Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/153288)

The rewrite relation of the following TRS is considered.

0(0(0(0(0(0(0(0(0(1(0(1(1(1(0(0(1(1(1(0(x1)))))))))))))))))))) → 1(0(0(0(0(0(0(0(1(0(0(0(1(1(0(0(1(1(0(0(x1)))))))))))))))))))) (1)
0(0(0(0(0(0(0(1(1(1(1(0(0(1(0(1(0(0(1(0(x1)))))))))))))))))))) → 0(1(0(0(0(0(1(0(1(0(0(0(0(0(0(0(0(0(0(1(x1)))))))))))))))))))) (2)
0(0(0(0(0(0(1(1(0(1(1(0(1(0(0(1(1(1(0(0(x1)))))))))))))))))))) → 0(0(1(0(1(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(x1)))))))))))))))))))) (3)
0(0(0(0(0(0(1(1(1(0(1(0(0(1(0(1(1(0(1(0(x1)))))))))))))))))))) → 0(0(0(0(1(0(1(1(0(0(0(1(0(1(0(0(0(1(0(0(x1)))))))))))))))))))) (4)
0(0(0(0(0(1(0(0(1(0(1(0(1(1(1(1(1(1(1(0(x1)))))))))))))))))))) → 0(0(1(1(1(1(0(1(0(0(0(1(1(1(0(0(0(1(1(0(x1)))))))))))))))))))) (5)
0(0(0(0(0(1(0(1(1(1(0(1(0(0(0(1(1(1(0(0(x1)))))))))))))))))))) → 1(0(1(0(0(0(0(1(0(1(0(0(1(0(0(0(1(0(0(1(x1)))))))))))))))))))) (6)
0(0(0(0(1(0(0(0(1(1(1(1(1(0(1(1(0(0(0(1(x1)))))))))))))))))))) → 0(1(1(1(1(0(1(0(0(1(0(1(0(0(0(0(1(0(0(1(x1)))))))))))))))))))) (7)
0(0(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(1(0(x1)))))))))))))))))))) → 0(0(0(0(0(1(0(0(0(1(0(0(1(0(0(0(0(1(0(1(x1)))))))))))))))))))) (8)
0(0(0(0(1(1(0(1(0(1(0(0(1(1(0(0(1(1(0(1(x1)))))))))))))))))))) → 0(0(0(1(1(0(0(0(0(1(0(1(0(1(1(0(1(1(0(1(x1)))))))))))))))))))) (9)
0(0(0(0(1(1(0(1(0(1(0(1(1(0(1(0(0(1(0(0(x1)))))))))))))))))))) → 0(0(0(0(0(0(0(0(1(1(0(0(1(0(1(1(1(1(0(0(x1)))))))))))))))))))) (10)
0(0(0(0(1(1(0(1(0(1(1(1(1(0(0(0(0(0(1(0(x1)))))))))))))))))))) → 1(0(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(0(1(0(x1)))))))))))))))))))) (11)
0(0(0(0(1(1(1(0(0(1(1(1(1(0(1(0(1(0(0(0(x1)))))))))))))))))))) → 0(1(1(0(1(0(0(1(1(0(0(1(0(0(1(1(0(1(0(0(x1)))))))))))))))))))) (12)
0(0(0(1(0(0(0(0(0(0(0(1(1(1(0(1(1(1(0(1(x1)))))))))))))))))))) → 0(1(0(0(1(1(0(0(0(1(1(0(0(1(0(0(1(0(0(1(x1)))))))))))))))))))) (13)
0(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(0(1(1(x1)))))))))))))))))))) → 0(1(1(0(0(0(1(0(0(1(0(1(0(0(0(0(0(0(1(0(x1)))))))))))))))))))) (14)
0(0(0(1(0(0(0(1(0(1(0(0(1(1(1(1(0(1(0(0(x1)))))))))))))))))))) → 0(1(1(1(0(1(1(0(0(0(0(0(1(0(0(0(0(0(0(1(x1)))))))))))))))))))) (15)
0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(1(0(1(0(x1)))))))))))))))))))) → 0(0(0(0(0(1(0(0(0(0(1(1(0(0(0(0(0(0(1(0(x1)))))))))))))))))))) (16)
0(0(0(1(0(1(1(0(1(1(0(0(0(1(1(0(1(0(0(0(x1)))))))))))))))))))) → 1(0(0(0(1(0(0(1(1(0(0(0(1(0(0(0(1(0(0(1(x1)))))))))))))))))))) (17)
0(0(0(1(1(0(0(0(0(1(0(1(1(1(0(1(1(0(0(0(x1)))))))))))))))))))) → 0(1(0(1(0(1(0(1(0(0(1(1(0(0(1(0(0(0(0(0(x1)))))))))))))))))))) (18)
0(0(0(1(1(0(0(1(1(0(1(1(1(1(1(0(0(0(0(0(x1)))))))))))))))))))) → 0(0(1(0(0(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(x1)))))))))))))))))))) (19)
0(0(0(1(1(0(1(0(1(1(0(1(0(0(0(0(0(0(0(1(x1)))))))))))))))))))) → 0(1(0(0(0(0(1(0(0(1(0(1(0(0(1(0(1(0(0(0(x1)))))))))))))))))))) (20)
0(0(0(1(1(1(0(0(0(0(1(1(0(0(1(0(1(0(0(0(x1)))))))))))))))))))) → 0(1(0(0(1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(0(x1)))))))))))))))))))) (21)
0(0(1(0(0(0(0(0(1(1(1(1(1(1(0(1(0(0(0(1(x1)))))))))))))))))))) → 0(1(0(1(1(0(1(1(0(0(0(0(1(0(1(1(0(0(0(1(x1)))))))))))))))))))) (22)
0(0(1(0(0(0(0(1(0(0(1(1(1(0(1(0(1(0(1(0(x1)))))))))))))))))))) → 0(1(0(1(1(0(0(0(0(0(1(0(0(1(0(0(0(1(0(1(x1)))))))))))))))))))) (23)
0(0(1(0(0(0(1(0(0(1(0(1(0(1(1(1(0(0(1(0(x1)))))))))))))))))))) → 0(1(1(0(0(1(0(1(0(1(0(0(0(0(0(1(0(0(0(1(x1)))))))))))))))))))) (24)
0(0(1(0(0(0(1(1(0(0(1(0(0(0(1(1(0(1(0(0(x1)))))))))))))))))))) → 0(0(0(1(0(0(1(0(0(0(0(0(0(0(0(0(0(1(0(0(x1)))))))))))))))))))) (25)
0(0(1(0(0(0(1(1(1(0(0(0(1(1(0(0(1(0(1(0(x1)))))))))))))))))))) → 1(0(0(1(0(0(1(0(0(0(0(0(0(0(1(0(1(1(0(0(x1)))))))))))))))))))) (26)
0(0(1(0(1(0(0(0(1(1(0(0(1(1(1(0(0(0(1(0(x1)))))))))))))))))))) → 1(0(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(0(0(0(x1)))))))))))))))))))) (27)
0(0(1(0(1(0(0(1(0(0(1(1(1(0(0(0(0(1(1(1(x1)))))))))))))))))))) → 0(1(1(0(1(1(0(1(0(0(1(0(0(0(0(0(1(1(0(1(x1)))))))))))))))))))) (28)
