Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/158620)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
1(2(0(1(0(1(1(0(2(1(2(0(0(2(1(1(0(0(0(0(x1)))))))))))))))))))) → 1(0(2(1(2(2(2(0(0(2(1(2(0(2(1(0(1(0(2(2(x1)))))))))))))))))))) (100)
1(2(0(1(0(1(2(2(1(2(2(2(2(2(1(0(1(0(0(0(x1)))))))))))))))))))) → 1(1(0(1(0(0(2(0(0(2(2(2(0(1(2(2(0(2(0(1(x1)))))))))))))))))))) (101)
1(1(0(0(2(1(2(0(2(0(0(1(0(1(1(1(1(0(0(0(x1)))))))))))))))))))) → 1(1(0(1(0(1(1(0(0(2(1(2(2(2(1(0(2(2(2(0(x1)))))))))))))))))))) (102)
0(1(0(2(1(2(1(0(2(1(0(2(0(1(2(0(2(0(0(0(x1)))))))))))))))))))) → 0(1(2(0(0(0(0(2(2(0(1(0(0(2(1(2(0(0(2(2(x1)))))))))))))))))))) (103)
1(1(2(1(1(1(2(0(2(0(2(0(2(2(1(1(2(0(0(0(x1)))))))))))))))))))) → 1(1(0(2(2(2(2(2(0(0(1(0(0(0(2(2(1(2(1(2(x1)))))))))))))))))))) (104)
1(2(1(1(2(1(0(2(0(2(2(1(1(1(2(2(2(0(0(0(x1)))))))))))))))))))) → 1(0(2(2(1(0(1(1(0(1(2(0(0(2(2(2(0(0(2(2(x1)))))))))))))))))))) (105)
1(2(0(1(0(2(2(2(0(1(0(0(1(1(2(0(0(1(0(0(x1)))))))))))))))))))) → 1(0(0(1(0(2(2(2(0(2(1(0(0(2(1(1(0(0(2(0(x1)))))))))))))))))))) (106)
1(1(2(2(0(0(1(0(2(0(2(1(2(1(2(1(1(1(0(0(x1)))))))))))))))))))) → 1(0(1(2(2(0(0(2(0(2(2(0(1(0(0(0(0(1(1(1(x1)))))))))))))))))))) (107)
2(2(2(0(0(0(0(1(2(2(2(1(0(0(1(2(1(1(0(0(x1)))))))))))))))))))) → 0(2(2(0(1(1(1(0(0(1(2(0(0(0(2(0(0(2(1(0(x1)))))))))))))))))))) (108)
1(1(2(1(1(1(2(2(1(2(0(0(0(2(1(0(2(1(0(0(x1)))))))))))))))))))) → 1(0(1(0(2(1(0(2(2(0(2(1(0(0(1(1(2(2(0(0(x1)))))))))))))))))))) (109)
2(1(1(2(0(2(0(0(0(1(1(0(2(1(2(0(2(1(0(0(x1)))))))))))))))))))) → 0(2(2(1(1(0(1(2(0(2(0(2(0(0(0(0(0(0(1(1(x1)))))))))))))))))))) (110)
1(2(1(0(1(0(0(2(2(0(2(1(2(1(2(2(2(1(0(0(x1)))))))))))))))))))) → 1(2(2(1(0(2(1(0(1(2(1(2(0(0(2(2(0(0(2(0(x1)))))))))))))))))))) (111)
1(0(1(1(0(2(1(0(2(0(2(0(1(2(2(0(0(2(0(0(x1)))))))))))))))))))) → 1(2(2(0(2(2(2(1(0(1(0(0(0(1(2(0(2(2(2(0(x1)))))))))))))))))))) (112)
0(0(2(0(1(0(2(0(0(2(1(2(1(1(0(1(0(2(0(0(x1)))))))))))))))))))) → 2(2(2(1(0(0(2(0(2(0(0(1(0(1(2(0(2(1(2(0(x1)))))))))))))))))))) (113)
0(2(2(1(0(0(1(1(2(0(2(2(0(2(2(1(0(2(0(0(x1)))))))))))))))))))) → 0(0(0(2(0(2(0(2(2(0(1(2(0(2(0(2(0(1(2(2(x1)))))))))))))))))))) (114)
0(0(1(0(2(0(1(0(0(2(1(2(2(0(2(0(1(2(0(0(x1)))))))))))))))))))) → 0(2(2(1(0(1(2(2(0(2(0(2(1(2(2(0(0(2(1(0(x1)))))))))))))))))))) (115)
