Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/152865)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[1(x1)] = x1 +
1
[0(x1)] = x1 +
0
all of the following rules can be deleted.
0(0(0(1(0(1(1(1(0(0(0(1(1(1(1(1(0(1(0(0(x1)))))))))))))))))))) → 0(0(1(0(0(0(1(1(1(1(0(0(0(1(0(1(0(1(0(1(x1)))))))))))))))))))) (6)
0(0(0(1(1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(0(x1)))))))))))))))))))) → 0(0(0(0(0(0(1(0(0(0(1(1(0(0(1(0(0(0(1(0(x1)))))))))))))))))))) (7)
0(0(1(0(0(0(1(1(1(0(1(0(1(0(0(0(0(1(1(0(x1)))))))))))))))))))) → 1(0(0(1(0(0(1(1(0(0(1(0(0(0(0(0(1(0(0(1(x1)))))))))))))))))))) (12)
0(0(1(1(0(0(1(0(1(0(1(0(1(0(0(1(1(0(0(0(x1)))))))))))))))))))) → 0(0(0(0(1(0(0(1(0(1(0(0(1(0(0(0(1(0(1(1(x1)))))))))))))))))))) (17)
0(1(0(0(0(0(0(0(1(1(0(1(0(1(0(1(1(0(0(0(x1)))))))))))))))))))) → 0(0(1(0(0(0(0(1(0(0(1(0(1(0(0(0(1(0(1(0(x1)))))))))))))))))))) (22)
0(1(0(0(0(1(0(0(0(0(0(1(0(0(1(0(1(0(1(0(x1)))))))))))))))))))) → 1(0(0(0(0(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(x1)))))))))))))))))))) (23)
0(1(0(0(1(0(1(1(0(0(1(0(1(1(1(1(0(1(0(0(x1)))))))))))))))))))) → 1(1(1(0(0(1(0(0(1(1(0(1(0(0(0(0(1(0(0(1(x1)))))))))))))))))))) (24)
0(1(0(1(0(0(1(0(0(0(0(1(0(1(0(1(0(1(1(0(x1)))))))))))))))))))) → 0(0(1(0(0(0(1(0(0(0(0(1(1(0(0(1(0(1(0(1(x1)))))))))))))))))))) (26)
0(1(0(1(1(0(1(1(0(1(0(1(0(0(0(0(1(0(1(0(x1)))))))))))))))))))) → 0(0(0(1(0(0(1(0(0(1(0(1(0(1(0(0(1(1(0(1(x1)))))))))))))))))))) (27)
0(1(0(1(1(1(0(1(0(0(1(1(0(1(0(0(1(1(0(0(x1)))))))))))))))))))) → 0(0(0(1(0(0(0(0(0(1(1(0(0(1(1(0(1(1(1(1(x1)))))))))))))))))))) (28)
0(1(1(0(1(0(0(1(0(0(0(0(1(0(1(0(1(0(1(0(x1)))))))))))))))))))) → 0(0(1(0(0(1(0(0(1(1(0(1(0(1(0(0(0(0(0(1(x1)))))))))))))))))))) (29)
0(1(1(0(1(0(1(0(1(0(0(0(1(0(1(1(0(1(0(0(x1)))))))))))))))))))) → 0(0(0(1(0(1(0(1(0(0(1(1(0(1(1(0(0(0(0(1(x1)))))))))))))))))))) (30)
0(1(1(1(0(1(0(0(1(1(1(1(0(0(1(1(1(0(1(0(x1)))))))))))))))))))) → 0(0(1(0(1(1(1(0(1(0(1(0(1(0(0(1(0(1(1(1(x1)))))))))))))))))))) (31)
0(1(1(1(1(1(1(0(0(0(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))))))))) → 0(1(0(1(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(x1)))))))))))))))))))) (32)
1(0(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(0(1(0(x1)))))))))))))))))))) → 1(1(1(0(0(0(0(0(1(0(0(1(0(1(0(0(0(0(0(1(x1)))))))))))))))))))) (34)
1(0(0(0(1(0(0(0(1(0(1(0(0(1(1(1(0(1(1(0(x1)))))))))))))))))))) → 1(1(0(0(0(0(0(0(1(1(0(1(0(0(1(1(0(0(1(0(x1)))))))))))))))))))) (36)
1(0(0(0(1(1(1(1(0(1(0(0(0(1(0(0(0(1(0(0(x1)))))))))))))))))))) → 1(1(0(0(0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(x1)))))))))))))))))))) (37)
1(0(0(0(1(1(1(1(0(1(0(1(1(1(0(0(0(0(0(0(x1)))))))))))))))))))) → 0(0(0(1(0(0(1(0(0(0(1(0(0(0(0(1(0(0(0(1(x1)))))))))))))))))))) (39)
1(0(0(1(0(0(0(0(0(1(1(1(1(1(1(0(1(0(0(0(x1)))))))))))))))))))) → 1(0(0(0(0(0(0(1(0(1(0(1(1(0(0(0(1(1(0(1(x1)))))))))))))))))))) (40)
1(0(0(1(0(1(0(0(0(1(1(1(1(0(0(0(1(0(0(1(x1)))))))))))))))))))) → 0(0(1(1(0(0(0(0(0(1(1(0(1(0(0(0(0(0(0(1(x1)))))))))))))))))))) (42)
1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(1(1(0(1(0(x1)))))))))))))))))))) → 0(1(1(1(1(0(0(0(0(0(0(0(1(1(0(0(0(0(1(0(x1)))))))))))))))))))) (43)
1(0(0(1(1(0(0(0(0(1(1(1(0(1(1(0(0(0(0(0(x1)))))))))))))))))))) → 1(0(0(0(0(1(1(0(0(1(0(0(0(1(1(0(0(0(0(0(x1)))))))))))))))))))) (44)
1(0(0(1(1(0(0(0(1(0(1(0(0(0(0(1(1(1(0(0(x1)))))))))))))))))))) → 0(0(0(0(0(0(0(1(0(0(0(0(0(1(0(1(0(1(0(0(x1)))))))))))))))))))) (45)
1(0(0(1(1(0(0(1(1(1(0(0(1(0(0(0(0(1(0(0(x1)))))))))))))))))))) → 1(0(0(0(0(0(0(1(1(0(0(0(0(0(1(1(1(0(0(0(x1)))))))))))))))))))) (46)
1(0(0(1(1(0(1(1(1(1(0(1(1(0(0(1(1(0(0(0(x1)))))))))))))))))))) → 0(0(0(1(0(0(1(1(1(0(0(1(0(1(0(1(0(1(0(0(x1)))))))))))))))))))) (48)
1(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(1(1(0(0(x1)))))))))))))))))))) → 1(0(1(0(0(1(1(1(0(0(0(0(0(0(1(1(1(0(0(1(x1)))))))))))))))))))) (49)
1(0(1(0(0(0(0(1(1(1(1(0(1(0(0(1(0(0(0(0(x1)))))))))))))))))))) → 1(0(0(0(0(0(0(1(1(0(0(0(0(0(1(0(0(1(0(0(x1)))))))))))))))))))) (51)
1(0(1(0(0(0(1(0(0(1(0(1(1(0(0(0(0(1(0(0(x1)))))))))))))))))))) → 1(0(1(0(0(0(0(1(0(1(0(1(1(0(0(0(0(0(0(0(x1)))))))))))))))))))) (52)