0(0(1(0(1(0(0(1(0(1(0(1(0(0(0(0(1(1(1(0(x1)))))))))))))))))))) → 0(0(0(1(0(0(0(0(0(1(1(0(0(0(0(0(1(1(1(0(x1)))))))))))))))))))) (29)
0(0(1(0(1(1(0(0(0(1(1(1(1(0(0(0(0(0(0(0(x1)))))))))))))))))))) → 0(0(1(0(0(0(1(0(0(0(0(1(0(1(1(0(0(0(1(0(x1)))))))))))))))))))) (30)
0(0(1(0(1(1(1(0(0(0(1(1(0(1(0(1(0(0(0(0(x1)))))))))))))))))))) → 0(0(1(1(0(1(0(1(1(0(0(0(0(0(0(0(0(1(1(0(x1)))))))))))))))))))) (31)
0(0(1(0(1(1(1(1(0(0(0(0(0(0(1(1(0(1(0(0(x1)))))))))))))))))))) → 0(0(1(0(0(0(1(0(1(1(1(0(0(0(1(0(0(0(0(1(x1)))))))))))))))))))) (32)
0(0(1(0(1(1(1(1(0(0(0(1(0(0(0(1(1(0(0(0(x1)))))))))))))))))))) → 0(1(0(0(1(0(0(1(0(0(0(1(0(1(0(0(1(0(0(1(x1)))))))))))))))))))) (33)
0(0(1(1(0(0(1(1(0(1(0(0(0(1(0(0(1(0(1(0(x1)))))))))))))))))))) → 1(0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(0(0(0(0(x1)))))))))))))))))))) (34)
0(0(1(1(0(1(0(0(0(0(1(1(0(0(1(0(0(1(0(0(x1)))))))))))))))))))) → 1(0(1(0(0(0(0(0(0(1(0(1(0(0(1(0(0(0(0(0(x1)))))))))))))))))))) (35)
0(0(1(1(0(1(1(1(0(0(0(0(1(0(0(1(0(1(0(0(x1)))))))))))))))))))) → 1(1(1(0(0(0(0(1(1(0(0(0(0(0(0(0(1(0(0(1(x1)))))))))))))))))))) (36)
0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(0(0(0(1(0(x1)))))))))))))))))))) → 0(1(1(0(0(0(1(0(0(0(0(1(1(0(1(0(1(1(1(0(x1)))))))))))))))))))) (37)
0(0(1(1(0(1(1(1(1(1(0(1(0(1(0(0(0(0(0(0(x1)))))))))))))))))))) → 0(0(1(0(0(0(0(1(1(0(1(0(1(1(0(1(1(0(1(0(x1)))))))))))))))))))) (38)
0(0(1(1(1(0(0(0(0(0(1(1(1(0(0(0(0(1(1(0(x1)))))))))))))))))))) → 0(0(0(0(0(1(1(1(0(0(0(0(0(0(1(0(0(1(1(1(x1)))))))))))))))))))) (39)
0(0(1(1(1(0(1(0(1(0(1(0(1(0(0(0(0(0(0(0(x1)))))))))))))))))))) → 0(0(1(0(1(0(0(0(0(1(0(1(0(0(0(1(0(1(1(0(x1)))))))))))))))))))) (40)
0(1(0(0(0(0(0(1(0(0(0(1(0(1(1(1(0(0(0(0(x1)))))))))))))))))))) → 0(0(0(0(0(0(1(0(1(0(0(1(0(0(1(0(1(1(0(0(x1)))))))))))))))))))) (41)
0(1(0(0(0(0(0(1(1(1(0(1(0(1(0(0(0(1(1(0(x1)))))))))))))))))))) → 0(0(0(1(0(0(0(0(1(1(0(0(0(1(0(1(1(0(0(1(x1)))))))))))))))))))) (42)
0(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(1(0(0(x1)))))))))))))))))))) → 0(0(0(0(0(0(0(0(0(1(0(1(1(0(0(0(1(0(1(1(x1)))))))))))))))))))) (43)
0(1(0(1(0(0(0(0(1(1(1(0(1(0(1(0(0(0(1(0(x1)))))))))))))))))))) → 0(0(0(1(0(0(1(0(0(1(1(0(1(0(0(1(0(0(0(0(x1)))))))))))))))))))) (44)
0(1(0(1(0(0(0(1(0(1(0(1(1(0(1(0(1(0(0(0(x1)))))))))))))))))))) → 0(0(1(0(0(1(1(0(0(1(1(0(0(0(0(0(1(0(1(0(x1)))))))))))))))))))) (45)
0(1(0(1(0(0(1(1(1(0(0(1(1(1(1(1(0(0(1(0(x1)))))))))))))))))))) → 0(1(0(1(0(1(0(0(0(1(1(1(1(1(1(0(0(1(1(0(x1)))))))))))))))))))) (46)
0(1(0(1(0(1(1(1(1(0(0(0(0(1(0(0(1(0(0(0(x1)))))))))))))))))))) → 1(1(0(1(1(0(0(1(0(0(0(0(0(0(1(1(0(0(0(0(x1)))))))))))))))))))) (47)
0(1(0(1(1(1(0(0(1(0(0(0(0(0(0(0(1(1(0(1(x1)))))))))))))))))))) → 0(0(0(0(0(1(0(1(0(1(1(1(0(1(0(0(0(1(0(1(x1)))))))))))))))))))) (48)
0(1(0(1(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(0(x1)))))))))))))))))))) → 0(0(0(0(0(1(1(0(0(1(0(1(0(1(0(0(0(0(1(1(x1)))))))))))))))))))) (49)
0(1(1(0(0(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(x1)))))))))))))))))))) → 1(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(0(1(0(0(x1)))))))))))))))))))) (50)
0(1(1(0(0(1(1(1(1(0(0(0(1(0(0(0(0(0(1(0(x1)))))))))))))))))))) → 1(0(0(0(1(1(0(1(1(0(1(0(0(0(0(0(0(0(1(0(x1)))))))))))))))))))) (51)
0(1(1(0(1(1(0(0(0(0(0(0(0(1(0(0(1(0(1(0(x1)))))))))))))))))))) → 0(0(0(0(1(1(1(0(0(0(0(0(1(0(0(0(1(0(0(0(x1)))))))))))))))))))) (52)
0(1(1(1(1(0(0(0(0(1(0(0(1(0(0(1(0(0(1(0(x1)))))))))))))))))))) → 1(1(0(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(0(0(x1)))))))))))))))))))) (53)
0(1(1(1(1(0(0(0(0(1(0(1(0(0(0(1(0(0(0(0(x1)))))))))))))))))))) → 0(0(0(1(1(0(0(1(1(1(0(0(0(0(0(0(1(0(0(0(x1)))))))))))))))))))) (54)
1(0(0(0(0(0(0(1(0(1(1(1(1(0(0(0(0(1(0(0(x1)))))))))))))))))))) → 0(1(0(1(0(0(0(1(0(0(1(1(0(0(0(1(0(0(1(0(x1)))))))))))))))))))) (55)
1(0(0(0(0(0(0(1(1(0(0(1(0(1(0(0(0(1(1(0(x1)))))))))))))))))))) → 0(1(1(0(0(0(0(0(0(1(0(0(1(1(0(0(0(1(0(0(x1)))))))))))))))))))) (56)