1(2(2(1(2(2(0(2(2(1(1(0(2(2(2(1(1(2(0(0(x1)))))))))))))))))))) → 1(2(2(2(2(2(0(1(1(0(0(2(0(1(2(1(2(2(0(0(x1)))))))))))))))))))) (116)
1(0(2(0(2(0(0(1(1(1(2(0(0(2(0(1(2(2(0(0(x1)))))))))))))))))))) → 1(0(2(0(1(0(2(0(2(0(0(0(2(2(0(2(1(0(0(2(x1)))))))))))))))))))) (117)
2(2(1(0(2(1(0(1(2(2(2(2(0(2(0(1(2(2(0(0(x1)))))))))))))))))))) → 1(0(0(1(0(0(0(2(0(0(0(2(0(0(1(0(2(2(1(0(x1)))))))))))))))))))) (118)
1(2(0(1(2(2(2(0(2(1(1(2(2(2(0(1(2(2(0(0(x1)))))))))))))))))))) → 1(1(2(2(0(0(2(0(1(2(1(0(0(0(2(2(0(2(0(2(x1)))))))))))))))))))) (119)
0(0(1(0(0(0(2(1(1(2(2(0(1(0(1(2(2(2(0(0(x1)))))))))))))))))))) → 0(0(1(2(2(2(1(1(2(0(0(1(1(0(0(2(0(0(2(0(x1)))))))))))))))))))) (120)
1(0(1(2(2(1(0(0(2(1(1(0(0(0(1(0(0(0(1(0(x1)))))))))))))))))))) → 1(2(1(2(2(2(0(0(0(2(2(1(0(0(1(1(0(2(0(2(x1)))))))))))))))))))) (121)
0(0(1(1(2(0(0(2(0(2(0(0(2(1(0(1(0(0(1(0(x1)))))))))))))))))))) → 1(2(0(2(2(0(2(2(0(0(2(2(2(1(0(0(1(2(2(2(x1)))))))))))))))))))) (122)
0(2(0(2(0(0(2(0(2(0(0(1(1(2(0(0(1(0(1(0(x1)))))))))))))))))))) → 2(1(0(2(0(1(2(1(2(2(0(2(0(2(0(2(2(2(1(0(x1)))))))))))))))))))) (123)
1(1(1(1(2(1(0(0(2(0(2(2(0(2(2(0(1(0(1(0(x1)))))))))))))))))))) → 1(0(2(0(0(2(2(0(1(2(2(0(0(0(1(2(1(1(1(0(x1)))))))))))))))))))) (124)
1(2(2(0(0(2(1(0(2(0(1(1(0(0(2(2(1(0(1(0(x1)))))))))))))))))))) → 1(0(2(2(0(1(2(1(0(2(2(2(1(2(2(0(2(2(0(1(x1)))))))))))))))))))) (125)
1(2(2(0(1(1(2(2(1(2(0(1(2(0(1(0(2(0(1(0(x1)))))))))))))))))))) → 0(2(1(0(2(0(0(0(0(1(2(0(2(1(0(2(0(2(2(2(x1)))))))))))))))))))) (126)
1(1(2(0(2(1(0(2(0(0(0(2(1(0(2(1(0(1(1(0(x1)))))))))))))))))))) → 1(1(0(0(0(0(0(1(0(1(2(0(2(0(0(0(1(0(2(2(x1)))))))))))))))))))) (127)
1(2(0(0(0(0(0(2(2(0(1(1(1(2(2(1(0(1(1(0(x1)))))))))))))))))))) → 1(1(2(0(2(2(1(1(2(1(0(2(2(2(1(1(2(2(0(0(x1)))))))))))))))))))) (128)
0(0(2(0(1(2(2(2(2(2(1(0(2(1(1(2(0(1(1(0(x1)))))))))))))))))))) → 2(1(1(2(2(0(2(0(1(2(2(0(0(2(1(1(2(1(2(0(x1)))))))))))))))))))) (129)
1(0(0(2(2(1(2(2(1(1(0(0(0(2(1(2(1(1(1(0(x1)))))))))))))))))))) → 0(0(2(0(0(0(0(0(0(2(1(2(0(1(1(2(2(1(2(0(x1)))))))))))))))))))) (130)
1(2(0(2(0(1(0(1(2(2(1(2(0(1(0(0(2(1(1(0(x1)))))))))))))))))))) → 0(2(2(2(2(2(2(2(1(2(0(1(0(0(2(2(0(2(1(0(x1)))))))))))))))))))) (131)