1(0(1(0(0(0(1(0(1(0(1(0(0(1(1(0(1(1(0(0(x1)))))))))))))))))))) → 1(0(0(0(0(1(1(0(1(1(0(0(1(0(1(0(0(1(0(0(x1)))))))))))))))))))) (54)
1(0(1(0(0(0(1(1(1(1(1(0(0(1(0(0(1(1(0(0(x1)))))))))))))))))))) → 0(0(0(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(0(x1)))))))))))))))))))) (55)
1(0(1(0(0(1(0(1(1(0(1(0(0(1(1(1(0(1(0(0(x1)))))))))))))))))))) → 1(0(0(1(0(1(0(1(0(0(1(0(0(0(1(1(0(0(1(1(x1)))))))))))))))))))) (56)
1(0(1(0(0(1(1(1(1(0(0(0(1(0(0(1(1(1(0(0(x1)))))))))))))))))))) → 1(1(1(0(1(0(0(0(0(1(0(1(0(1(0(0(0(0(1(1(x1)))))))))))))))))))) (58)
1(0(1(0(1(0(0(0(0(0(1(1(0(1(0(1(0(0(0(1(x1)))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(0(0(1(0(0(1(0(0(1(0(0(x1)))))))))))))))))))) (59)
1(0(1(0(1(0(1(0(1(0(1(1(1(0(1(0(0(1(0(0(x1)))))))))))))))))))) → 1(1(1(0(1(0(0(0(0(1(1(0(1(0(0(0(0(0(1(1(x1)))))))))))))))))))) (60)
1(0(1(0(1(1(0(0(0(0(0(0(0(1(0(0(0(1(1(0(x1)))))))))))))))))))) → 0(1(0(0(0(0(0(0(0(0(1(1(0(0(0(0(0(0(1(0(x1)))))))))))))))))))) (62)
1(0(1(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(0(x1)))))))))))))))))))) → 0(1(0(1(0(0(0(0(0(1(1(0(0(0(1(0(1(0(1(0(x1)))))))))))))))))))) (63)
1(0(1(0(1(1(1(0(1(0(1(1(1(0(0(0(1(0(0(0(x1)))))))))))))))))))) → 0(0(0(1(1(1(0(0(0(0(0(1(0(0(1(1(1(0(0(0(x1)))))))))))))))))))) (64)
1(0(1(1(0(0(0(0(0(0(1(0(0(1(0(0(0(1(1(1(x1)))))))))))))))))))) → 1(1(0(0(0(0(0(1(0(0(1(0(0(0(1(1(0(0(0(1(x1)))))))))))))))))))) (65)
1(0(1(1(0(0(0(0(1(0(1(0(1(0(1(0(0(0(0(0(x1)))))))))))))))))))) → 1(0(0(0(1(0(0(0(0(0(0(1(1(0(0(1(0(0(0(1(x1)))))))))))))))))))) (67)
1(0(1(1(0(0(1(0(0(0(1(1(1(0(0(0(0(1(0(1(x1)))))))))))))))))))) → 0(0(0(0(1(1(1(0(1(0(0(0(1(0(0(0(0(0(0(1(x1)))))))))))))))))))) (68)
1(0(1(1(0(1(1(0(0(1(1(0(0(1(1(0(0(0(1(0(x1)))))))))))))))))))) → 0(1(0(0(0(1(1(0(0(0(0(1(0(1(0(0(0(0(1(1(x1)))))))))))))))))))) (70)
1(0(1(1(1(0(0(0(0(1(0(1(0(0(1(1(1(1(0(0(x1)))))))))))))))))))) → 1(0(1(0(1(0(0(0(1(1(0(0(0(1(0(1(0(1(0(1(x1)))))))))))))))))))) (72)
1(1(0(0(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(0(x1)))))))))))))))))))) → 0(0(1(0(0(0(1(0(0(0(0(0(0(0(0(1(0(0(0(0(x1)))))))))))))))))))) (74)
1(1(0(0(0(1(0(0(0(1(0(1(1(1(0(1(1(0(0(0(x1)))))))))))))))))))) → 1(0(1(0(1(0(0(0(1(0(1(0(0(0(1(1(0(0(0(1(x1)))))))))))))))))))) (75)
1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(0(0(1(0(0(x1)))))))))))))))))))) → 1(1(0(1(0(0(0(0(0(0(1(1(0(1(0(1(1(0(0(0(x1)))))))))))))))))))) (77)
1(1(0(0(0(1(1(0(1(0(1(0(1(1(0(1(0(0(0(0(x1)))))))))))))))))))) → 1(0(0(0(0(0(0(1(1(0(1(0(0(1(1(0(1(0(1(0(x1)))))))))))))))))))) (78)
1(1(0(0(1(0(1(0(0(1(0(0(1(0(0(0(1(1(1(0(x1)))))))))))))))))))) → 0(1(0(0(1(0(0(0(1(0(0(0(1(1(0(0(0(1(0(0(x1)))))))))))))))))))) (79)
1(1(0(1(0(1(1(1(1(1(1(0(0(0(0(0(0(0(1(0(x1)))))))))))))))))))) → 1(0(1(0(1(1(0(1(0(1(0(1(0(0(0(0(1(0(0(1(x1)))))))))))))))))))) (84)
1(1(0(1(1(1(0(0(0(0(1(1(1(0(1(1(1(0(1(0(x1)))))))))))))))))))) → 0(1(0(1(1(1(0(0(0(0(1(1(0(0(1(0(0(0(1(1(x1)))))))))))))))))))) (85)
1(1(0(1(1(1(0(1(0(1(0(0(1(0(1(0(0(0(0(0(x1)))))))))))))))))))) → 1(0(0(0(0(0(0(1(1(0(1(0(0(1(0(1(0(0(1(1(x1)))))))))))))))))))) (86)
1(1(1(0(0(0(1(1(0(0(1(1(0(1(0(0(1(0(0(0(x1)))))))))))))))))))) → 1(1(0(0(1(1(1(1(0(0(0(1(0(0(0(0(0(0(0(1(x1)))))))))))))))))))) (88)
1(1(1(0(0(1(1(0(0(1(0(1(1(1(0(0(1(1(0(0(x1)))))))))))))))))))) → 1(0(1(1(0(1(0(0(0(1(0(1(0(0(0(1(0(1(1(1(x1)))))))))))))))))))) (90)
1(1(1(0(1(0(0(1(0(0(1(0(1(1(1(0(0(1(1(0(x1)))))))))))))))))))) → 0(0(1(0(1(0(1(0(1(0(0(1(0(0(0(1(1(0(1(0(x1)))))))))))))))))))) (91)
1(1(1(0(1(0(1(1(1(0(1(0(0(1(1(0(0(1(1(0(x1)))))))))))))))))))) → 0(1(0(1(1(1(0(1(0(0(1(0(0(0(0(1(1(0(0(1(x1)))))))))))))))))))) (93)
1(1(1(1(0(1(1(0(0(0(1(0(0(0(0(1(0(0(0(0(x1)))))))))))))))))))) → 1(0(0(0(0(0(0(1(1(0(0(1(0(0(0(1(0(1(0(0(x1)))))))))))))))))))) (94)
1(1(1(1(1(0(0(0(0(1(0(0(1(0(0(0(0(0(1(1(x1)))))))))))))))))))) → 0(0(0(1(0(0(0(0(1(0(1(0(1(1(0(0(0(0(0(1(x1)))))))))))))))))))) (95)
1(1(1(1(1(0(0(1(0(1(0(1(0(1(1(1(0(0(0(0(x1)))))))))))))))))))) → 1(0(1(0(0(1(0(1(0(0(0(1(1(0(0(1(1(0(1(1(x1)))))))))))))))))))) (97)
1(1(1(1(1(0(0(1(1(1(1(1(1(0(0(0(1(1(1(1(x1)))))))))))))))))))) → 1(0(1(1(0(1(1(0(0(0(1(1(0(0(0(1(0(0(1(0(x1)))))))))))))))))))) (98)
1(1(1(1(1(0(1(1(1(0(0(1(1(0(0(0(0(0(0(0(x1)))))))))))))))))))) → 1(1(1(0(0(0(1(0(0(0(1(1(0(1(1(0(0(0(1(0(x1)))))))))))))))))))) (99)

