1(2(2(2(1(1(0(1(0(2(0(0(0(1(x1)))))))))))))))))))) → 0(1(2(0(2(2(1(0(2(1(1(1(2(0(1(0(0(1(1(1(x1)))))))))))))))))))) (33)
0(2(1(1(1(1(1(2(1(1(1(2(1(0(2(1(1(1(2(2(x1)))))))))))))))))))) → 2(0(0(1(1(0(1(1(1(1(0(2(0(0(1(2(1(0(0(2(x1)))))))))))))))))))) (34)
0(2(1(1(2(0(2(0(2(0(2(0(1(1(0(0(1(1(0(0(x1)))))))))))))))))))) → 0(0(1(1(0(0(1(1(1(0(0(1(1(1(0(0(2(0(0(2(x1)))))))))))))))))))) (35)
0(2(2(0(2(2(1(1(1(0(1(0(2(1(1(1(1(1(0(1(x1)))))))))))))))))))) → 2(0(1(0(2(0(1(1(1(0(1(1(1(0(0(0(1(1(1(1(x1)))))))))))))))))))) (36)
0(2(2(2(0(1(1(1(1(1(2(2(2(0(1(0(0(0(0(1(x1)))))))))))))))))))) → 1(2(0(2(1(0(1(1(2(0(0(0(0(1(1(1(2(1(0(1(x1)))))))))))))))))))) (37)
1(0(0(1(0(1(2(0(0(0(1(2(1(0(1(0(0(0(0(1(x1)))))))))))))))))))) → 1(0(1(2(0(1(2(0(1(1(0(0(1(1(1(1(0(2(1(0(x1)))))))))))))))))))) (38)
1(0(0(1(1(2(0(2(2(1(1(1(1(1(0(1(2(2(2(1(x1)))))))))))))))))))) → 1(0(0(0(1(0(2(0(0(1(0(0(2(1(1(1(0(1(1(0(x1)))))))))))))))))))) (39)
1(0(0(2(0(1(0(2(2(0(2(1(0(0(1(1(2(2(0(0(x1)))))))))))))))))))) → 1(1(1(2(2(0(1(0(1(1(1(0(2(1(0(0(1(2(2(2(x1)))))))))))))))))))) (40)
1(0(0(2(0(1(1(0(0(2(2(0(0(0(0(2(0(1(1(1(x1)))))))))))))))))))) → 1(0(0(1(1(0(0(1(0(0(1(1(1(0(0(2(2(0(0(0(x1)))))))))))))))))))) (41)
1(0(0(2(2(2(1(0(1(2(1(1(1(1(1(1(0(2(1(1(x1)))))))))))))))))))) → 0(2(0(0(1(1(1(1(1(1(2(1(1(2(1(1(1(2(0(0(x1)))))))))))))))))))) (42)
1(0(1(0(0(0(0(0(2(0(0(1(1(1(0(2(0(0(2(0(x1)))))))))))))))))))) → 2(0(0(0(1(0(1(1(2(1(1(2(1(1(0(0(0(1(1(1(x1)))))))))))))))))))) (43)
1(0(1(1(0(2(0(0(0(0(0(2(1(2(0(2(1(1(0(2(x1)))))))))))))))))))) → 0(2(0(1(1(2(0(0(0(0(0(2(0(1(1(1(1(1(1(0(x1)))))))))))))))))))) (44)
1(0(1(1(1(0(1(0(1(0(2(1(1(2(0(0(2(1(1(0(x1)))))))))))))))))))) → 0(1(1(0(0(1(1(0(1(0(2(1(1(2(0(2(0(1(1(1(x1)))))))))))))))))))) (45)
1(0(1(1(1(2(2(0(0(0(2(0(0(1(2(1(1(0(2(0(x1)))))))))))))))))))) → 2(0(2(2(1(0(0(0(0(0(1(1(1(2(0(1(0(0(0(0(x1)))))))))))))))))))) (46)
1(0(1(1(2(0(0(0(2(2(2(2(0(1(1(0(0(0(2(1(x1)))))))))))))))))))) → 1(0(0(1(1(1(0(0(1(2(0(2(1(0(0(0(1(0(1(0(x1)))))))))))))))))))) (47)
1(0(1(1(2(1(0(2(0(2(1(0(0(1(1(0(0(0(0(1(x1)))))))))))))))))))) → 1(0(2(0(1(1(1(0(0(0(0(2(1(1(1(0(0(0(0(1(x1)))))))))))))))))))) (48)
1(0(1(2(1(1(2(1(1(0(0(0(2(2(2(2(1(1(0(1(x1)))))))))))))))))))) → 0(0(0(0(0(2(0(1(1(2(1(0(0(1(0(1(0(1(1(0(x1)))))))))))))))))))) (49)