1(0(0(0(0(0(1(1(1(0(0(1(1(0(1(1(0(0(0(0(x1)))))))))))))))))))) → 1(0(0(0(0(0(0(0(0(0(1(1(0(0(0(0(1(0(1(1(x1)))))))))))))))))))) (57)
1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(0(1(0(1(0(x1)))))))))))))))))))) → 0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(0(1(x1)))))))))))))))))))) (58)
1(0(0(0(0(1(1(1(1(0(0(1(0(0(0(0(0(0(1(1(x1)))))))))))))))))))) → 1(0(0(0(0(0(1(1(0(1(0(0(0(0(1(1(0(1(0(1(x1)))))))))))))))))))) (59)
1(0(0(0(1(0(0(0(1(0(0(1(0(1(0(0(1(1(1(0(x1)))))))))))))))))))) → 0(0(0(0(1(0(0(0(0(0(0(1(0(0(0(1(1(1(0(0(x1)))))))))))))))))))) (60)
1(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(0(1(0(0(x1)))))))))))))))))))) → 0(0(0(1(0(0(0(1(0(1(0(0(0(1(1(0(1(0(0(1(x1)))))))))))))))))))) (61)
1(0(0(0(1(1(0(0(0(1(0(1(0(0(0(1(0(1(1(0(x1)))))))))))))))))))) → 1(0(0(0(0(1(1(0(0(0(0(1(1(0(0(1(0(1(0(0(x1)))))))))))))))))))) (62)
1(0(0(0(1(1(0(0(1(0(1(1(0(0(1(1(0(0(0(0(x1)))))))))))))))))))) → 1(1(0(0(1(0(0(0(0(0(0(1(1(0(0(1(1(0(0(0(x1)))))))))))))))))))) (63)
1(0(0(0(1(1(1(0(0(1(0(0(0(0(0(1(1(0(1(0(x1)))))))))))))))))))) → 1(0(1(0(0(0(0(0(0(0(0(0(0(0(0(1(1(0(1(1(x1)))))))))))))))))))) (64)
1(0(0(1(0(0(1(0(0(0(0(1(0(0(1(1(0(0(1(0(x1)))))))))))))))))))) → 1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(0(0(1(0(0(x1)))))))))))))))))))) (65)
1(0(0(1(0(0(1(1(1(0(0(0(1(0(0(0(1(0(1(0(x1)))))))))))))))))))) → 0(1(0(1(1(1(0(0(0(1(0(1(0(0(0(0(1(0(0(0(x1)))))))))))))))))))) (66)
1(0(0(1(0(1(0(0(0(0(1(1(1(0(0(0(1(0(1(0(x1)))))))))))))))))))) → 0(0(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(0(0(0(x1)))))))))))))))))))) (67)
1(0(0(1(0(1(0(1(0(0(0(1(1(1(0(0(1(0(0(1(x1)))))))))))))))))))) → 1(0(1(0(0(1(0(0(0(0(0(1(0(1(1(1(0(1(0(1(x1)))))))))))))))))))) (68)
1(0(0(1(0(1(1(0(0(1(0(0(1(1(0(0(1(0(0(0(x1)))))))))))))))))))) → 1(0(0(1(0(0(1(0(1(1(1(0(0(0(0(0(0(0(0(1(x1)))))))))))))))))))) (69)
1(0(0(1(0(1(1(1(0(0(0(0(1(0(0(1(1(0(0(0(x1)))))))))))))))))))) → 0(0(1(0(0(1(1(0(0(0(0(0(1(0(1(0(1(0(1(0(x1)))))))))))))))))))) (70)
1(0(0(1(0(1(1(1(0(0(1(0(1(1(0(1(1(0(1(1(x1)))))))))))))))))))) → 1(0(1(0(0(1(0(1(1(0(1(1(1(0(0(1(0(1(0(1(x1)))))))))))))))))))) (71)
1(0(0(1(1(0(0(0(1(1(0(1(0(0(1(1(0(0(0(0(x1)))))))))))))))))))) → 1(0(1(0(0(1(0(1(0(0(0(1(0(0(0(0(1(0(1(0(x1)))))))))))))))))))) (72)
1(0(0(1(1(0(0(1(0(1(0(0(0(0(1(0(0(1(0(0(x1)))))))))))))))))))) → 0(0(0(1(0(1(0(0(1(1(0(0(0(0(0(0(1(0(0(1(x1)))))))))))))))))))) (73)
1(0(0(1(1(1(1(0(0(0(0(1(0(1(0(1(1(0(0(0(x1)))))))))))))))))))) → 1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(0(1(0(x1)))))))))))))))))))) (74)
1(0(1(0(0(0(1(0(1(1(0(1(0(0(0(0(0(1(0(0(x1)))))))))))))))))))) → 0(0(1(0(0(0(1(1(0(0(0(0(1(0(0(1(0(0(0(0(x1)))))))))))))))))))) (75)
1(0(1(0(0(1(1(0(1(0(0(1(1(0(1(0(0(0(0(0(x1)))))))))))))))))))) → 1(0(1(0(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(x1)))))))))))))))))))) (76)
1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(0(0(1(0(x1)))))))))))))))))))) → 1(0(0(1(0(1(0(1(1(1(0(0(0(0(1(0(1(0(1(0(x1)))))))))))))))))))) (77)
1(0(1(1(1(0(0(1(0(1(1(0(0(0(0(0(1(0(0(0(x1)))))))))))))))))))) → 1(1(0(0(1(1(1(0(0(0(0(0(0(0(0(1(0(0(0(0(x1)))))))))))))))))))) (78)
1(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(0(0(0(x1)))))))))))))))))))) → 1(1(0(1(0(0(0(0(1(0(0(0(0(0(0(0(0(1(0(0(x1)))))))))))))))))))) (79)
1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(0(0(1(0(0(x1)))))))))))))))))))) → 0(1(1(0(0(0(1(0(0(0(0(0(0(0(0(0(0(0(0(1(x1)))))))))))))))))))) (80)
1(1(0(0(0(0(1(1(0(1(1(0(1(0(0(0(0(0(1(0(x1)))))))))))))))))))) → 0(0(1(0(0(0(0(0(1(0(0(0(0(0(0(1(1(0(1(1(x1)))))))))))))))))))) (81)
1(1(0(0(0(1(0(0(1(0(0(1(0(0(1(0(0(0(1(0(x1)))))))))))))))))))) → 0(0(0(0(0(0(0(0(0(1(0(1(0(0(0(1(1(1(1(0(x1)))))))))))))))))))) (82)
1(1(0(0(0(1(0(1(1(0(0(0(1(1(0(0(0(1(0(0(x1)))))))))))))))))))) → 0(0(0(1(0(1(1(1(0(0(0(0(1(0(1(0(1(0(0(0(x1)))))))))))))))))))) (83)
1(1(0(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(0(1(x1)))))))))))))))))))) → 1(1(0(0(0(1(1(0(1(0(0(1(0(1(0(0(0(1(0(1(x1)))))))))))))))))))) (84)
1(1(0(0(1(0(0(0(0(0(1(0(0(1(0(0(0(1(1(0(x1)))))))))))))))))))) → 0(1(0(0(0(0(0(0(0(1(1(1(0(0(0(1(1(0(0(0(x1)))))))))))))))))))) (85)