1.1 Split

We split R in the relative problem D/R-D and R-D, where the rules D

0(0(0(0(1(0(1(1(1(0(1(0(0(0(1(0(1(0(0(1(x1)))))))))))))))))))) → 0(1(1(1(0(1(0(1(1(0(0(0(0(0(0(0(0(0(1(1(x1)))))))))))))))))))) (2)
0(0(0(1(0(0(1(1(1(0(1(1(0(1(1(0(1(0(1(1(x1)))))))))))))))))))) → 0(1(0(1(1(1(1(1(0(1(0(0(0(1(1(1(0(0(0(1(x1)))))))))))))))))))) (4)
0(0(0(1(0(1(1(1(0(0(0(1(0(1(1(0(1(0(1(1(x1)))))))))))))))))))) → 0(0(0(1(1(1(0(0(1(0(1(1(0(1(1(1(0(0(0(1(x1)))))))))))))))))))) (5)
0(0(0(1(1(0(1(1(1(0(1(1(1(0(1(0(0(0(0(0(x1)))))))))))))))))))) → 0(0(1(0(0(1(1(1(0(0(0(0(1(1(1(1(1(0(0(0(x1)))))))))))))))))))) (8)
0(0(1(0(0(0(0(1(0(0(1(0(1(0(0(1(1(1(0(1(x1)))))))))))))))))))) → 0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(0(0(0(x1)))))))))))))))))))) (9)
0(0(1(0(0(0(1(0(1(0(1(1(0(1(0(0(0(0(1(0(x1)))))))))))))))))))) → 0(0(0(0(0(0(1(1(0(0(0(0(1(1(1(1(0(0(1(0(x1)))))))))))))))))))) (11)
0(0(1(0(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(1(x1)))))))))))))))))))) → 0(0(1(1(0(1(0(0(1(0(1(0(0(0(0(1(1(0(0(1(x1)))))))))))))))))))) (13)
0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(1(1(x1)))))))))))))))))))) → 1(1(1(0(1(1(1(1(0(0(0(0(0(0(0(0(0(0(1(1(x1)))))))))))))))))))) (14)
0(0(1(0(0(1(1(1(0(0(1(1(1(0(1(0(1(1(0(1(x1)))))))))))))))))))) → 0(1(1(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(1(x1)))))))))))))))))))) (15)
0(0(1(0(1(0(1(0(0(1(1(1(0(0(1(1(1(0(1(0(x1)))))))))))))))))))) → 0(1(0(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(0(0(x1)))))))))))))))))))) (16)
0(0(1(1(0(1(0(1(1(1(1(0(1(1(0(1(0(1(0(0(x1)))))))))))))))))))) → 0(1(0(1(0(0(1(0(0(1(1(1(1(1(0(1(1(1(0(0(x1)))))))))))))))))))) (19)
0(0(1(1(1(0(1(0(1(0(0(1(1(0(0(0(1(0(0(1(x1)))))))))))))))))))) → 1(1(0(0(0(0(0(0(0(0(0(0(1(1(1(0(1(1(1(1(x1)))))))))))))))))))) (20)
0(0(1(1(1(0(1(0(1(1(0(0(1(0(1(1(0(1(0(1(x1)))))))))))))))))))) → 0(1(0(0(1(0(0(0(1(1(0(1(1(1(0(1(1(1(1(0(x1)))))))))))))))))))) (21)
0(1(0(1(0(0(0(1(0(0(1(0(0(1(0(1(1(0(1(1(x1)))))))))))))))))))) → 0(1(1(1(0(0(0(0(0(0(1(0(1(0(1(1(0(1(0(1(x1)))))))))))))))))))) (25)
1(0(0(0(0(0(0(0(1(1(1(0(0(1(1(1(0(1(0(1(x1)))))))))))))))))))) → 1(0(0(0(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(1(x1)))))))))))))))))))) (33)
1(0(0(0(0(1(0(1(1(0(0(1(0(0(1(0(1(1(0(0(x1)))))))))))))))))))) → 1(0(0(1(0(0(0(0(0(1(0(1(0(0(1(1(1(1(0(0(x1)))))))))))))))))))) (35)
1(0(0(0(1(1(1(1(0(1(0(1(1(0(0(0(1(1(0(0(x1)))))))))))))))))))) → 1(0(0(0(1(1(0(0(0(0(0(1(1(1(1(1(1(1(0(0(x1)))))))))))))))))))) (38)
1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(1(0(1(x1)))))))))))))))))))) → 1(1(0(1(1(0(1(0(1(0(0(0(0(0(1(1(0(0(0(1(x1)))))))))))))))))))) (41)
1(0(0(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(x1)))))))))))))))))))) → 1(0(1(1(1(1(0(0(1(0(0(0(1(1(0(1(0(1(1(1(x1)))))))))))))))))))) (47)
1(0(1(0(0(0(1(0(1(0(0(1(1(1(1(0(0(1(0(1(x1)))))))))))))))))))) → 1(0(0(0(1(0(1(0(0(1(0(1(1(1(1(0(0(0(1(1(x1)))))))))))))))))))) (53)
1(0(1(0(1(0(1(0(1(1(1(0(1(1(1(0(0(1(0(0(x1)))))))))))))))))))) → 1(0(1(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(x1)))))))))))))))))))) (61)
1(0(1(1(0(0(0(0(0(1(0(1(0(1(1(1(0(1(0(1(x1)))))))))))))))))))) → 1(1(1(1(0(0(0(1(0(0(0(0(0(0(1(0(1(1(1(1(x1)))))))))))))))))))) (66)
1(0(1(1(0(1(0(0(0(0(1(0(1(0(1(0(1(1(1(0(x1)))))))))))))))))))) → 1(0(0(1(1(1(1(1(0(1(0(0(1(0(1(0(0(1(0(0(x1)))))))))))))))))))) (69)
1(0(1(1(0(1(1(0(0(1(1(0(1(0(1(0(1(0(1(0(x1)))))))))))))))))))) → 1(0(1(1(0(1(1(1(0(0(1(0(1(1(0(0(0(1(1(0(x1)))))))))))))))))))) (71)
1(0(1(1(1(1(0(0(0(1(0(0(0(1(1(1(0(1(0(1(x1)))))))))))))))))))) → 1(1(0(0(1(1(1(1(0(1(0(1(0(0(0(0(0(1(1(1(x1)))))))))))))))))))) (73)
1(1(0(0(0(1(0(0(1(0(1(1(0(0(1(1(1(0(1(0(x1)))))))))))))))))))) → 1(0(0(0(1(1(0(0(0(1(1(1(1(1(1(0(0(0(1(0(x1)))))))))))))))))))) (76)
1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(1(1(1(1(1(x1)))))))))))))))))))) → 1(0(0(0(0(1(1(0(0(1(1(1(1(0(0(0(1(1(1(1(x1)))))))))))))))))))) (80)
1(1(0(1(0(1(0(0(0(0(0(0(1(0(1(1(1(0(0(1(x1)))))))))))))))))))) → 1(0(0(0(0(0(0(1(1(0(0(0(0(1(1(1(1(0(1(1(x1)))))))))))))))))))) (81)
1(1(0(1(0(1(0(1(1(0(0(0(1(0(0(1(1(0(1(1(x1)))))))))))))))))))) → 1(1(1(0(1(1(0(1(0(0(1(1(0(1(1(0(0(0(0(1(x1)))))))))))))))))))) (82)
1(1(0(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(0(0(x1)))))))))))))))))))) → 1(0(1(0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(x1)))))))))))))))))))) (83)
1(1(1(0(0(0(1(0(1(1(0(1(0(0(0(1(0(1(0(1(x1)))))))))))))))))))) → 1(0(1(1(0(1(1(1(0(0(1(0(0(0(0(1(1(0(0(1(x1)))))))))))))))))))) (87)
1(1(1(0(0(1(0(1(1(0(0(1(0(0(1(0(1(1(0(1(x1)))))))))))))))))))) → 1(1(0(0(0(1(1(0(1(0(1(1(1(1(0(1(0(0(0(1(x1)))))))))))))))))))) (89)
1(1(1(1(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(x1)))))))))))))))))))) → 1(1(1(0(0(0(0(1(1(0(0(1(0(1(1(0(1(1(1(0(x1)))))))))))))))))))) (96)
are deleted.