1(2(2(1(0(2(0(1(1(1(0(1(1(1(1(0(0(2(1(0(x1)))))))))))))))))))) → 0(2(0(2(1(0(1(2(2(1(0(2(1(2(2(0(2(2(1(0(x1)))))))))))))))))))) (132)
1(1(1(0(2(0(0(1(0(1(2(2(0(1(2(2(0(2(1(0(x1)))))))))))))))))))) → 1(1(1(2(1(2(0(0(0(0(2(1(0(1(2(0(0(2(0(2(x1)))))))))))))))))))) (133)
1(0(0(2(0(0(1(2(2(0(0(0(1(1(1(0(1(2(1(0(x1)))))))))))))))))))) → 1(2(2(1(1(0(2(2(0(0(1(0(0(0(2(1(0(1(2(0(x1)))))))))))))))))))) (134)
1(1(2(2(2(0(0(1(2(2(2(1(2(2(1(0(1(2(1(0(x1)))))))))))))))))))) → 1(1(0(2(2(0(1(2(2(0(1(0(2(2(2(2(1(2(2(2(x1)))))))))))))))))))) (135)
1(1(0(2(1(1(0(2(1(1(0(2(0(0(2(0(1(2(1(0(x1)))))))))))))))))))) → 1(0(2(0(0(1(2(0(1(0(1(2(2(1(0(2(2(2(1(0(x1)))))))))))))))))))) (136)
1(0(0(0(1(2(2(1(0(2(2(0(0(1(0(2(1(2(1(0(x1)))))))))))))))))))) → 1(1(1(0(0(2(2(1(0(0(0(2(2(0(2(0(2(0(0(2(x1)))))))))))))))))))) (137)
1(0(2(1(2(0(1(2(2(1(1(0(1(0(2(0(0(0(2(0(x1)))))))))))))))))))) → 1(2(2(0(0(0(0(2(2(2(2(1(0(0(0(2(0(2(0(1(x1)))))))))))))))))))) (138)
1(1(2(1(1(1(1(2(1(0(2(0(2(1(0(2(0(0(2(0(x1)))))))))))))))))))) → 1(1(0(0(2(1(2(2(2(0(0(2(2(1(2(1(2(1(2(1(x1)))))))))))))))))))) (139)
2(0(1(1(0(2(1(2(1(2(0(2(0(2(0(1(1(0(2(0(x1)))))))))))))))))))) → 0(1(2(1(0(2(0(2(0(2(2(1(0(2(2(2(1(1(1(0(x1)))))))))))))))))))) (140)
1(2(2(0(2(1(2(0(0(0(1(1(0(2(1(0(2(0(2(0(x1)))))))))))))))))))) → 1(0(2(2(1(0(0(0(2(0(0(0(0(2(2(2(0(0(1(0(x1)))))))))))))))))))) (141)
1(2(0(1(1(0(0(2(0(1(0(2(0(1(0(1(2(0(2(0(x1)))))))))))))))))))) → 1(0(0(2(2(0(1(2(2(0(1(2(1(1(0(0(0(1(2(0(x1)))))))))))))))))))) (142)
0(0(2(1(1(2(2(0(0(0(1(1(2(2(0(1(0(1(2(0(x1)))))))))))))))))))) → 0(0(1(1(2(2(2(2(0(2(0(2(2(0(1(1(2(2(0(1(x1)))))))))))))))))))) (143)
1(2(1(2(0(2(2(1(1(0(1(2(0(2(2(2(1(1(2(0(x1)))))))))))))))))))) → 2(0(0(2(2(0(0(1(2(2(2(0(2(0(0(0(0(1(0(2(x1)))))))))))))))))))) (144)
2(0(2(1(2(2(1(0(2(2(2(2(0(2(2(2(1(1(2(0(x1)))))))))))))))))))) → 1(0(0(0(2(0(2(0(0(2(0(2(1(0(0(2(1(2(0(2(x1)))))))))))))))))))) (145)
0(2(2(2(2(1(0(1(2(2(0(2(0(2(2(0(2(1(2(0(x1)))))))))))))))))))) → 0(0(2(0(0(2(0(0(0(0(1(0(1(2(0(2(0(0(2(0(x1)))))))))))))))))))) (146)
1(0(2(1(0(0(2(1(0(1(2(1(0(1(0(2(2(1(2(0(x1)))))))))))))))))))) → 1(2(0(2(2(0(0(0(0(1(0(2(0(0(1(2(2(1(0(2(x1)))))))))))))))))))) (147)
1(1(1(0(0(2(2(2(2(1(1(2(1(1(0(0(0(2(2(0(x1)))))))))))))))))))) → 1(0(0(1(1(2(0(2(0(1(1(2(0(2(2(2(0(2(2(0(x1)))))))))))))))))))) (148)