1(1(0(0(1(1(0(0(1(0(0(0(0(0(1(1(1(0(0(0(x1)))))))))))))))))))) → 0(0(1(0(1(1(1(0(1(0(0(1(0(0(0(1(0(0(0(0(x1)))))))))))))))))))) (86)
1(1(0(0(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(x1)))))))))))))))))))) → 1(0(1(0(0(0(0(0(0(0(1(0(1(1(0(0(1(0(0(1(x1)))))))))))))))))))) (87)
1(1(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(0(x1)))))))))))))))))))) → 0(0(0(0(0(0(0(1(0(0(0(0(1(0(1(1(1(0(1(1(x1)))))))))))))))))))) (88)
1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(0(1(0(1(0(x1)))))))))))))))))))) → 1(1(0(1(1(1(0(1(0(0(1(0(1(1(1(0(1(0(1(0(x1)))))))))))))))))))) (89)
1(1(0(1(0(1(0(0(0(0(1(0(0(1(0(0(0(0(1(0(x1)))))))))))))))))))) → 0(0(0(0(0(1(1(0(1(0(0(0(0(0(0(0(0(0(0(1(x1)))))))))))))))))))) (90)
1(1(0(1(0(1(0(0(0(1(1(1(0(0(0(0(1(0(0(0(x1)))))))))))))))))))) → 0(0(0(0(0(1(0(1(0(1(0(0(1(0(0(1(0(0(0(0(x1)))))))))))))))))))) (91)
1(1(1(0(0(0(0(0(0(0(1(0(0(0(0(0(1(0(0(0(x1)))))))))))))))))))) → 0(0(0(1(0(0(0(0(0(0(0(0(0(0(0(0(1(0(0(1(x1)))))))))))))))))))) (92)
1(1(1(0(0(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(x1)))))))))))))))))))) → 1(0(1(1(0(0(1(1(0(1(0(0(0(1(0(1(0(1(0(0(x1)))))))))))))))))))) (93)
1(1(1(0(1(0(0(1(0(0(0(1(1(1(0(0(0(0(0(0(x1)))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(0(1(0(1(0(0(1(0(1(1(0(x1)))))))))))))))))))) (94)
1(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(0(0(0(0(x1)))))))))))))))))))) → 1(0(1(0(1(0(0(0(0(0(0(0(0(1(0(0(1(0(0(1(x1)))))))))))))))))))) (95)
1(1(1(0(1(1(1(1(0(0(0(1(0(0(0(0(0(0(0(0(x1)))))))))))))))))))) → 0(1(0(0(1(1(0(0(0(0(1(0(0(1(0(1(1(0(1(0(x1)))))))))))))))))))) (96)
1(1(1(1(1(0(0(0(0(0(0(1(1(1(0(0(0(1(0(0(x1)))))))))))))))))))) → 1(1(0(1(0(0(1(0(1(0(1(0(0(1(0(0(0(1(1(0(x1)))))))))))))))))))) (97)
1(1(1(1(1(0(1(0(0(1(1(0(1(0(0(0(1(0(0(0(x1)))))))))))))))))))) → 1(1(1(1(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(x1)))))))))))))))))))) (98)
1(1(1(1(1(1(0(0(0(1(0(0(0(0(1(0(0(0(0(0(x1)))))))))))))))))))) → 1(0(0(1(0(0(0(0(0(0(1(1(0(0(1(0(0(0(1(1(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
0(1(1(1(0(0(1(1(1(0(1(0(0(0(0(0(0(0(0(0(x1)))))))))))))))))))) → 0(0(1(1(0(0(1(1(0(0(0(1(0(0(0(0(0(0(0(1(x1)))))))))))))))))))) (100)
0(1(0(0(1(0(1(0(0(1(1(1(1(0(0(0(0(0(0(0(x1)))))))))))))))))))) → 1(0(0(0(0(0(0(0(0(0(0(1(0(1(0(0(0(0(1(0(x1)))))))))))))))))))) (101)
0(0(1(1(1(0(0(1(0(1(1(0(1(1(0(0(0(0(0(0(x1)))))))))))))))))))) → 1(0(1(0(0(1(0(0(0(0(1(0(0(1(0(1(0(1(0(0(x1)))))))))))))))))))) (102)
0(1(0(1(1(0(1(0(0(1(0(1(1(1(0(0(0(0(0(0(x1)))))))))))))))))))) → 0(0(1(0(0(0(1(0(1(0(0(0(1(1(0(1(0(0(0(0(x1)))))))))))))))))))) (103)
0(1(1(1(1(1(1(1(0(1(0(1(0(0(1(0(0(0(0(0(x1)))))))))))))))))))) → 0(1(1(0(0(0(1(1(1(0(0(0(1(0(1(1(1(1(0(0(x1)))))))))))))))))))) (104)
0(0(1(1(1(0(0(0(1(0(1(1(1(0(1(0(0(0(0(0(x1)))))))))))))))))))) → 1(0(0(1(0(0(0(1(0(0(1(0(1(0(0(0(0(1(0(1(x1)))))))))))))))))))) (105)
1(0(0(0(1(1(0(1(1(1(1(1(0(0(0(1(0(0(0(0(x1)))))))))))))))))))) → 1(0(0(1(0(0(0(0(1(0(1(0(0(1(0(1(1(1(1(0(x1)))))))))))))))))))) (106)
0(1(0(1(0(0(0(1(1(0(1(0(0(0(1(1(0(0(0(0(x1)))))))))))))))))))) → 1(0(1(0(0(0(0(1(0(0(1(0(0(0(1(0(0(0(0(0(x1)))))))))))))))))))) (107)
1(0(1(1(0(0(1(1(0(0(1(0(1(0(1(1(0(0(0(0(x1)))))))))))))))))))) → 1(0(1(1(0(1(1(0(1(0(1(0(0(0(0(1(1(0(0(0(x1)))))))))))))))))))) (108)
0(0(1(0(0(1(0(1(1(0(1(0(1(0(1(1(0(0(0(0(x1)))))))))))))))))))) → 0(0(1(1(1(1(0(1(0(0(1(1(0(0(0(0(0(0(0(0(x1)))))))))))))))))))) (109)
0(1(0(0(0(0(0(1(1(1(1(0(1(0(1(1(0(0(0(0(x1)))))))))))))))))))) → 0(1(0(0(0(0(1(0(0(0(1(1(0(1(0(0(0(1(0(1(x1)))))))))))))))))))) (110)
0(0(0(1(0(1(0(1(1(1(1(0(0(1(1(1(0(0(0(0(x1)))))))))))))))))))) → 0(0(1(0(1(1(0(0(1(0(0(1(1(0(0(1(0(1(1(0(x1)))))))))))))))))))) (111)
1(0(1(1(1(0(1(1(1(0(0(0(0(0(0(0(1(0(0(0(x1)))))))))))))))))))) → 1(0(0(1(0(0(1(0(0(1(1(0(0(0(1(1(0(0(1(0(x1)))))))))))))))))))) (112)
1(1(0(0(1(1(1(0(0(0(1(0(0(0(0(0(1(0(0(0(x1)))))))))))))))))))) → 0(1(0(0(0(0(0(0(1(0(1(0(0(1(0(0(0(1(1(0(x1)))))))))))))))))))) (113)