1.1.1 Closure Under Flat Contexts

Using the flat contexts

{1(☐), 0(☐)}

We obtain the transformed TRS
1(0(0(0(0(1(0(1(1(1(0(1(0(0(0(1(0(1(0(0(1(x1))))))))))))))))))))) → 1(0(1(1(1(0(1(0(1(1(0(0(0(0(0(0(0(0(0(1(1(x1))))))))))))))))))))) (100)
1(0(0(0(1(0(0(1(1(1(0(1(1(0(1(1(0(1(0(1(1(x1))))))))))))))))))))) → 1(0(1(0(1(1(1(1(1(0(1(0(0(0(1(1(1(0(0(0(1(x1))))))))))))))))))))) (101)
1(0(0(0(1(0(1(1(1(0(0(0(1(0(1(1(0(1(0(1(1(x1))))))))))))))))))))) → 1(0(0(0(1(1(1(0(0(1(0(1(1(0(1(1(1(0(0(0(1(x1))))))))))))))))))))) (102)
1(0(0(0(1(1(0(1(1(1(0(1(1(1(0(1(0(0(0(0(0(x1))))))))))))))))))))) → 1(0(0(1(0(0(1(1(1(0(0(0(0(1(1(1(1(1(0(0(0(x1))))))))))))))))))))) (103)
1(0(0(1(0(0(0(0(1(0(0(1(0(1(0(0(1(1(1(0(1(x1))))))))))))))))))))) → 1(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(0(0(0(x1))))))))))))))))))))) (104)
1(0(0(1(0(0(0(1(0(1(0(1(1(0(1(0(0(0(0(1(0(x1))))))))))))))))))))) → 1(0(0(0(0(0(0(1(1(0(0(0(0(1(1(1(1(0(0(1(0(x1))))))))))))))))))))) (105)
1(0(0(1(0(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(1(x1))))))))))))))))))))) → 1(0(0(1(1(0(1(0(0(1(0(1(0(0(0(0(1(1(0(0(1(x1))))))))))))))))))))) (106)
1(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(1(1(x1))))))))))))))))))))) → 1(1(1(1(0(1(1(1(1(0(0(0(0(0(0(0(0(0(0(1(1(x1))))))))))))))))))))) (107)
1(0(0(1(0(0(1(1(1(0(0(1(1(1(0(1(0(1(1(0(1(x1))))))))))))))))))))) → 1(0(1(1(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(1(x1))))))))))))))))))))) (108)
1(0(0(1(0(1(0(1(0(0(1(1(1(0(0(1(1(1(0(1(0(x1))))))))))))))))))))) → 1(0(1(0(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(0(0(x1))))))))))))))))))))) (109)
1(0(0(1(1(0(1(0(1(1(1(1(0(1(1(0(1(0(1(0(0(x1))))))))))))))))))))) → 1(0(1(0(1(0(0(1(0(0(1(1(1(1(1(0(1(1(1(0(0(x1))))))))))))))))))))) (110)
1(0(0(1(1(1(0(1(0(1(0(0(1(1(0(0(0(1(0(0(1(x1))))))))))))))))))))) → 1(1(1(0(0(0(0(0(0(0(0(0(0(1(1(1(0(1(1(1(1(x1))))))))))))))))))))) (111)
1(0(0(1(1(1(0(1(0(1(1(0(0(1(0(1(1(0(1(0(1(x1))))))))))))))))))))) → 1(0(1(0(0(1(0(0(0(1(1(0(1(1(1(0(1(1(1(1(0(x1))))))))))))))))))))) (112)
1(0(1(0(1(0(0(0(1(0(0(1(0(0(1(0(1(1(0(1(1(x1))))))))))))))))))))) → 1(0(1(1(1(0(0(0(0(0(0(1(0(1(0(1(1(0(1(0(1(x1))))))))))))))))))))) (113)
1(1(0(0(0(0(0(0(0(1(1(1(0(0(1(1(1(0(1(0(1(x1))))))))))))))))))))) → 1(1(0(0(0(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(1(x1))))))))))))))))))))) (114)
1(1(0(0(0(0(1(0(1(1(0(0(1(0(0(1(0(1(1(0(0(x1))))))))))))))))))))) → 1(1(0(0(1(0(0(0(0(0(1(0(1(0(0(1(1(1(1(0(0(x1))))))))))))))))))))) (115)
1(1(0(0(0(1(1(1(1(0(1(0(1(1(0(0(0(1(1(0(0(x1))))))))))))))))))))) → 1(1(0(0(0(1(1(0(0(0(0(0(1(1(1(1(1(1(1(0(0(x1))))))))))))))))))))) (116)
1(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(1(0(1(x1))))))))))))))))))))) → 1(1(1(0(1(1(0(1(0(1(0(0(0(0(0(1(1(0(0(0(1(x1))))))))))))))))))))) (117)
1(1(0(0(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(x1))))))))))))))))))))) → 1(1(0(1(1(1(1(0(0(1(0(0(0(1(1(0(1(0(1(1(1(x1))))))))))))))))))))) (118)
1(1(0(1(0(0(0(1(0(1(0(0(1(1(1(1(0(0(1(0(1(x1))))))))))))))))))))) → 1(1(0(0(0(1(0(1(0(0(1(0(1(1(1(1(0(0(0(1(1(x1))))))))))))))))))))) (119)
1(1(0(1(0(1(0(1(0(1(1(1(0(1(1(1(0(0(1(0(0(x1))))))))))))))))))))) → 1(1(0(1(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(x1))))))))))))))))))))) (120)
1(1(0(1(1(0(0(0(0(0(1(0(1(0(1(1(1(0(1(0(1(x1))))))))))))))))))))) → 1(1(1(1(1(0(0(0(1(0(0(0(0(0(0(1(0(1(1(1(1(x1))))))))))))))))))))) (121)
1(1(0(1(1(0(1(0(0(0(0(1(0(1(0(1(0(1(1(1(0(x1))))))))))))))))))))) → 1(1(0(0(1(1(1(1(1(0(1(0(0(1(0(1(0(0(1(0(0(x1))))))))))))))))))))) (122)
1(1(0(1(1(0(1(1(0(0(1(1(0(1(0(1(0(1(0(1(0(x1))))))))))))))))))))) → 1(1(0(1(1(0(1(1(1(0(0(1(0(1(1(0(0(0(1(1(0(x1))))))))))))))))))))) (123)
1(1(0(1(1(1(1(0(0(0(1(0(0(0(1(1(1(0(1(0(1(x1))))))))))))))))))))) → 1(1(1(0(0(1(1(1(1(0(1(0(1(0(0(0(0(0(1(1(1(x1))))))))))))))))))))) (124)
1(1(1(0(0(0(1(0(0(1(0(1(1(0(0(1(1(1(0(1(0(x1))))))))))))))))))))) → 1(1(0(0(0(1(1(0(0(0(1(1(1(1(1(1(0(0(0(1(0(x1))))))))))))))))))))) (125)