1(0(1(2(1(2(2(0(2(0(0(2(0(1(1(0(0(0(1(1(x1)))))))))))))))))))) → 0(1(1(1(2(1(1(1(1(0(0(0(2(0(0(1(2(2(0(1(x1)))))))))))))))))))) (50)
1(0(2(0(1(1(2(1(0(0(0(1(0(1(1(2(0(2(1(2(x1)))))))))))))))))))) → 0(0(0(1(1(2(0(1(2(0(0(0(0(1(0(2(1(1(0(2(x1)))))))))))))))))))) (51)
1(0(2(0(1(1(2(1(1(0(2(1(1(2(2(0(1(0(1(2(x1)))))))))))))))))))) → 1(1(1(1(2(0(2(1(1(1(2(0(1(0(1(2(1(2(1(1(x1)))))))))))))))))))) (52)
1(0(2(0(2(0(0(2(0(0(0(0(1(0(2(2(0(1(0(1(x1)))))))))))))))))))) → 1(1(2(0(2(2(0(2(2(0(1(0(1(1(0(0(2(0(0(1(x1)))))))))))))))))))) (53)
1(0(2(1(1(0(0(1(1(0(2(1(2(1(0(0(1(2(1(2(x1)))))))))))))))))))) → 1(1(1(0(1(0(2(0(1(0(0(1(0(1(2(2(0(1(0(0(x1)))))))))))))))))))) (54)
1(0(2(2(1(1(1(1(1(0(1(0(0(0(2(0(2(2(0(1(x1)))))))))))))))))))) → 1(0(0(0(1(1(0(0(2(1(2(2(1(1(1(0(0(2(0(1(x1)))))))))))))))))))) (55)
1(1(0(0(0(0(1(2(0(0(0(0(2(0(2(2(2(0(2(1(x1)))))))))))))))))))) → 1(1(0(1(2(0(2(0(0(0(0(2(1(0(2(1(0(0(0(1(x1)))))))))))))))))))) (56)
1(1(0(0(1(1(2(0(2(0(2(0(2(2(0(1(1(1(1(2(x1)))))))))))))))))))) → 2(1(1(0(2(0(0(0(1(1(2(0(1(1(1(1(2(0(0(1(x1)))))))))))))))))))) (57)
1(1(0(0(2(2(1(1(1(1(1(2(0(2(0(1(2(1(1(2(x1)))))))))))))))))))) → 0(1(0(2(0(0(1(1(0(0(1(1(1(1(1(1(0(1(2(1(x1)))))))))))))))))))) (58)
1(1(0(1(0(0(1(0(0(1(2(1(2(1(1(0(0(2(0(0(x1)))))))))))))))))))) → 1(1(2(0(0(1(2(1(1(1(0(1(0(2(1(1(1(1(1(0(x1)))))))))))))))))))) (59)
1(1(0(1(0(1(0(0(2(0(0(2(0(2(0(2(1(1(0(1(x1)))))))))))))))))))) → 1(1(1(0(1(1(1(1(2(1(0(0(1(0(1(1(0(1(2(0(x1)))))))))))))))))))) (60)
1(1(0(1(1(1(1(0(2(2(2(0(2(0(2(2(1(1(1(0(x1)))))))))))))))))))) → 0(1(2(0(1(2(2(1(1(1(1(0(1(2(0(1(0(1(0(0(x1)))))))))))))))))))) (61)
1(1(0(1(1(2(0(1(2(1(1(2(0(0(0(1(0(2(1(2(x1)))))))))))))))))))) → 1(2(1(1(1(1(1(1(0(0(1(0(1(2(1(1(2(0(2(0(x1)))))))))))))))))))) (62)
1(1(0(1(1(2(1(1(2(2(1(1(0(0(2(1(1(0(0(0(x1)))))))))))))))))))) → 1(1(1(0(1(1(1(1(2(1(1(1(2(0(2(1(1(0(0(0(x1)))))))))))))))))))) (63)
1(1(0(2(0(0(0(0(1(2(0(2(2(2(2(0(1(1(1(1(x1)))))))))))))))))))) → 2(0(1(1(2(1(2(0(1(2(0(2(1(0(1(1(1(1(1(0(x1)))))))))))))))))))) (64)
1(1(0(2(0(1(0(2(0(2(0(2(0(2(1(1(0(0(2(1(x1)))))))))))))))))))) → 0(1(2(1(1(0(0(2(1(2(2(0(1(1(2(1(1(1(1(1(x1)))))))))))))))))))) (65)
1(1(0(2(1(1(1(1(2(2(2(0(0(0(0(2(2(2(2(1(x1)))))))))))))))))))) → 0(0(2(1(0(1(1(0(0(2(0(2(1(0(1(0(0(1(2(0(x1)))))))))))))))))))) (66)