0(0(1(0(1(1(1(1(0(0(1(0(1(0(0(0(1(0(0(0(x1)))))))))))))))))))) → 1(0(0(0(0(0(0(1(0(0(0(0(0(1(1(0(1(1(1(0(x1)))))))))))))))))))) (114)
0(1(0(1(0(0(0(1(0(1(0(1(0(0(1(0(1(0(0(0(x1)))))))))))))))))))) → 0(1(0(0(0(0(0(0(1(1(0(0(0(0(1(0(0(0(0(0(x1)))))))))))))))))))) (115)
0(0(0(1(0(1(1(0(0(0(1(1(0(1(1(0(1(0(0(0(x1)))))))))))))))))))) → 1(0(0(1(0(0(0(1(0(0(0(1(1(0(0(1(0(0(0(1(x1)))))))))))))))))))) (116)
0(0(0(1(1(0(1(1(1(0(1(0(0(0(0(1(1(0(0(0(x1)))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(0(1(0(1(0(1(0(1(0(x1)))))))))))))))))))) (117)
0(0(0(0(0(1(1(1(1(1(0(1(1(0(0(1(1(0(0(0(x1)))))))))))))))))))) → 0(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(0(1(0(0(x1)))))))))))))))))))) (118)
1(0(0(0(0(0(0(0(1(0(1(1(0(1(0(1(1(0(0(0(x1)))))))))))))))))))) → 0(0(0(1(0(1(0(0(1(0(1(0(0(1(0(0(0(0(1(0(x1)))))))))))))))))))) (119)
0(0(0(1(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(x1)))))))))))))))))))) → 0(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(0(x1)))))))))))))))))))) (120)
1(0(0(0(1(0(1(1(1(1(1(1(0(0(0(0(0(1(0(0(x1)))))))))))))))))))) → 1(0(0(0(1(1(0(1(0(0(0(0(1(1(0(1(1(0(1(0(x1)))))))))))))))))))) (121)
0(1(0(1(0(1(0(1(1(1(0(0(1(0(0(0(0(1(0(0(x1)))))))))))))))))))) → 1(0(1(0(0(0(1(0(0(1(0(0(0(0(0(1(1(0(1(0(x1)))))))))))))))))))) (122)
0(1(0(0(1(1(1(0(1(0(1(0(0(1(0(0(0(1(0(0(x1)))))))))))))))))))) → 1(0(0(0(1(0(0(0(0(0(1(0(1(0(1(0(0(1(1(0(x1)))))))))))))))))))) (123)
0(0(1(0(1(1(0(0(0(1(0(0(1(1(0(0(0(1(0(0(x1)))))))))))))))))))) → 0(0(1(0(0(0(0(0(0(0(0(0(0(1(0(0(1(0(0(0(x1)))))))))))))))))))) (124)
0(1(0(1(0(0(1(1(0(0(0(1(1(1(0(0(0(1(0(0(x1)))))))))))))))))))) → 0(0(1(1(0(1(0(0(0(0(0(0(0(1(0(0(1(0(0(1(x1)))))))))))))))))))) (125)
0(1(0(0(0(1(1(1(0(0(1(1(0(0(0(1(0(1(0(0(x1)))))))))))))))))))) → 0(0(0(0(1(1(0(0(1(1(0(0(0(0(1(0(0(1(0(1(x1)))))))))))))))))))) (126)
1(1(1(0(0(0(0(1(1(1(0(0(1(0(0(1(0(1(0(0(x1)))))))))))))))))))) → 1(0(1(1(0(0(0(0(0(1(0(0(1(0(1(1(0(1(1(0(x1)))))))))))))))))))) (127)
0(1(1(1(0(0(0(0(1(0(1(0(1(0(0(1(0(1(0(0(x1)))))))))))))))))))) → 0(1(1(1(0(0(0(0(0(1(1(0(0(0(0(0(1(0(0(0(x1)))))))))))))))))))) (128)
0(0(0(0(0(0(0(1(1(1(1(0(0(0(1(1(0(1(0(0(x1)))))))))))))))))))) → 0(1(0(0(0(1(1(0(1(0(0(0(0(1(0(0(0(1(0(0(x1)))))))))))))))))))) (129)
0(0(0(0(1(0(1(0(1(1(0(0(0(1(1(1(0(1(0(0(x1)))))))))))))))))))) → 0(1(1(0(0(0(0(0(0(0(0(1(1(0(1(0(1(1(0(0(x1)))))))))))))))))))) (130)
0(0(1(0(1(1(0(0(0(0(0(0(1(1(1(1(0(1(0(0(x1)))))))))))))))))))) → 1(0(0(0(0(1(0(0(0(1(1(1(0(1(0(0(0(1(0(0(x1)))))))))))))))))))) (131)
0(0(0(1(1(0(0(0(1(0(0(0(1(1(1(1(0(1(0(0(x1)))))))))))))))))))) → 1(0(0(1(0(0(1(0(1(0(0(0(1(0(0(1(0(0(1(0(x1)))))))))))))))))))) (132)
0(1(0(1(0(0(1(0(0(0(1(0(1(1(0(0(1(1(0(0(x1)))))))))))))))))))) → 0(0(0(0(1(0(0(0(0(0(0(0(0(0(1(0(0(0(0(1(x1)))))))))))))))))))) (133)
0(0(1(0(0(1(0(0(1(1(0(0(0(0(1(0(1(1(0(0(x1)))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(0(1(0(0(0(0(0(0(1(0(1(x1)))))))))))))))))))) (134)
0(0(1(0(1(0(0(1(0(0(0(0(1(1(1(0(1(1(0(0(x1)))))))))))))))))))) → 1(0(0(1(0(0(0(0(0(0(0(1(1(0(0(0(0(1(1(1(x1)))))))))))))))))))) (135)
0(1(0(0(0(1(0(0(1(0(0(1(1(1(1(0(1(1(0(0(x1)))))))))))))))))))) → 0(1(1(1(0(1(0(1(1(0(0(0(0(1(0(0(0(1(1(0(x1)))))))))))))))))))) (136)
0(0(0(0(0(0(1(0(1(0(1(1(1(1(1(0(1(1(0(0(x1)))))))))))))))))))) → 0(1(0(1(1(0(1(1(0(1(0(1(1(0(0(0(0(1(0(0(x1)))))))))))))))))))) (137)
0(1(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(0(x1)))))))))))))))))))) → 1(1(1(0(0(1(0(0(0(0(0(0(1(1(1(0(0(0(0(0(x1)))))))))))))))))))) (138)
0(0(0(0(0(0(0(1(0(1(0(1(0(1(0(1(1(1(0(0(x1)))))))))))))))))))) → 0(1(1(0(1(0(0(0(1(0(1(0(0(0(0(1(0(1(0(0(x1)))))))))))))))))))) (139)
0(0(0(0(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(x1)))))))))))))))))))) → 0(0(1(1(0(1(0(0(1(0(0(1(0(1(0(0(0(0(0(0(x1)))))))))))))))))))) (140)
0(1(1(0(0(0(1(0(1(0(1(1(1(0(0(0(0(0(1(0(x1)))))))))))))))))))) → 1(0(0(1(1(0(1(0(0(0(1(1(0(0(0(0(1(0(0(0(x1)))))))))))))))))))) (141)
0(0(1(0(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(x1)))))))))))))))))))) → 1(1(0(1(0(0(0(1(1(0(1(0(0(0(0(0(0(0(0(0(x1)))))))))))))))))))) (142)