1(1(1(1(2(1(2(0(0(2(0(2(1(0(0(1(0(2(2(0(x1)))))))))))))))))))) → 1(2(0(0(2(2(1(0(0(2(1(0(1(2(1(0(2(2(2(0(x1)))))))))))))))))))) (149)
1(0(1(0(1(2(2(0(1(1(2(2(0(0(2(1(0(2(2(0(x1)))))))))))))))))))) → 1(2(0(1(0(0(2(2(0(1(2(0(0(1(1(2(1(0(2(0(x1)))))))))))))))))))) (150)
1(0(0(1(0(0(2(1(1(1(2(0(0(2(0(0(1(2(2(0(x1)))))))))))))))))))) → 1(0(2(0(0(1(2(0(0(2(0(2(0(2(1(0(0(1(0(2(x1)))))))))))))))))))) (151)
1(1(2(2(0(2(0(1(1(1(0(2(0(2(2(1(1(2(2(0(x1)))))))))))))))))))) → 0(2(0(2(2(2(0(0(1(1(0(0(0(2(0(2(0(0(0(2(x1)))))))))))))))))))) (152)
1(2(1(2(0(1(2(2(0(0(1(2(1(0(0(2(1(2(2(0(x1)))))))))))))))))))) → 1(2(2(1(0(1(2(0(2(1(2(2(0(2(2(0(0(1(0(0(x1)))))))))))))))))))) (153)
1(1(2(2(1(1(0(0(2(1(1(2(1(0(0(2(2(2(2(0(x1)))))))))))))))))))) → 1(1(2(2(1(2(2(2(0(2(1(2(0(0(2(2(0(0(0(1(x1)))))))))))))))))))) (154)
1(1(0(2(1(0(2(1(1(2(0(0(0(2(1(0(0(0(0(1(x1)))))))))))))))))))) → 1(0(0(0(2(1(1(2(0(0(2(0(0(2(0(1(2(1(2(0(x1)))))))))))))))))))) (155)
1(2(0(1(0(0(2(2(2(1(1(0(1(2(0(1(0(0(0(1(x1)))))))))))))))))))) → 1(2(0(2(1(0(1(2(2(0(1(0(1(0(2(1(0(2(2(1(x1)))))))))))))))))))) (156)
1(2(0(1(2(0(2(0(2(2(0(0(2(2(1(1(2(0(0(1(x1)))))))))))))))))))) → 1(0(2(0(0(0(2(2(2(2(2(2(1(1(0(2(0(1(2(0(x1)))))))))))))))))))) (157)
1(1(2(1(2(2(1(1(0(0(0(0(2(1(2(1(0(2(0(1(x1)))))))))))))))))))) → 2(0(0(2(2(2(2(2(2(0(2(1(2(2(0(2(2(1(0(1(x1)))))))))))))))))))) (158)
1(1(2(2(0(2(1(0(2(0(1(0(2(2(2(0(1(2(0(1(x1)))))))))))))))))))) → 0(2(0(2(0(0(2(0(2(0(1(0(2(0(1(0(0(0(0(0(x1)))))))))))))))))))) (159)
1(2(1(2(2(1(0(2(2(0(0(0(1(0(1(0(2(2(0(1(x1)))))))))))))))))))) → 0(2(0(0(0(2(0(0(2(0(2(2(2(0(0(0(2(2(2(0(x1)))))))))))))))))))) (160)
1(1(1(1(0(1(0(2(2(2(2(0(2(2(1(2(2(2(0(1(x1)))))))))))))))))))) → 0(2(0(0(2(1(0(0(1(2(2(2(0(0(0(0(0(2(1(1(x1)))))))))))))))))))) (161)
1(2(2(1(2(2(0(1(0(0(0(2(2(1(2(0(2(0(1(1(x1)))))))))))))))))))) → 1(2(0(2(1(2(2(2(0(0(2(1(2(2(2(1(2(1(2(0(x1)))))))))))))))))))) (162)
0(2(1(2(0(1(0(2(2(2(2(0(2(0(2(2(2(0(1(1(x1)))))))))))))))))))) → 2(0(1(0(0(0(2(2(2(1(0(0(2(2(1(2(0(0(0(1(x1)))))))))))))))))))) (163)
1(2(0(1(2(2(1(2(1(0(0(1(0(0(0(2(0(1(1(1(x1)))))))))))))))))))) → 1(2(2(1(1(0(2(2(2(1(2(0(0(1(0(2(2(1(1(1(x1)))))))))))))))))))) (164)
1(1(0(0(0(0(1(1(0(0(2(2(2(2(0(2(0(1(1(1(x1)))))))))))))))))))) → 1(2(0(0(1(2(0(2(2(2(0(0(0(1(1(1(0(2(0(1(x1)))))))))))))))))))) (165)