1(1(1(0(1(0(0(1(1(2(0(1(2(2(1(1(0(2(1(2(x1)))))))))))))))))))) → 1(1(1(1(0(0(2(1(1(2(2(1(1(1(2(0(0(0(0(2(x1)))))))))))))))))))) (67)
1(1(1(0(1(1(1(2(1(2(0(0(1(2(2(2(1(1(1(2(x1)))))))))))))))))))) → 1(1(0(1(1(1(0(0(0(1(1(1(1(0(2(2(0(0(2(2(x1)))))))))))))))))))) (68)
1(1(1(0(1(1(2(0(2(0(0(2(0(2(2(2(1(1(1(1(x1)))))))))))))))))))) → 1(0(0(1(1(1(2(0(1(0(2(0(2(0(2(0(1(1(0(0(x1)))))))))))))))))))) (69)
1(1(2(0(0(2(0(2(0(0(2(1(1(1(0(0(1(2(2(1(x1)))))))))))))))))))) → 2(0(1(1(0(0(0(1(2(0(1(1(1(2(0(2(0(0(0(1(x1)))))))))))))))))))) (70)
1(1(2(0(1(2(0(0(2(1(2(2(0(1(0(1(0(1(1(1(x1)))))))))))))))))))) → 0(1(0(1(0(0(1(1(0(2(0(1(1(0(1(2(0(0(0(0(x1)))))))))))))))))))) (71)
1(1(2(0(2(2(0(0(2(0(0(0(1(1(2(0(1(0(1(0(x1)))))))))))))))))))) → 0(1(2(0(2(1(2(0(0(2(0(0(0(1(1(0(1(1(0(0(x1)))))))))))))))))))) (72)
1(2(0(0(0(0(0(0(0(1(2(1(2(0(1(1(0(2(2(1(x1)))))))))))))))))))) → 0(0(0(1(0(1(0(1(1(0(1(1(0(0(0(0(1(1(1(2(x1)))))))))))))))))))) (73)
1(2(0(1(1(2(0(1(1(2(0(1(0(1(2(0(1(0(2(2(x1)))))))))))))))))))) → 0(2(1(2(0(0(1(1(1(2(2(0(0(1(1(1(1(1(0(1(x1)))))))))))))))))))) (74)
1(2(1(0(0(0(2(1(1(0(1(0(0(0(0(2(0(0(0(1(x1)))))))))))))))))))) → 0(1(2(1(1(1(1(1(1(0(1(0(1(2(1(0(1(1(1(1(x1)))))))))))))))))))) (75)
1(2(1(1(1(1(2(0(0(0(0(1(0(2(2(0(2(2(2(1(x1)))))))))))))))))))) → 1(2(0(0(2(0(2(0(0(0(2(0(0(1(2(2(1(1(1(1(x1)))))))))))))))))))) (76)
1(2(2(1(0(1(1(1(2(2(1(0(0(1(2(1(1(1(2(1(x1)))))))))))))))))))) → 0(2(1(0(1(0(1(1(2(2(1(1(1(2(0(1(1(1(2(1(x1)))))))))))))))))))) (77)
1(2(2(1(1(1(0(0(1(0(0(1(0(1(0(0(0(2(2(1(x1)))))))))))))))))))) → 0(0(1(0(1(0(0(0(0(1(1(2(1(0(0(1(0(0(2(1(x1)))))))))))))))))))) (78)
1(2(2(1(2(1(1(2(0(2(2(1(2(0(1(1(1(1(0(1(x1)))))))))))))))))))) → 1(1(1(1(1(0(0(0(0(0(2(0(2(0(2(0(1(2(1(1(x1)))))))))))))))))))) (79)
1(2(2(2(1(0(0(0(2(0(1(2(0(0(1(0(0(1(1(1(x1)))))))))))))))))))) → 1(2(0(0(1(0(1(1(2(2(0(0(1(1(1(2(0(1(1(0(x1)))))))))))))))))))) (80)
1(2(2(2(1(0(1(2(1(1(1(1(1(2(1(2(1(1(0(1(x1)))))))))))))))))))) → 1(0(0(1(2(0(2(0(1(1(1(0(0(2(1(1(2(0(2(1(x1)))))))))))))))))))) (81)
1(2(2(2(1(1(0(0(0(0(2(1(0(2(0(0(1(1(1(1(x1)))))))))))))))))))) → 0(0(1(0(1(1(2(0(1(1(1(0(0(1(2(0(0(0(0(0(x1)))))))))))))))))))) (82)
2(0(0(1(1(2(1(0(0(2(1(1(0(2(1(1(1(1(0(2(x1)))))))))))))))))))) → 0(0(1(1(0(1(2(0(1(0(0(0(1(2(1(1(2(0(2(0(x1)))))))))))))))))))) (83)