0(1(0(0(0(1(0(1(0(1(1(1(0(0(0(0(1(0(1(0(x1)))))))))))))))))))) → 0(0(0(0(1(0(0(1(0(1(1(0(0(1(0(0(1(0(0(0(x1)))))))))))))))))))) (143)
0(0(0(1(0(1(0(1(1(0(1(0(1(0(0(0(1(0(1(0(x1)))))))))))))))))))) → 0(1(0(1(0(0(0(0(0(1(1(0(0(1(1(0(0(1(0(0(x1)))))))))))))))))))) (144)
0(1(0(0(1(1(1(1(1(0(0(1(1(1(0(0(1(0(1(0(x1)))))))))))))))))))) → 0(1(1(0(0(1(1(1(1(1(1(0(0(0(1(0(1(0(1(0(x1)))))))))))))))))))) (145)
0(0(0(1(0(0(1(0(0(0(0(1(1(1(1(0(1(0(1(0(x1)))))))))))))))))))) → 0(0(0(0(1(1(0(0(0(0(0(0(1(0(0(1(1(0(1(1(x1)))))))))))))))))))) (146)
1(0(1(1(0(0(0(0(0(0(0(1(0(0(1(1(1(0(1(0(x1)))))))))))))))))))) → 1(0(1(0(0(0(1(0(1(1(1(0(1(0(1(0(0(0(0(0(x1)))))))))))))))))))) (147)
0(0(1(0(0(1(0(0(0(0(0(1(1(0(1(1(1(0(1(0(x1)))))))))))))))))))) → 1(1(0(0(0(0(1(0(1(0(1(0(0(1(1(0(0(0(0(0(x1)))))))))))))))))))) (148)
0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(1(1(0(x1)))))))))))))))))))) → 0(0(1(0(0(1(1(0(1(0(0(1(0(0(0(0(0(0(1(1(x1)))))))))))))))))))) (149)
0(1(0(0(0(0(0(1(0(0(0(1(1(1(1(0(0(1(1(0(x1)))))))))))))))))))) → 0(1(0(0(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(x1)))))))))))))))))))) (150)
0(1(0(1(0(0(1(0(0(0(0(0(0(0(1(1(0(1(1(0(x1)))))))))))))))))))) → 0(0(0(1(0(0(0(1(0(0(0(0(0(1(1(1(0(0(0(0(x1)))))))))))))))))))) (151)
0(1(0(0(1(0(0(1(0(0(1(0(0(0(0(1(1(1(1(0(x1)))))))))))))))))))) → 0(0(0(1(0(0(0(0(0(0(0(1(0(1(1(1(0(0(1(1(x1)))))))))))))))))))) (152)
0(0(0(0(1(0(0(0(1(0(1(0(0(0(0(1(1(1(1(0(x1)))))))))))))))))))) → 0(0(0(1(0(0(0(0(0(0(1(1(1(0(0(1(1(0(0(0(x1)))))))))))))))))))) (153)
0(0(1(0(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(1(x1)))))))))))))))))))) → 0(1(0(0(1(0(0(0(1(1(0(0(1(0(0(0(1(0(1(0(x1)))))))))))))))))))) (154)
0(1(1(0(0(0(1(0(1(0(0(1(1(0(0(0(0(0(0(1(x1)))))))))))))))))))) → 0(0(1(0(0(0(1(1(0(0(1(0(0(0(0(0(0(1(1(0(x1)))))))))))))))))))) (155)
0(0(0(0(1(1(0(1(1(0(0(1(1(1(0(0(0(0(0(1(x1)))))))))))))))))))) → 1(1(0(1(0(0(0(0(1(1(0(0(0(0(0(0(0(0(0(1(x1)))))))))))))))))))) (156)
0(1(0(1(0(0(0(1(0(0(1(1(0(1(1(0(0(0(0(1(x1)))))))))))))))))))) → 1(0(0(0(0(1(1(1(0(0(0(0(1(1(0(0(1(0(0(0(x1)))))))))))))))))))) (157)
1(1(0(0(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(x1)))))))))))))))))))) → 1(0(1(0(1(1(0(0(0(0(1(0(1(1(0(0(0(0(0(1(x1)))))))))))))))))))) (158)
0(1(1(1(0(0(1(0(1(0(0(1(0(0(0(1(0(0(0(1(x1)))))))))))))))))))) → 0(0(1(1(1(0(0(0(1(0(0(0(0(0(0(1(0(0(0(0(x1)))))))))))))))))))) (159)
0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(0(0(0(1(x1)))))))))))))))))))) → 1(0(0(1(0(1(1(0(0(0(1(0(1(0(0(0(1(0(0(0(x1)))))))))))))))))))) (160)
0(1(1(0(1(0(0(0(1(0(1(0(0(0(1(1(0(0(0(1(x1)))))))))))))))))))) → 0(0(1(0(1(0(0(1(1(0(0(0(0(1(1(0(0(0(0(1(x1)))))))))))))))))))) (161)
0(0(0(0(1(1(0(0(1(1(0(1(0(0(1(1(0(0(0(1(x1)))))))))))))))))))) → 0(0(0(1(1(0(0(1(1(0(0(0(0(0(0(1(0(0(1(1(x1)))))))))))))))))))) (162)
0(1(0(1(1(0(0(0(0(0(1(0(0(1(1(1(0(0(0(1(x1)))))))))))))))))))) → 1(1(0(1(1(0(0(0(0(0(0(0(0(0(0(0(0(1(0(1(x1)))))))))))))))))))) (163)
0(1(0(0(1(1(0(0(1(0(0(0(0(1(0(0(1(0(0(1(x1)))))))))))))))))))) → 0(0(1(0(0(1(0(1(0(0(0(0(0(1(0(0(0(1(0(1(x1)))))))))))))))))))) (164)
0(1(0(1(0(0(0(1(0(0(0(1(1(1(0(0(1(0(0(1(x1)))))))))))))))))))) → 0(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(0(x1)))))))))))))))))))) (165)
0(1(0(1(0(0(0(1(1(1(0(0(0(0(1(0(1(0(0(1(x1)))))))))))))))))))) → 0(0(0(1(1(0(0(0(1(0(1(0(0(0(0(1(0(0(0(0(x1)))))))))))))))))))) (166)
1(0(0(1(0(0(1(1(1(0(0(0(1(0(1(0(1(0(0(1(x1)))))))))))))))))))) → 1(0(1(0(1(1(1(0(1(0(0(0(0(0(1(0(0(1(0(1(x1)))))))))))))))))))) (167)
0(0(0(1(0(0(1(1(0(0(1(0(0(1(1(0(1(0(0(1(x1)))))))))))))))))))) → 1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(1(0(0(1(x1)))))))))))))))))))) (168)
0(0(0(1(1(0(0(1(0(0(0(0(1(1(1(0(1(0(0(1(x1)))))))))))))))))))) → 0(1(0(1(0(1(0(1(0(0(0(0(0(1(1(0(0(1(0(0(x1)))))))))))))))))))) (169)
1(1(0(1(1(0(1(1(0(1(0(0(1(1(1(0(1(0(0(1(x1)))))))))))))))))))) → 1(0(1(0(1(0(0(1(1(1(0(1(1(0(1(0(0(1(0(1(x1)))))))))))))))))))) (170)