1(0(1(0(1(0(2(0(2(0(2(2(2(1(1(2(0(1(1(1(x1)))))))))))))))))))) → 0(0(1(2(1(0(0(1(1(0(2(0(2(0(2(2(0(0(2(1(x1)))))))))))))))))))) (166)
1(0(2(1(0(1(0(2(2(0(1(2(0(2(0(2(0(2(1(1(x1)))))))))))))))))))) → 1(2(1(0(2(0(2(2(0(1(2(2(1(2(1(2(0(0(0(0(x1)))))))))))))))))))) (167)
1(1(2(1(0(2(2(0(1(1(2(2(0(0(0(0(2(2(1(1(x1)))))))))))))))))))) → 0(0(0(2(1(2(1(2(2(2(2(0(1(0(2(0(0(2(2(0(x1)))))))))))))))))))) (168)
1(1(0(0(0(2(0(1(2(2(1(1(2(0(1(0(1(0(2(1(x1)))))))))))))))))))) → 1(1(0(0(2(2(1(1(2(2(0(1(0(0(0(1(1(0(2(2(x1)))))))))))))))))))) (169)
1(2(2(2(2(1(2(2(2(1(1(1(1(0(0(0(2(0(2(1(x1)))))))))))))))))))) → 0(0(2(1(2(1(2(2(2(1(2(2(0(0(0(0(0(2(2(2(x1)))))))))))))))))))) (170)
1(0(2(1(2(2(1(2(0(2(2(1(1(2(1(0(2(0(2(1(x1)))))))))))))))))))) → 0(2(2(0(2(2(1(2(0(2(2(2(0(0(0(0(1(0(0(2(x1)))))))))))))))))))) (171)
1(1(0(0(2(0(1(2(0(2(1(2(2(2(0(0(1(1(2(1(x1)))))))))))))))))))) → 2(2(2(2(0(2(0(2(2(2(2(0(0(2(0(1(2(0(0(2(x1)))))))))))))))))))) (172)
1(1(0(2(1(0(0(1(1(0(2(0(0(1(0(2(2(1(2(1(x1)))))))))))))))))))) → 2(1(0(2(2(2(2(1(1(0(2(0(0(2(0(0(2(0(2(2(x1)))))))))))))))))))) (173)
0(2(0(2(0(1(1(1(1(2(2(0(2(2(1(1(0(2(2(1(x1)))))))))))))))))))) → 2(2(2(2(0(1(0(1(0(2(1(2(0(1(1(2(2(2(0(1(x1)))))))))))))))))))) (174)
1(2(1(0(0(2(2(0(2(2(0(1(0(0(0(1(1(2(2(1(x1)))))))))))))))))))) → 1(1(2(1(2(2(0(0(1(2(2(2(2(2(2(2(1(0(0(0(x1)))))))))))))))))))) (175)
1(2(2(0(0(2(1(0(2(1(2(2(0(2(0(1(1(2(2(1(x1)))))))))))))))))))) → 1(1(0(2(0(0(2(2(2(2(0(2(0(1(0(1(1(0(2(0(x1)))))))))))))))))))) (176)
1(0(0(2(1(1(0(1(0(2(2(2(0(1(2(2(2(2(2(1(x1)))))))))))))))))))) → 0(0(0(0(0(0(0(2(0(0(2(2(1(0(1(0(2(2(1(0(x1)))))))))))))))))))) (177)
1(1(1(1(1(0(0(0(0(2(0(2(1(2(0(0(1(0(0(2(x1)))))))))))))))))))) → 1(2(1(0(1(0(2(2(2(0(1(1(0(0(0(1(0(2(0(2(x1)))))))))))))))))))) (178)
1(1(2(1(2(2(0(1(1(0(2(2(2(1(0(0(2(0(0(2(x1)))))))))))))))))))) → 0(0(0(0(0(0(0(0(0(0(0(0(1(2(0(2(1(2(2(2(x1)))))))))))))))))))) (179)
2(1(0(1(2(1(1(1(2(2(1(0(1(2(0(0(2(0(0(2(x1)))))))))))))))))))) → 2(2(1(1(1(0(2(2(2(2(0(2(0(1(0(1(1(2(2(2(x1)))))))))))))))))))) (180)
1(0(1(1(1(0(1(2(2(0(0(2(1(2(0(0(2(0(0(2(x1)))))))))))))))))))) → 1(0(2(0(1(1(0(1(0(2(1(2(0(0(0(0(2(1(2(2(x1)))))))))))))))))))) (181)