1(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(1(1(1(1(1(x1))))))))))))))))))))) → 1(1(0(0(0(0(1(1(0(0(1(1(1(1(0(0(0(1(1(1(1(x1))))))))))))))))))))) (126)
1(1(1(0(1(0(1(0(0(0(0(0(0(1(0(1(1(1(0(0(1(x1))))))))))))))))))))) → 1(1(0(0(0(0(0(0(1(1(0(0(0(0(1(1(1(1(0(1(1(x1))))))))))))))))))))) (127)
1(1(1(0(1(0(1(0(1(1(0(0(0(1(0(0(1(1(0(1(1(x1))))))))))))))))))))) → 1(1(1(1(0(1(1(0(1(0(0(1(1(0(1(1(0(0(0(0(1(x1))))))))))))))))))))) (128)
1(1(1(0(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(0(0(x1))))))))))))))))))))) → 1(1(0(1(0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(x1))))))))))))))))))))) (129)
1(1(1(1(0(0(0(1(0(1(1(0(1(0(0(0(1(0(1(0(1(x1))))))))))))))))))))) → 1(1(0(1(1(0(1(1(1(0(0(1(0(0(0(0(1(1(0(0(1(x1))))))))))))))))))))) (130)
1(1(1(1(0(0(1(0(1(1(0(0(1(0(0(1(0(1(1(0(1(x1))))))))))))))))))))) → 1(1(1(0(0(0(1(1(0(1(0(1(1(1(1(0(1(0(0(0(1(x1))))))))))))))))))))) (131)
1(1(1(1(1(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(x1))))))))))))))))))))) → 1(1(1(1(0(0(0(0(1(1(0(0(1(0(1(1(0(1(1(1(0(x1))))))))))))))))))))) (132)
0(0(0(0(0(1(0(1(1(1(0(1(0(0(0(1(0(1(0(0(1(x1))))))))))))))))))))) → 0(0(1(1(1(0(1(0(1(1(0(0(0(0(0(0(0(0(0(1(1(x1))))))))))))))))))))) (133)
0(0(0(0(1(0(0(1(1(1(0(1(1(0(1(1(0(1(0(1(1(x1))))))))))))))))))))) → 0(0(1(0(1(1(1(1(1(0(1(0(0(0(1(1(1(0(0(0(1(x1))))))))))))))))))))) (134)
0(0(0(0(1(0(1(1(1(0(0(0(1(0(1(1(0(1(0(1(1(x1))))))))))))))))))))) → 0(0(0(0(1(1(1(0(0(1(0(1(1(0(1(1(1(0(0(0(1(x1))))))))))))))))))))) (135)
0(0(0(0(1(1(0(1(1(1(0(1(1(1(0(1(0(0(0(0(0(x1))))))))))))))))))))) → 0(0(0(1(0(0(1(1(1(0(0(0(0(1(1(1(1(1(0(0(0(x1))))))))))))))))))))) (136)
0(0(0(1(0(0(0(0(1(0(0(1(0(1(0(0(1(1(1(0(1(x1))))))))))))))))))))) → 0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(0(0(0(x1))))))))))))))))))))) (137)
0(0(0(1(0(0(0(1(0(1(0(1(1(0(1(0(0(0(0(1(0(x1))))))))))))))))))))) → 0(0(0(0(0(0(0(1(1(0(0(0(0(1(1(1(1(0(0(1(0(x1))))))))))))))))))))) (138)
0(0(0(1(0(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(1(x1))))))))))))))))))))) → 0(0(0(1(1(0(1(0(0(1(0(1(0(0(0(0(1(1(0(0(1(x1))))))))))))))))))))) (139)
0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(1(1(x1))))))))))))))))))))) → 0(1(1(1(0(1(1(1(1(0(0(0(0(0(0(0(0(0(0(1(1(x1))))))))))))))))))))) (140)
0(0(0(1(0(0(1(1(1(0(0(1(1(1(0(1(0(1(1(0(1(x1))))))))))))))))))))) → 0(0(1(1(1(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(1(x1))))))))))))))))))))) (141)
0(0(0(1(0(1(0(1(0(0(1(1(1(0(0(1(1(1(0(1(0(x1))))))))))))))))))))) → 0(0(1(0(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(0(0(x1))))))))))))))))))))) (142)
0(0(0(1(1(0(1(0(1(1(1(1(0(1(1(0(1(0(1(0(0(x1))))))))))))))))))))) → 0(0(1(0(1(0(0(1(0(0(1(1(1(1(1(0(1(1(1(0(0(x1))))))))))))))))))))) (143)
0(0(0(1(1(1(0(1(0(1(0(0(1(1(0(0(0(1(0(0(1(x1))))))))))))))))))))) → 0(1(1(0(0(0(0(0(0(0(0(0(0(1(1(1(0(1(1(1(1(x1))))))))))))))))))))) (144)
0(0(0(1(1(1(0(1(0(1(1(0(0(1(0(1(1(0(1(0(1(x1))))))))))))))))))))) → 0(0(1(0(0(1(0(0(0(1(1(0(1(1(1(0(1(1(1(1(0(x1))))))))))))))))))))) (145)
0(0(1(0(1(0(0(0(1(0(0(1(0(0(1(0(1(1(0(1(1(x1))))))))))))))))))))) → 0(0(1(1(1(0(0(0(0(0(0(1(0(1(0(1(1(0(1(0(1(x1))))))))))))))))))))) (146)
0(1(0(0(0(0(0(0(0(1(1(1(0(0(1(1(1(0(1(0(1(x1))))))))))))))))))))) → 0(1(0(0(0(0(1(0(0(0(1(1(1(0(0(0(0(1(1(1(1(x1))))))))))))))))))))) (147)
0(1(0(0(0(0(1(0(1(1(0(0(1(0(0(1(0(1(1(0(0(x1))))))))))))))))))))) → 0(1(0(0(1(0(0(0(0(0(1(0(1(0(0(1(1(1(1(0(0(x1))))))))))))))))))))) (148)
0(1(0(0(0(1(1(1(1(0(1(0(1(1(0(0(0(1(1(0(0(x1))))))))))))))))))))) → 0(1(0(0(0(1(1(0(0(0(0(0(1(1(1(1(1(1(1(0(0(x1))))))))))))))))))))) (149)
0(1(0(0(1(0(0(0(1(1(0(1(0(0(1(0(0(1(1(0(1(x1))))))))))))))))))))) → 0(1(1(0(1(1(0(1(0(1(0(0(0(0(0(1(1(0(0(0(1(x1))))))))))))))))))))) (150)
0(1(0(0(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(x1))))))))))))))))))))) → 0(1(0(1(1(1(1(0(0(1(0(0(0(1(1(0(1(0(1(1(1(x1))))))))))))))))))))) (151)
0(1(0(1(0(0(0(1(0(1(0(0(1(1(1(1(0(0(1(0(1(x1))))))))))))))))))))) → 0(1(0(0(0(1(0(1(0(0(1(0(1(1(1(1(0(0(0(1(1(x1))))))))))))))))))))) (152)