0(0(0(0(1(1(0(0(1(0(1(1(0(0(0(1(1(0(0(1(x1)))))))))))))))))))) → 0(1(0(1(0(0(0(0(1(0(0(0(1(0(1(0(0(1(0(1(x1)))))))))))))))))))) (171)
0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(1(1(0(0(1(x1)))))))))))))))))))) → 1(0(0(1(0(0(0(0(0(0(1(1(0(0(1(0(1(0(0(0(x1)))))))))))))))))))) (172)
0(0(0(1(1(0(1(0(1(0(0(0(0(1(1(1(1(0(0(1(x1)))))))))))))))))))) → 0(1(0(1(0(0(0(1(1(0(0(0(1(0(1(0(0(1(1(1(x1)))))))))))))))))))) (173)
0(0(1(0(0(0(0(0(1(0(1(1(0(1(0(0(0(1(0(1(x1)))))))))))))))))))) → 0(0(0(0(1(0(0(1(0(0(0(0(1(1(0(0(0(1(0(0(x1)))))))))))))))))))) (174)
0(0(0(0(0(1(0(1(1(0(0(1(0(1(1(0(0(1(0(1(x1)))))))))))))))))))) → 1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(0(1(0(1(x1)))))))))))))))))))) (175)
0(1(0(0(1(1(1(0(1(0(0(0(0(0(0(1(1(1(0(1(x1)))))))))))))))))))) → 0(1(0(1(0(1(0(0(0(0(1(1(1(0(1(0(1(0(0(1(x1)))))))))))))))))))) (176)
0(0(0(1(0(0(0(0(0(1(1(0(1(0(0(1(1(1(0(1(x1)))))))))))))))))))) → 0(0(0(0(1(0(0(0(0(0(0(0(0(1(1(1(0(0(1(1(x1)))))))))))))))))))) (177)
0(0(0(0(0(0(1(1(0(1(1(0(1(0(0(0(0(0(1(1(x1)))))))))))))))))))) → 0(0(1(0(0(0(0(0(0(0(0(1(0(0(0(0(1(0(1(1(x1)))))))))))))))))))) (178)
0(0(1(0(0(1(0(0(1(0(0(1(1(0(0(0(0(0(1(1(x1)))))))))))))))))))) → 1(0(0(0(0(0(0(0(0(0(0(0(0(1(0(0(0(1(1(0(x1)))))))))))))))))))) (179)
0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(0(1(1(x1)))))))))))))))))))) → 1(1(0(1(1(0(0(0(0(0(0(1(0(0(0(0(0(1(0(0(x1)))))))))))))))))))) (180)
0(1(0(0(0(1(0(0(1(0(0(1(0(0(1(0(0(0(1(1(x1)))))))))))))))))))) → 0(1(1(1(1(0(0(0(1(0(1(0(0(0(0(0(0(0(0(0(x1)))))))))))))))))))) (181)
0(0(1(0(0(0(1(1(0(0(0(1(1(0(1(0(0(0(1(1(x1)))))))))))))))))))) → 0(0(0(1(0(1(0(1(0(0(0(0(1(1(1(0(1(0(0(0(x1)))))))))))))))))))) (182)
1(0(0(0(1(1(1(0(0(0(0(1(0(1(1(0(0(0(1(1(x1)))))))))))))))))))) → 1(0(1(0(0(0(1(0(1(0(0(1(0(1(1(0(0(0(1(1(x1)))))))))))))))))))) (183)
0(1(1(0(0(0(1(0(0(1(0(0(0(0(0(1(0(0(1(1(x1)))))))))))))))))))) → 0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(0(0(1(0(x1)))))))))))))))))))) (184)
0(0(0(1(1(1(0(0(0(0(0(1(0(0(1(1(0(0(1(1(x1)))))))))))))))))))) → 0(0(0(0(1(0(0(0(1(0(0(1(0(1(1(1(0(1(0(0(x1)))))))))))))))))))) (185)
0(1(0(0(0(1(1(0(0(0(0(0(0(1(1(1(0(0(1(1(x1)))))))))))))))))))) → 1(0(0(1(0(0(1(1(0(1(0(0(0(0(0(0(0(1(0(1(x1)))))))))))))))))))) (186)
0(0(1(0(1(1(1(0(0(0(1(0(0(0(0(0(1(0(1(1(x1)))))))))))))))))))) → 1(1(0(1(1(1(0(1(0(0(0(0(1(0(0(0(0(0(0(0(x1)))))))))))))))))))) (187)
0(1(0(1(0(1(1(0(1(0(1(1(1(1(0(0(1(0(1(1(x1)))))))))))))))))))) → 0(1(0(1(0(1(1(1(0(1(0(0(1(0(1(1(1(0(1(1(x1)))))))))))))))))))) (188)
0(1(0(0(0(0(1(0(0(1(0(0(0(0(1(0(1(0(1(1(x1)))))))))))))))))))) → 1(0(0(0(0(0(0(0(0(0(0(1(0(1(1(0(0(0(0(0(x1)))))))))))))))))))) (189)
0(0(0(1(0(0(0(0(1(1(1(0(0(0(1(0(1(0(1(1(x1)))))))))))))))))))) → 0(0(0(0(1(0(0(1(0(0(1(0(1(0(1(0(0(0(0(0(x1)))))))))))))))))))) (190)
0(0(0(1(0(0(0(0(0(1(0(0(0(0(0(0(0(1(1(1(x1)))))))))))))))))))) → 1(0(0(1(0(0(0(0(0(0(0(0(0(0(0(0(1(0(0(0(x1)))))))))))))))))))) (191)
0(1(1(0(0(1(1(0(0(1(0(0(0(0(1(0(0(1(1(1(x1)))))))))))))))))))) → 0(0(1(0(1(0(1(0(0(0(1(0(1(1(0(0(1(1(0(1(x1)))))))))))))))))))) (192)
0(0(0(0(0(0(1(1(1(0(0(0(1(0(0(1(0(1(1(1(x1)))))))))))))))))))) → 0(1(1(0(1(0(0(1(0(1(0(1(0(0(1(0(0(0(0(0(x1)))))))))))))))))))) (193)
0(0(0(0(1(0(0(0(0(0(1(0(0(0(1(1(0(1(1(1(x1)))))))))))))))))))) → 1(0(0(1(0(0(1(0(0(0(0(0(0(0(0(1(0(1(0(1(x1)))))))))))))))))))) (194)
0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(0(1(1(1(x1)))))))))))))))))))) → 0(1(0(1(1(0(1(0(0(1(0(0(0(0(1(1(0(0(1(0(x1)))))))))))))))))))) (195)
0(0(1(0(0(0(1(1(1(0(0(0(0(0(0(1(1(1(1(1(x1)))))))))))))))))))) → 0(1(1(0(0(0(1(0(0(1(0(1(0(1(0(0(1(0(1(1(x1)))))))))))))))))))) (196)
0(0(0(1(0(0(0(1(0(1(1(0(0(1(0(1(1(1(1(1(x1)))))))))))))))))))) → 0(0(0(0(1(0(0(0(1(1(0(1(1(0(1(0(1(1(1(1(x1)))))))))))))))))))) (197)
0(0(0(0(0(1(0(0(0(0(1(0(0(0(1(1(1(1(1(1(x1)))))))))))))))))))) → 1(1(0(0(0(1(0(0(1(1(0(0(0(0(0(0(1(0(0(1(x1)))))))))))))))))))) (198)

1.1 Closure Under Flat Contexts

Using the flat contexts

{0(☐), 1(☐)}

We obtain the transformed TRS

There are 131 ruless (increase limit for explicit display).