0(2(1(1(0(2(2(0(0(1(2(2(2(0(1(1(2(0(0(2(x1)))))))))))))))))))) → 1(0(1(0(2(2(2(1(2(0(2(2(0(0(2(1(0(2(2(1(x1)))))))))))))))))))) (182)
1(2(0(1(0(2(2(2(0(2(0(1(1(2(0(1(0(1(0(2(x1)))))))))))))))))))) → 1(2(0(1(0(2(0(2(2(2(2(2(1(0(2(1(1(0(0(1(x1)))))))))))))))))))) (183)
0(2(0(0(0(2(2(2(1(0(1(2(2(0(2(2(0(1(0(2(x1)))))))))))))))))))) → 2(0(2(2(2(0(0(2(2(2(1(0(2(2(1(2(1(0(0(2(x1)))))))))))))))))))) (184)
1(1(0(0(0(2(1(2(1(1(2(0(1(2(1(2(1(1(0(2(x1)))))))))))))))))))) → 1(2(1(1(1(0(2(2(2(1(0(2(2(2(2(1(2(1(0(1(x1)))))))))))))))))))) (185)
1(2(0(1(0(0(1(0(0(2(1(2(2(0(2(2(1(1(0(2(x1)))))))))))))))))))) → 0(2(2(0(0(0(0(0(1(2(2(0(2(0(2(2(2(0(1(2(x1)))))))))))))))))))) (186)
0(0(0(2(1(2(2(2(1(1(0(2(2(2(0(0(2(1(0(2(x1)))))))))))))))))))) → 0(2(2(0(2(1(2(0(2(2(2(2(2(0(0(1(0(1(2(2(x1)))))))))))))))))))) (187)
2(0(2(2(2(1(2(2(1(2(2(2(0(1(1(0(2(1(0(2(x1)))))))))))))))))))) → 2(0(1(2(2(1(2(2(1(1(2(0(1(0(0(2(2(0(0(2(x1)))))))))))))))))))) (188)
1(2(0(2(2(0(0(2(1(0(1(0(0(2(1(1(2(1(0(2(x1)))))))))))))))))))) → 0(0(0(1(2(0(0(0(0(0(2(2(0(0(2(0(1(0(2(0(x1)))))))))))))))))))) (189)
0(1(1(2(0(1(0(2(0(1(2(0(0(0(1(2(2(2(0(2(x1)))))))))))))))))))) → 0(2(0(1(1(2(0(1(0(0(2(2(2(2(2(1(2(1(2(2(x1)))))))))))))))))))) (190)
1(2(2(2(0(0(0(0(0(2(1(1(2(2(2(0(1(2(1(2(x1)))))))))))))))))))) → 1(0(2(2(2(2(0(1(2(0(2(2(0(2(2(0(2(1(2(1(x1)))))))))))))))))))) (191)
2(2(2(2(2(1(1(2(0(0(2(1(1(2(1(0(1(0(2(2(x1)))))))))))))))))))) → 0(1(2(1(1(1(0(2(1(0(0(0(0(1(0(0(2(2(0(0(x1)))))))))))))))))))) (192)
1(2(0(1(0(2(0(2(0(1(0(2(2(0(2(2(2(1(2(2(x1)))))))))))))))))))) → 1(2(2(1(2(2(2(2(0(0(2(2(0(1(0(2(0(2(2(0(x1)))))))))))))))))))) (193)
1(0(0(2(0(2(1(2(2(2(2(0(1(1(2(2(2(1(2(2(x1)))))))))))))))))))) → 1(2(2(0(2(1(1(0(2(0(2(0(0(2(1(2(1(0(0(0(x1)))))))))))))))))))) (194)
0(2(0(2(0(0(0(1(1(0(1(1(2(2(1(0(0(2(2(2(x1)))))))))))))))))))) → 2(0(2(0(2(1(1(2(1(2(2(0(2(1(1(0(2(0(2(2(x1)))))))))))))))))))) (195)
0(0(0(0(2(0(2(2(0(1(1(0(2(0(1(1(0(2(2(2(x1)))))))))))))))))))) → 0(0(1(2(0(1(0(2(0(0(0(1(1(2(2(0(0(0(0(2(x1)))))))))))))))))))) (196)
1(2(2(2(2(0(1(1(0(0(0(2(2(1(1(1(0(2(2(2(x1)))))))))))))))))))) → 0(1(2(2(1(0(1(0(2(0(0(2(0(0(2(2(0(0(0(2(x1)))))))))))))))))))) (197)
0(1(0(1(2(1(2(1(0(0(2(1(0(1(2(2(0(2(2(2(x1)))))))))))))))))))) → 0(0(2(2(0(2(1(0(2(1(0(2(1(0(1(2(2(0(1(1(x1)))))))))))))))))))) (198)