0(1(0(1(0(1(0(1(0(1(1(1(0(1(1(1(0(0(1(0(0(x1))))))))))))))))))))) → 0(1(0(1(0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(x1))))))))))))))))))))) (153)
0(1(0(1(1(0(0(0(0(0(1(0(1(0(1(1(1(0(1(0(1(x1))))))))))))))))))))) → 0(1(1(1(1(0(0(0(1(0(0(0(0(0(0(1(0(1(1(1(1(x1))))))))))))))))))))) (154)
0(1(0(1(1(0(1(0(0(0(0(1(0(1(0(1(0(1(1(1(0(x1))))))))))))))))))))) → 0(1(0(0(1(1(1(1(1(0(1(0(0(1(0(1(0(0(1(0(0(x1))))))))))))))))))))) (155)
0(1(0(1(1(0(1(1(0(0(1(1(0(1(0(1(0(1(0(1(0(x1))))))))))))))))))))) → 0(1(0(1(1(0(1(1(1(0(0(1(0(1(1(0(0(0(1(1(0(x1))))))))))))))))))))) (156)
0(1(0(1(1(1(1(0(0(0(1(0(0(0(1(1(1(0(1(0(1(x1))))))))))))))))))))) → 0(1(1(0(0(1(1(1(1(0(1(0(1(0(0(0(0(0(1(1(1(x1))))))))))))))))))))) (157)
0(1(1(0(0(0(1(0(0(1(0(1(1(0(0(1(1(1(0(1(0(x1))))))))))))))))))))) → 0(1(0(0(0(1(1(0(0(0(1(1(1(1(1(1(0(0(0(1(0(x1))))))))))))))))))))) (158)
0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(1(1(1(1(1(x1))))))))))))))))))))) → 0(1(0(0(0(0(1(1(0(0(1(1(1(1(0(0(0(1(1(1(1(x1))))))))))))))))))))) (159)
0(1(1(0(1(0(1(0(0(0(0(0(0(1(0(1(1(1(0(0(1(x1))))))))))))))))))))) → 0(1(0(0(0(0(0(0(1(1(0(0(0(0(1(1(1(1(0(1(1(x1))))))))))))))))))))) (160)
0(1(1(0(1(0(1(0(1(1(0(0(0(1(0(0(1(1(0(1(1(x1))))))))))))))))))))) → 0(1(1(1(0(1(1(0(1(0(0(1(1(0(1(1(0(0(0(0(1(x1))))))))))))))))))))) (161)
0(1(1(0(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(0(0(x1))))))))))))))))))))) → 0(1(0(1(0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(x1))))))))))))))))))))) (162)
0(1(1(1(0(0(0(1(0(1(1(0(1(0(0(0(1(0(1(0(1(x1))))))))))))))))))))) → 0(1(0(1(1(0(1(1(1(0(0(1(0(0(0(0(1(1(0(0(1(x1))))))))))))))))))))) (163)
0(1(1(1(0(0(1(0(1(1(0(0(1(0(0(1(0(1(1(0(1(x1))))))))))))))))))))) → 0(1(1(0(0(0(1(1(0(1(0(1(1(1(1(0(1(0(0(0(1(x1))))))))))))))))))))) (164)
0(1(1(1(1(1(0(0(1(0(1(0(0(1(0(0(1(1(0(1(0(x1))))))))))))))))))))) → 0(1(1(1(0(0(0(0(1(1(0(0(1(0(1(1(0(1(1(1(0(x1))))))))))))))))))))) (165)
1(0(0(0(0(0(0(1(1(0(1(1(1(1(0(1(0(0(1(0(0(x1))))))))))))))))))))) → 1(0(0(1(1(1(0(1(1(0(1(0(1(1(0(0(0(0(0(0(0(x1))))))))))))))))))))) (166)
1(0(0(0(0(1(0(1(1(1(0(1(0(0(1(1(1(1(0(1(0(x1))))))))))))))))))))) → 1(0(0(0(0(1(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(x1))))))))))))))))))))) (167)
1(0(0(1(0(0(0(1(0(0(1(1(1(1(0(0(1(0(1(0(1(x1))))))))))))))))))))) → 1(0(0(1(1(1(0(0(0(1(1(0(0(0(1(0(1(0(1(0(1(x1))))))))))))))))))))) (168)
1(0(0(1(1(0(0(1(1(1(1(1(0(0(1(0(0(0(0(0(1(x1))))))))))))))))))))) → 1(0(0(1(1(1(1(1(0(0(0(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))))) (169)
1(1(0(0(1(1(1(1(0(1(0(0(1(1(1(0(0(1(0(1(0(x1))))))))))))))))))))) → 1(1(0(0(1(0(0(1(0(0(1(1(0(1(1(1(0(1(1(1(0(x1))))))))))))))))))))) (170)
1(1(0(1(0(0(1(1(1(0(1(1(1(1(0(0(1(0(1(1(0(x1))))))))))))))))))))) → 1(1(0(1(1(1(0(1(0(1(1(0(0(1(1(1(0(0(1(1(0(x1))))))))))))))))))))) (171)
1(1(1(1(0(1(0(0(1(1(1(0(0(0(1(0(0(0(1(0(0(x1))))))))))))))))))))) → 1(1(0(0(1(1(1(0(0(1(1(0(1(1(0(0(0(0(1(0(0(x1))))))))))))))))))))) (172)
0(0(0(0(0(0(0(1(1(0(1(1(1(1(0(1(0(0(1(0(0(x1))))))))))))))))))))) → 0(0(0(1(1(1(0(1(1(0(1(0(1(1(0(0(0(0(0(0(0(x1))))))))))))))))))))) (173)
0(0(0(0(0(1(0(1(1(1(0(1(0(0(1(1(1(1(0(1(0(x1))))))))))))))))))))) → 0(0(0(0(0(1(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(x1))))))))))))))))))))) (174)
0(0(0(1(0(0(0(1(0(0(1(1(1(1(0(0(1(0(1(0(1(x1))))))))))))))))))))) → 0(0(0(1(1(1(0(0(0(1(1(0(0(0(1(0(1(0(1(0(1(x1))))))))))))))))))))) (175)
0(0(0(1(1(0(0(1(1(1(1(1(0(0(1(0(0(0(0(0(1(x1))))))))))))))))))))) → 0(0(0(1(1(1(1(1(0(0(0(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))))) (176)
0(1(0(0(1(1(1(1(0(1(0(0(1(1(1(0(0(1(0(1(0(x1))))))))))))))))))))) → 0(1(0(0(1(0(0(1(0(0(1(1(0(1(1(1(0(1(1(1(0(x1))))))))))))))))))))) (177)
0(1(0(1(0(0(1(1(1(0(1(1(1(1(0(0(1(0(1(1(0(x1))))))))))))))))))))) → 0(1(0(1(1(1(0(1(0(1(1(0(0(1(1(1(0(0(1(1(0(x1))))))))))))))))))))) (178)
0(1(1(1(0(1(0(0(1(1(1(0(0(0(1(0(0(0(1(0(0(x1))))))))))))))))))))) → 0(1(0(0(1(1(1(0(0(1(1(0(1(1(0(0(0(0(1(0(0(x1))))))))))))))))))))) (179)