2(0(0(2(1(0(1(1(1(1(1(0(2(0(1(1(0(2(2(1(x1)))))))))))))))))))) → 1(1(0(2(0(1(1(2(1(1(0(0(1(1(0(0(1(1(0(1(x1)))))))))))))))))))) (84)
2(0(1(0(0(0(0(2(0(0(0(0(2(1(1(0(0(2(1(2(x1)))))))))))))))))))) → 0(0(0(2(1(1(0(0(1(1(1(0(0(1(1(2(2(0(0(1(x1)))))))))))))))))))) (85)
2(0(1(0(1(1(1(0(1(1(1(1(0(2(1(2(1(0(0(2(x1)))))))))))))))))))) → 1(1(2(0(1(0(0(0(0(0(1(1(1(0(2(2(0(0(0(0(x1)))))))))))))))))))) (86)
2(0(1(0(2(0(1(2(2(1(1(1(1(0(2(0(1(1(2(1(x1)))))))))))))))))))) → 0(0(0(0(1(2(0(1(1(2(1(1(1(1(0(1(1(2(2(1(x1)))))))))))))))))))) (87)
2(0(1(1(0(1(1(2(0(0(0(2(1(0(2(0(0(2(0(0(x1)))))))))))))))))))) → 0(0(1(2(0(1(1(0(1(2(2(0(0(1(0(0(2(1(1(1(x1)))))))))))))))))))) (88)
2(0(2(1(0(0(0(1(2(0(0(0(0(1(1(2(2(0(2(1(x1)))))))))))))))))))) → 2(1(0(0(1(2(0(0(0(1(2(1(1(1(0(0(0(0(2(1(x1)))))))))))))))))))) (89)
2(1(0(0(0(1(0(2(2(2(1(1(0(1(1(1(1(1(1(2(x1)))))))))))))))))))) → 2(0(0(0(0(0(0(0(1(2(1(1(0(0(2(1(0(0(0(0(x1)))))))))))))))))))) (90)
2(1(0(0(1(1(0(2(1(0(1(1(0(1(2(1(0(1(0(1(x1)))))))))))))))))))) → 1(1(2(0(2(2(2(1(1(1(1(1(1(1(1(1(1(2(1(2(x1)))))))))))))))))))) (91)
2(1(0(2(1(0(0(0(0(1(2(2(0(1(2(0(1(0(1(1(x1)))))))))))))))))))) → 0(0(0(0(0(1(2(2(1(1(1(1(2(2(0(1(2(0(0(2(x1)))))))))))))))))))) (92)
2(1(1(0(2(1(0(2(0(1(2(2(1(1(1(1(1(0(0(1(x1)))))))))))))))))))) → 1(0(1(0(1(2(0(0(0(0(1(1(2(1(1(2(0(0(1(1(x1)))))))))))))))))))) (93)
2(1(1(1(0(1(1(0(1(2(0(1(2(2(1(1(1(0(1(2(x1)))))))))))))))))))) → 1(0(1(1(1(0(0(0(2(1(1(0(0(1(2(0(1(2(0(2(x1)))))))))))))))))))) (94)
2(1(1(1(1(0(1(1(1(2(2(0(1(2(2(1(2(0(2(1(x1)))))))))))))))))))) → 2(1(0(0(0(0(0(1(0(1(2(1(1(2(0(1(1(1(1(0(x1)))))))))))))))))))) (95)
2(1(1(2(1(1(2(0(1(1(2(0(2(0(0(1(1(0(1(2(x1)))))))))))))))))))) → 1(1(0(0(2(0(1(1(2(1(1(2(1(1(0(0(1(1(0(0(x1)))))))))))))))))))) (96)
2(2(0(0(0(1(2(0(1(2(0(2(1(1(1(0(0(0(1(2(x1)))))))))))))))))))) → 0(0(0(0(0(0(2(2(1(0(0(1(2(0(1(1(2(1(1(1(x1)))))))))))))))))))) (97)
2(2(2(0(0(0(1(2(0(0(0(0(2(0(0(1(1(0(0(2(x1)))))))))))))))))))) → 2(0(0(0(1(2(0(0(1(1(2(2(1(2(0(0(2(0(1(1(x1)))))))))))))))))))) (98)
2(2(2(1(1(1(0(1(1(2(1(1(1(0(1(1(2(1(1(1(x1)))))))))))))))))))) → 0(0(1(1(2(0(1(1(1(1(0(0(2(0(0(1(1(0(2(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 207 ruless (increase limit for explicit display).