1.1 Closure Under Flat Contexts

Using the flat contexts

{1(☐), 2(☐), 0(☐)}

We obtain the transformed TRS

There are 171 ruless (increase limit for explicit display).

1.1.1 Semantic Labeling

Root-labeling is applied.

We obtain the labeled TRS

There are 513 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

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

There are 381 ruless (increase limit for explicit display).

1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[00(x1)] = 1 · x1
[01(x1)] = 1 · x1 + 9
[10(x1)] = 1 · x1
[02(x1)] = 1 · x1 + 5
[20(x1)] = 1 · x1
[21(x1)] = 1 · x1
[12(x1)] = 1 · x1 + 4
[22(x1)] = 1 · x1 + 4
[11(x1)] = 1 · x1 + 5
all of the following rules can be deleted.

There are 119 ruless (increase limit for explicit display).

1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[12(x1)] = 1 · x1 + 1
[20(x1)] = 1 · x1 + 2
[01(x1)] = 1 · x1 + 2
[22(x1)] = 1 · x1 + 2
[21(x1)] = 1 · x1
[10(x1)] = 1 · x1
[00(x1)] = 1 · x1
[02(x1)] = 1 · x1 + 1
[11(x1)] = 1 · x1
all of the following rules can be deleted.
12(22(22(20(00(00(00(01(12(22(22(21(10(00(01(12(21(11(10(00(01(x1))))))))))))))))))))) → 10(02(22(20(01(11(11(10(00(01(12(20(00(00(02(20(00(02(21(10(01(x1))))))))))))))))))))) (496)
12(22(22(20(00(00(00(01(12(22(22(21(10(00(01(12(21(11(10(00(02(x1))))))))))))))))))))) → 10(02(22(20(01(11(11(10(00(01(12(20(00(00(02(20(00(02(21(10(02(x1))))))))))))))))))))) (497)
12(22(22(20(00(00(00(01(12(22(22(21(10(00(01(12(21(11(10(00(00(x1))))))))))))))))))))) → 10(02(22(20(01(11(11(10(00(01(12(20(00(00(02(20(00(02(21(10(00(x1))))))))))))))))))))) (498)

1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[12(x1)] = 1 · x1
[20(x1)] = 1 · x1
[01(x1)] = 1 · x1 + 3
[22(x1)] = 1 · x1 + 1
[21(x1)] = 1 · x1
[10(x1)] = 1 · x1 + 1
[00(x1)] = 1 · x1
[02(x1)] = 1 · x1
[11(x1)] = 1 · x1 + 3
all of the following rules can be deleted.
22(22(22(20(00(00(00(01(12(22(22(21(10(00(01(12(21(11(10(00(01(x1))))))))))))))))))))) → 20(02(22(20(01(11(11(10(00(01(12(20(00(00(02(20(00(02(21(10(01(x1))))))))))))))))))))) (499)
22(22(22(20(00(00(00(01(12(22(22(21(10(00(01(12(21(11(10(00(02(x1))))))))))))))))))))) → 20(02(22(20(01(11(11(10(00(01(12(20(00(00(02(20(00(02(21(10(02(x1))))))))))))))))))))) (500)
22(22(22(20(00(00(00(01(12(22(22(21(10(00(01(12(21(11(10(00(00(x1))))))))))))))))))))) → 20(02(22(20(01(11(11(10(00(01(12(20(00(00(02(20(00(02(21(10(00(x1))))))))))))))))))))) (501)