1.1.1.1 Semantic Labeling

The following interpretations form a model of the rules.

As carrier we take the set {0,1}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 2):

[1(x1)] = 2x1 + 0
[0(x1)] = 2x1 + 1

We obtain the labeled TRS

There are 160 ruless (increase limit for explicit display).

1.1.1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[10(x1)] = x1 +
0
[11(x1)] = x1 +
1
[00(x1)] = x1 +
1
[01(x1)] = x1 +
0
all of the following rules can be deleted.

There are 134 ruless (increase limit for explicit display).

1.1.1.1.1.1 R is empty

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

1.1.2 Closure Under Flat Contexts

Using the flat contexts

{1(☐), 0(☐)}

We obtain the transformed TRS
1(0(0(0(0(0(0(1(1(0(1(1(1(1(0(1(0(0(1(0(0(x1))))))))))))))))))))) → 1(0(0(1(1(1(0(1(1(0(1(0(1(1(0(0(0(0(0(0(0(x1))))))))))))))))))))) (166)
1(0(0(0(0(1(0(1(1(1(0(1(0(0(1(1(1(1(0(1(0(x1))))))))))))))))))))) → 1(0(0(0(0(1(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(x1))))))))))))))))))))) (167)
1(0(0(1(0(0(0(1(0(0(1(1(1(1(0(0(1(0(1(0(1(x1))))))))))))))))))))) → 1(0(0(1(1(1(0(0(0(1(1(0(0(0(1(0(1(0(1(0(1(x1))))))))))))))))))))) (168)
1(0(0(1(1(0(0(1(1(1(1(1(0(0(1(0(0(0(0(0(1(x1))))))))))))))))))))) → 1(0(0(1(1(1(1(1(0(0(0(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))))) (169)
1(1(0(0(1(1(1(1(0(1(0(0(1(1(1(0(0(1(0(1(0(x1))))))))))))))))))))) → 1(1(0(0(1(0(0(1(0(0(1(1(0(1(1(1(0(1(1(1(0(x1))))))))))))))))))))) (170)
1(1(0(1(0(0(1(1(1(0(1(1(1(1(0(0(1(0(1(1(0(x1))))))))))))))))))))) → 1(1(0(1(1(1(0(1(0(1(1(0(0(1(1(1(0(0(1(1(0(x1))))))))))))))))))))) (171)
1(1(1(1(0(1(0(0(1(1(1(0(0(0(1(0(0(0(1(0(0(x1))))))))))))))))))))) → 1(1(0(0(1(1(1(0(0(1(1(0(1(1(0(0(0(0(1(0(0(x1))))))))))))))))))))) (172)
0(0(0(0(0(0(0(1(1(0(1(1(1(1(0(1(0(0(1(0(0(x1))))))))))))))))))))) → 0(0(0(1(1(1(0(1(1(0(1(0(1(1(0(0(0(0(0(0(0(x1))))))))))))))))))))) (173)
0(0(0(0(0(1(0(1(1(1(0(1(0(0(1(1(1(1(0(1(0(x1))))))))))))))))))))) → 0(0(0(0(0(1(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(x1))))))))))))))))))))) (174)
0(0(0(1(0(0(0(1(0(0(1(1(1(1(0(0(1(0(1(0(1(x1))))))))))))))))))))) → 0(0(0(1(1(1(0(0(0(1(1(0(0(0(1(0(1(0(1(0(1(x1))))))))))))))))))))) (175)
0(0(0(1(1(0(0(1(1(1(1(1(0(0(1(0(0(0(0(0(1(x1))))))))))))))))))))) → 0(0(0(1(1(1(1(1(0(0(0(0(0(0(0(1(0(1(1(1(0(x1))))))))))))))))))))) (176)
0(1(0(0(1(1(1(1(0(1(0(0(1(1(1(0(0(1(0(1(0(x1))))))))))))))))))))) → 0(1(0(0(1(0(0(1(0(0(1(1(0(1(1(1(0(1(1(1(0(x1))))))))))))))))))))) (177)
0(1(0(1(0(0(1(1(1(0(1(1(1(1(0(0(1(0(1(1(0(x1))))))))))))))))))))) → 0(1(0(1(1(1(0(1(0(1(1(0(0(1(1(1(0(0(1(1(0(x1))))))))))))))))))))) (178)
0(1(1(1(0(1(0(0(1(1(1(0(0(0(1(0(0(0(1(0(0(x1))))))))))))))))))))) → 0(1(0(0(1(1(1(0(0(1(1(0(1(1(0(0(0(0(1(0(0(x1))))))))))))))))))))) (179)