1.1 Semantic Labeling

Root-labeling is applied.

We obtain the labeled TRS

There are 621 ruless (increase limit for explicit display).

1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[00(x1)] = 1 · x1 + 1
[01(x1)] = 1 · x1
[12(x1)] = 1 · x1 + 5
[21(x1)] = 1 · x1
[20(x1)] = 1 · x1
[02(x1)] = 1 · x1 + 5
[10(x1)] = 1 · x1 + 3
[11(x1)] = 1 · x1
[22(x1)] = 1 · x1 + 4
all of the following rules can be deleted.

There are 602 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[01(x1)] = 1 · x1 + 5
[10(x1)] = 1 · x1 + 2
[12(x1)] = 1 · x1 + 1
[21(x1)] = 1 · x1 + 1
[11(x1)] = 1 · x1 + 5
[20(x1)] = 1 · x1
[02(x1)] = 1 · x1
[22(x1)] = 1 · x1 + 2
[00(x1)] = 1 · x1 + 3
all of the following rules can be deleted.
01(10(01(12(21(11(12(20(02(21(10(01(12(22(22(21(11(11(11(11(x1)))))))))))))))))))) → 01(10(02(20(00(02(20(02(21(12(20(00(01(10(00(01(11(11(12(21(x1)))))))))))))))))))) (278)
01(12(21(10(01(12(20(01(10(02(22(20(02(20(01(12(20(00(01(10(x1)))))))))))))))))))) → 01(12(21(12(21(10(00(02(20(01(12(20(02(20(00(00(02(20(01(10(x1)))))))))))))))))))) (307)
01(12(21(10(01(12(20(01(10(02(22(20(02(20(01(12(20(00(01(11(x1)))))))))))))))))))) → 01(12(21(12(21(10(00(02(20(01(12(20(02(20(00(00(02(20(01(11(x1)))))))))))))))))))) (308)
01(12(21(10(01(12(20(01(10(02(22(20(02(20(01(12(20(00(01(12(x1)))))))))))))))))))) → 01(12(21(12(21(10(00(02(20(01(12(20(02(20(00(00(02(20(01(12(x1)))))))))))))))))))) (309)
02(20(01(12(21(10(00(01(12(20(00(01(12(21(11(10(01(10(02(22(x1)))))))))))))))))))) → 01(11(11(11(10(02(20(01(12(21(10(02(21(10(00(02(21(12(20(02(x1)))))))))))))))))))) (312)
10(00(01(10(01(12(20(00(00(01(12(21(10(01(10(00(00(00(01(12(x1)))))))))))))))))))) → 10(01(12(20(01(12(20(01(11(10(00(01(11(11(11(10(02(21(10(02(x1)))))))))))))))))))) (321)
00(01(10(00(01(10(01(12(22(21(12(21(11(11(11(12(20(00(01(11(11(x1))))))))))))))))))))) → 02(20(00(02(21(11(11(11(12(20(01(10(00(01(10(01(11(10(00(00(01(x1))))))))))))))))))))) (443)
00(01(10(00(01(10(01(12(22(21(12(21(11(11(11(12(20(00(01(11(12(x1))))))))))))))))))))) → 02(20(00(02(21(11(11(11(12(20(01(10(00(01(10(01(11(10(00(00(02(x1))))))))))))))))))))) (444)
20(01(10(00(01(10(01(12(22(21(12(21(11(11(11(12(20(00(01(11(12(x1))))))))))))))))))))) → 22(20(00(02(21(11(11(11(12(20(01(10(00(01(10(01(11(10(00(00(02(x1))))))))))))))))))))) (450)