1.1.1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
12#(20(01(12(22(21(12(21(10(00(01(10(00(00(02(20(01(11(11(11(x1)))))))))))))))))))) → 12#(22(21(11(10(02(22(22(21(12(20(00(01(10(02(22(21(11(11(11(x1)))))))))))))))))))) (820)
12#(20(01(12(22(21(12(21(10(00(01(10(00(00(02(20(01(11(11(11(x1)))))))))))))))))))) → 12#(20(00(01(10(02(22(21(11(11(11(x1))))))))))) (821)
12#(20(01(12(22(21(12(21(10(00(01(10(00(00(02(20(01(11(11(11(x1)))))))))))))))))))) → 20#(00(01(10(02(22(21(11(11(11(x1)))))))))) (822)
12#(20(01(12(22(21(12(21(10(00(01(10(00(00(02(20(01(11(11(11(x1)))))))))))))))))))) → 00#(01(10(02(22(21(11(11(11(x1))))))))) (823)
12#(20(01(12(22(21(12(21(10(00(01(10(00(00(02(20(01(11(11(12(x1)))))))))))))))))))) → 12#(22(21(11(10(02(22(22(21(12(20(00(01(10(02(22(21(11(11(12(x1)))))))))))))))))))) (824)
12#(20(01(12(22(21(12(21(10(00(01(10(00(00(02(20(01(11(11(12(x1)))))))))))))))))))) → 12#(20(00(01(10(02(22(21(11(11(12(x1))))))))))) (825)
12#(20(01(12(22(21(12(21(10(00(01(10(00(00(02(20(01(11(11(12(x1)))))))))))))))))))) → 20#(00(01(10(02(22(21(11(11(12(x1)))))))))) (826)
12#(20(01(12(22(21(12(21(10(00(01(10(00(00(02(20(01(11(11(12(x1)))))))))))))))))))) → 00#(01(10(02(22(21(11(11(12(x1))))))))) (827)
12#(20(01(12(22(21(12(21(10(00(01(10(00(00(02(20(01(11(11(10(x1)))))))))))))))))))) → 12#(22(21(11(10(02(22(22(21(12(20(00(01(10(02(22(21(11(11(10(x1)))))))))))))))))))) (828)
12#(20(01(12(22(21(12(21(10(00(01(10(00(00(02(20(01(11(11(10(x1)))))))))))))))))))) → 12#(20(00(01(10(02(22(21(11(11(10(x1))))))))))) (829)
12#(20(01(12(22(21(12(21(10(00(01(10(00(00(02(20(01(11(11(10(x1)))))))))))))))))))) → 20#(00(01(10(02(22(21(11(11(10(x1)))))))))) (830)
12#(20(01(12(22(21(12(21(10(00(01(10(00(00(02(20(01(11(11(10(x1)))))))))))))))))))) → 00#(01(10(02(22(21(11(11(10(x1))))))))) (831)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(21(x1)))))))))))))))))))) → 20#(01(12(22(21(12(22(21(11(12(20(01(10(00(02(22(20(00(02(21(x1)))))))))))))))))))) (832)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(21(x1)))))))))))))))))))) → 12#(22(21(12(22(21(11(12(20(01(10(00(02(22(20(00(02(21(x1)))))))))))))))))) (833)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(21(x1)))))))))))))))))))) → 12#(22(21(11(12(20(01(10(00(02(22(20(00(02(21(x1))))))))))))))) (834)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(21(x1)))))))))))))))))))) → 12#(20(01(10(00(02(22(20(00(02(21(x1))))))))))) (835)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(21(x1)))))))))))))))))))) → 20#(01(10(00(02(22(20(00(02(21(x1)))))))))) (836)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(21(x1)))))))))))))))))))) → 00#(02(22(20(00(02(21(x1))))))) (837)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(21(x1)))))))))))))))))))) → 20#(00(02(21(x1)))) (838)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(21(x1)))))))))))))))))))) → 00#(02(21(x1))) (839)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(22(x1)))))))))))))))))))) → 20#(01(12(22(21(12(22(21(11(12(20(01(10(00(02(22(20(00(02(22(x1)))))))))))))))))))) (840)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(22(x1)))))))))))))))))))) → 12#(22(21(12(22(21(11(12(20(01(10(00(02(22(20(00(02(22(x1)))))))))))))))))) (841)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(22(x1)))))))))))))))))))) → 12#(22(21(11(12(20(01(10(00(02(22(20(00(02(22(x1))))))))))))))) (842)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(22(x1)))))))))))))))))))) → 12#(20(01(10(00(02(22(20(00(02(22(x1))))))))))) (843)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(22(x1)))))))))))))))))))) → 20#(01(10(00(02(22(20(00(02(22(x1)))))))))) (844)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(22(x1)))))))))))))))))))) → 00#(02(22(20(00(02(22(x1))))))) (845)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(22(x1)))))))))))))))))))) → 20#(00(02(22(x1)))) (846)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(22(x1)))))))))))))))))))) → 00#(02(22(x1))) (847)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(20(x1)))))))))))))))))))) → 20#(01(12(22(21(12(22(21(11(12(20(01(10(00(02(22(20(00(02(20(x1)))))))))))))))))))) (848)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(20(x1)))))))))))))))))))) → 12#(22(21(12(22(21(11(12(20(01(10(00(02(22(20(00(02(20(x1)))))))))))))))))) (849)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(20(x1)))))))))))))))))))) → 12#(22(21(11(12(20(01(10(00(02(22(20(00(02(20(x1))))))))))))))) (850)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(20(x1)))))))))))))))))))) → 12#(20(01(10(00(02(22(20(00(02(20(x1))))))))))) (851)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(20(x1)))))))))))))))))))) → 20#(01(10(00(02(22(20(00(02(20(x1)))))))))) (852)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(20(x1)))))))))))))))))))) → 00#(02(22(20(00(02(20(x1))))))) (853)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(20(x1)))))))))))))))))))) → 20#(00(02(20(x1)))) (854)
20#(02(22(22(21(12(22(21(12(22(22(20(01(11(10(02(21(10(02(20(x1)))))))))))))))))))) → 00#(02(20(x1))) (855)
00#(02(21(11(10(02(22(20(00(01(12(22(22(20(01(11(12(20(00(02(21(x1))))))))))))))))))))) → 12#(20(02(22(20(00(02(21(10(02(22(21(11(x1))))))))))))) (856)
00#(02(21(11(10(02(22(20(00(01(12(22(22(20(01(11(12(20(00(02(21(x1))))))))))))))))))))) → 20#(02(22(20(00(02(21(10(02(22(21(11(x1)))))))))))) (857)
00#(02(21(11(10(02(22(20(00(01(12(22(22(20(01(11(12(20(00(02(21(x1))))))))))))))))))))) → 20#(00(02(21(10(02(22(21(11(x1))))))))) (858)
00#(02(21(11(10(02(22(20(00(01(12(22(22(20(01(11(12(20(00(02(21(x1))))))))))))))))))))) → 00#(02(21(10(02(22(21(11(x1)))))))) (859)

1.1.1.1.1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.