1.1.2.1 Closure Under Flat Contexts

Using the flat contexts

{1(☐), 0(☐)}

We obtain the transformed TRS
1(1(0(0(0(0(0(0(1(1(0(1(1(1(1(0(1(0(0(1(0(0(x1)))))))))))))))))))))) → 1(1(0(0(1(1(1(0(1(1(0(1(0(1(1(0(0(0(0(0(0(0(x1)))))))))))))))))))))) (340)
1(1(0(0(0(0(1(0(1(1(1(0(1(0(0(1(1(1(1(0(1(0(x1)))))))))))))))))))))) → 1(1(0(0(0(0(1(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(x1)))))))))))))))))))))) (341)
1(1(0(0(1(0(0(0(1(0(0(1(1(1(1(0(0(1(0(1(0(1(x1)))))))))))))))))))))) → 1(1(0(0(1(1(1(0(0(0(1(1(0(0(0(1(0(1(0(1(0(1(x1)))))))))))))))))))))) (342)
1(1(0(0(1(1(0(0(1(1(1(1(1(0(0(1(0(0(0(0(0(1(x1)))))))))))))))))))))) → 1(1(0(0(1(1(1(1(1(0(0(0(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))))))))))) (343)
1(1(1(0(0(1(1(1(1(0(1(0(0(1(1(1(0(0(1(0(1(0(x1)))))))))))))))))))))) → 1(1(1(0(0(1(0(0(1(0(0(1(1(0(1(1(1(0(1(1(1(0(x1)))))))))))))))))))))) (344)
1(1(1(0(1(0(0(1(1(1(0(1(1(1(1(0(0(1(0(1(1(0(x1)))))))))))))))))))))) → 1(1(1(0(1(1(1(0(1(0(1(1(0(0(1(1(1(0(0(1(1(0(x1)))))))))))))))))))))) (345)
1(1(1(1(1(0(1(0(0(1(1(1(0(0(0(1(0(0(0(1(0(0(x1)))))))))))))))))))))) → 1(1(1(0(0(1(1(1(0(0(1(1(0(1(1(0(0(0(0(1(0(0(x1)))))))))))))))))))))) (346)
1(0(0(0(0(0(0(0(1(1(0(1(1(1(1(0(1(0(0(1(0(0(x1)))))))))))))))))))))) → 1(0(0(0(1(1(1(0(1(1(0(1(0(1(1(0(0(0(0(0(0(0(x1)))))))))))))))))))))) (347)
1(0(0(0(0(0(1(0(1(1(1(0(1(0(0(1(1(1(1(0(1(0(x1)))))))))))))))))))))) → 1(0(0(0(0(0(1(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(x1)))))))))))))))))))))) (348)
1(0(0(0(1(0(0(0(1(0(0(1(1(1(1(0(0(1(0(1(0(1(x1)))))))))))))))))))))) → 1(0(0(0(1(1(1(0(0(0(1(1(0(0(0(1(0(1(0(1(0(1(x1)))))))))))))))))))))) (349)
1(0(0(0(1(1(0(0(1(1(1(1(1(0(0(1(0(0(0(0(0(1(x1)))))))))))))))))))))) → 1(0(0(0(1(1(1(1(1(0(0(0(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))))))))))) (350)
1(0(1(0(0(1(1(1(1(0(1(0(0(1(1(1(0(0(1(0(1(0(x1)))))))))))))))))))))) → 1(0(1(0(0(1(0(0(1(0(0(1(1(0(1(1(1(0(1(1(1(0(x1)))))))))))))))))))))) (351)
1(0(1(0(1(0(0(1(1(1(0(1(1(1(1(0(0(1(0(1(1(0(x1)))))))))))))))))))))) → 1(0(1(0(1(1(1(0(1(0(1(1(0(0(1(1(1(0(0(1(1(0(x1)))))))))))))))))))))) (352)
1(0(1(1(1(0(1(0(0(1(1(1(0(0(0(1(0(0(0(1(0(0(x1)))))))))))))))))))))) → 1(0(1(0(0(1(1(1(0(0(1(1(0(1(1(0(0(0(0(1(0(0(x1)))))))))))))))))))))) (353)
0(1(0(0(0(0(0(0(1(1(0(1(1(1(1(0(1(0(0(1(0(0(x1)))))))))))))))))))))) → 0(1(0(0(1(1(1(0(1(1(0(1(0(1(1(0(0(0(0(0(0(0(x1)))))))))))))))))))))) (354)
0(1(0(0(0(0(1(0(1(1(1(0(1(0(0(1(1(1(1(0(1(0(x1)))))))))))))))))))))) → 0(1(0(0(0(0(1(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(x1)))))))))))))))))))))) (355)
0(1(0(0(1(0(0(0(1(0(0(1(1(1(1(0(0(1(0(1(0(1(x1)))))))))))))))))))))) → 0(1(0(0(1(1(1(0(0(0(1(1(0(0(0(1(0(1(0(1(0(1(x1)))))))))))))))))))))) (356)
0(1(0(0(1(1(0(0(1(1(1(1(1(0(0(1(0(0(0(0(0(1(x1)))))))))))))))))))))) → 0(1(0(0(1(1(1(1(1(0(0(0(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))))))))))) (357)
0(1(1(0(0(1(1(1(1(0(1(0(0(1(1(1(0(0(1(0(1(0(x1)))))))))))))))))))))) → 0(1(1(0(0(1(0(0(1(0(0(1(1(0(1(1(1(0(1(1(1(0(x1)))))))))))))))))))))) (358)
0(1(1(0(1(0(0(1(1(1(0(1(1(1(1(0(0(1(0(1(1(0(x1)))))))))))))))))))))) → 0(1(1(0(1(1(1(0(1(0(1(1(0(0(1(1(1(0(0(1(1(0(x1)))))))))))))))))))))) (359)
0(1(1(1(1(0(1(0(0(1(1(1(0(0(0(1(0(0(0(1(0(0(x1)))))))))))))))))))))) → 0(1(1(0(0(1(1(1(0(0(1(1(0(1(1(0(0(0(0(1(0(0(x1)))))))))))))))))))))) (360)
0(0(0(0(0(0(0(0(1(1(0(1(1(1(1(0(1(0(0(1(0(0(x1)))))))))))))))))))))) → 0(0(0(0(1(1(1(0(1(1(0(1(0(1(1(0(0(0(0(0(0(0(x1)))))))))))))))))))))) (361)
0(0(0(0(0(0(1(0(1(1(1(0(1(0(0(1(1(1(1(0(1(0(x1)))))))))))))))))))))) → 0(0(0(0(0(0(1(1(0(1(0(1(1(0(0(1(1(0(1(1(1(0(x1)))))))))))))))))))))) (362)
0(0(0(0(1(0(0(0(1(0(0(1(1(1(1(0(0(1(0(1(0(1(x1)))))))))))))))))))))) → 0(0(0(0(1(1(1(0(0(0(1(1(0(0(0(1(0(1(0(1(0(1(x1)))))))))))))))))))))) (363)
0(0(0(0(1(1(0(0(1(1(1(1(1(0(0(1(0(0(0(0(0(1(x1)))))))))))))))))))))) → 0(0(0(0(1(1(1(1(1(0(0(0(0(0(0(0(1(0(1(1(1(0(x1)))))))))))))))))))))) (364)
0(0(1(0(0(1(1(1(1(0(1(0(0(1(1(1(0(0(1(0(1(0(x1)))))))))))))))))))))) → 0(0(1(0(0(1(0(0(1(0(0(1(1(0(1(1(1(0(1(1(1(0(x1)))))))))))))))))))))) (365)
0(0(1(0(1(0(0(1(1(1(0(1(1(1(1(0(0(1(0(1(1(0(x1)))))))))))))))))))))) → 0(0(1(0(1(1(1(0(1(0(1(1(0(0(1(1(1(0(0(1(1(0(x1)))))))))))))))))))))) (366)
0(0(1(1(1(0(1(0(0(1(1(1(0(0(0(1(0(0(0(1(0(0(x1)))))))))))))))))))))) → 0(0(1(0(0(1(1(1(0(0(1(1(0(1(1(0(0(0(0(1(0(0(x1)))))))))))))))))))))) (367)

1.1.2.1.1 Semantic Labeling

The following interpretations form a model of the rules.

As carrier we take the set {0,...,3}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 4):

[1(x1)] = 2x1 + 0
[0(x1)] = 2x1 + 1

We obtain the labeled TRS

There are 112 ruless (increase limit for explicit display).

1.1.2.1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[10(x1)] = x1 +
1
[12(x1)] = x1 +
0
[11(x1)] = x1 +
0
[13(x1)] = x1 +
3/2
[00(x1)] = x1 +
0
[02(x1)] = x1 +
1
[01(x1)] = x1 +
3/2
[03(x1)] = x1 +
0
all of the following rules can be deleted.

There are 112 ruless (increase limit for explicit display).

1.1.2.1.1.1.1 R is empty

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