11(11(12(20(02(22(20(00(02(20(00(00(01(11(12(20(01(10(01(10(00(x1))))))))))))))))))))) → 10(01(12(20(02(21(12(20(00(02(20(00(00(01(11(10(01(11(10(00(00(x1))))))))))))))))))))) (706)
11(11(12(20(02(22(20(00(02(20(00(00(01(11(12(20(01(10(01(10(01(x1))))))))))))))))))))) → 10(01(12(20(02(21(12(20(00(02(20(00(00(01(11(10(01(11(10(00(01(x1))))))))))))))))))))) (707)
11(11(12(20(02(22(20(00(02(20(00(00(01(11(12(20(01(10(01(10(02(x1))))))))))))))))))))) → 10(01(12(20(02(21(12(20(00(02(20(00(00(01(11(10(01(11(10(00(02(x1))))))))))))))))))))) (708)
12(21(10(02(21(10(00(00(00(01(12(22(20(01(12(20(01(10(01(11(11(x1))))))))))))))))))))) → 10(00(00(00(00(01(12(22(21(11(11(11(12(22(20(01(12(20(00(02(21(x1))))))))))))))))))))) (833)
22(21(11(11(10(01(11(10(01(12(20(01(12(22(21(11(11(10(01(12(20(x1))))))))))))))))))))) → 21(10(01(11(11(10(00(00(02(21(11(10(00(01(12(20(01(12(20(02(20(x1))))))))))))))))))))) (853)
22(21(11(11(10(01(11(10(01(12(20(01(12(22(21(11(11(10(01(12(21(x1))))))))))))))))))))) → 21(10(01(11(11(10(00(00(02(21(11(10(00(01(12(20(01(12(20(02(21(x1))))))))))))))))))))) (854)
22(21(11(11(10(01(11(10(01(12(20(01(12(22(21(11(11(10(01(12(22(x1))))))))))))))))))))) → 21(10(01(11(11(10(00(00(02(21(11(10(00(01(12(20(01(12(20(02(22(x1))))))))))))))))))))) (855)

1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[02(x1)] = 1 · x1
[20(x1)] = 1 · x1 + 9
[01(x1)] = 1 · x1
[12(x1)] = 1 · x1
[21(x1)] = 1 · x1 + 6
[10(x1)] = 1 · x1
[00(x1)] = 1 · x1 + 2
[11(x1)] = 1 · x1
[22(x1)] = 1 · x1
all of the following rules can be deleted.
02(20(01(12(21(10(00(01(12(20(00(01(12(21(11(10(01(10(02(20(x1)))))))))))))))))))) → 01(11(11(11(10(02(20(01(12(21(10(02(21(10(00(02(21(12(20(00(x1)))))))))))))))))))) (310)
10(00(01(10(01(12(20(00(00(01(12(21(10(01(10(00(00(00(01(11(x1)))))))))))))))))))) → 10(01(12(20(01(12(20(01(11(10(00(01(11(11(11(10(02(21(10(01(x1)))))))))))))))))))) (320)
20(01(10(00(01(10(01(12(22(21(12(21(11(11(11(12(20(00(01(11(11(x1))))))))))))))))))))) → 22(20(00(02(21(11(11(11(12(20(01(10(00(01(10(01(11(10(00(00(01(x1))))))))))))))))))))) (449)

1.1.1.1.1.1 R is empty

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