1.1.1 Semantic Labeling

Root-labeling is applied.

We obtain the labeled TRS

There are 262 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

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

There are 212 ruless (increase limit for explicit display).

1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[01(x1)] = 1 · x1
[11(x1)] = 1 · x1
[10(x1)] = 1 · x1
[00(x1)] = 1 · x1 + 1
all of the following rules can be deleted.
10(00(00(01(11(10(01(11(11(11(11(10(00(00(01(10(00(00(00(00(x1)))))))))))))))))))) → 10(00(01(10(00(00(00(01(10(01(10(00(01(10(01(11(11(11(10(00(x1)))))))))))))))))))) (269)
10(00(00(01(11(10(01(11(11(11(11(10(00(00(01(10(00(00(00(01(x1)))))))))))))))))))) → 10(00(01(10(00(00(00(01(10(01(10(00(01(10(01(11(11(11(10(01(x1)))))))))))))))))))) (270)
00(00(01(10(01(10(01(11(11(11(10(00(01(11(11(10(00(00(00(00(x1)))))))))))))))))))) → 00(01(10(01(11(10(00(01(10(00(01(11(10(00(01(10(01(11(10(00(x1)))))))))))))))))))) (277)
00(00(01(10(01(10(01(11(11(11(10(00(01(11(11(10(00(00(00(01(x1)))))))))))))))))))) → 00(01(10(01(11(10(00(01(10(00(01(11(10(00(01(10(01(11(10(01(x1)))))))))))))))))))) (278)
10(01(11(11(10(01(11(11(10(00(00(00(00(00(00(01(10(00(00(00(x1)))))))))))))))))))) → 10(00(01(10(00(01(10(00(01(11(10(00(00(01(11(10(00(01(10(00(x1)))))))))))))))))))) (279)
10(01(11(11(10(01(11(11(10(00(00(00(00(00(00(01(10(00(00(01(x1)))))))))))))))))))) → 10(00(01(10(00(01(10(00(01(11(10(00(00(01(11(10(00(01(10(01(x1)))))))))))))))))))) (280)
00(00(00(00(01(11(11(11(11(10(01(11(10(00(01(11(10(00(00(00(x1)))))))))))))))))))) → 00(00(01(10(01(11(11(10(01(11(10(01(11(10(00(00(01(10(00(00(x1)))))))))))))))))))) (285)
00(00(00(00(01(11(11(11(11(10(01(11(10(00(01(11(10(00(00(01(x1)))))))))))))))))))) → 00(00(01(10(01(11(11(10(01(11(10(01(11(10(00(00(01(10(00(01(x1)))))))))))))))))))) (286)
10(00(00(01(10(01(11(11(11(11(11(10(00(00(00(00(01(10(00(00(x1)))))))))))))))))))) → 10(00(00(01(11(10(01(10(00(00(00(01(11(10(01(11(10(01(10(00(x1)))))))))))))))))))) (289)
10(00(00(01(10(01(11(11(11(11(11(10(00(00(00(00(01(10(00(01(x1)))))))))))))))))))) → 10(00(00(01(11(10(01(10(00(00(00(01(11(10(01(11(10(01(10(01(x1)))))))))))))))))))) (290)
11(11(10(00(00(00(01(11(11(10(00(01(10(00(01(10(01(10(00(00(x1)))))))))))))))))))) → 10(01(11(10(00(00(00(00(01(10(00(01(10(01(11(10(01(11(10(00(x1)))))))))))))))))))) (297)
11(11(10(00(00(00(01(11(11(10(00(01(10(00(01(10(01(10(00(01(x1)))))))))))))))))))) → 10(01(11(10(00(00(00(00(01(10(00(01(10(01(11(10(01(11(10(01(x1)))))))))))))))))))) (298)
00(00(00(00(00(01(10(01(10(01(11(11(11(11(10(01(11(10(00(00(x1)))))))))))))))))))) → 01(10(01(11(10(01(11(10(01(10(01(11(10(00(00(00(01(10(00(00(x1)))))))))))))))))))) (311)
00(00(00(00(00(01(10(01(10(01(11(11(11(11(10(01(11(10(00(01(x1)))))))))))))))))))) → 01(10(01(11(10(01(11(10(01(10(01(11(10(00(00(00(01(10(00(01(x1)))))))))))))))))))) (312)
00(00(00(00(00(00(01(10(01(10(01(10(01(10(01(11(11(10(00(00(x1)))))))))))))))))))) → 01(11(10(01(10(00(00(01(10(01(10(00(00(00(01(10(01(10(00(00(x1)))))))))))))))))))) (313)
00(00(00(00(00(00(01(10(01(10(01(10(01(10(01(11(11(10(00(01(x1)))))))))))))))))))) → 01(11(10(01(10(00(00(01(10(01(10(00(00(00(01(10(01(10(00(01(x1)))))))))))))))))))) (314)
00(00(00(01(11(11(10(01(10(00(00(01(10(00(00(00(00(01(10(00(x1)))))))))))))))))))) → 00(01(11(10(01(10(00(01(10(00(01(10(01(10(00(00(00(00(00(00(x1)))))))))))))))))))) (315)
00(00(00(01(11(11(10(01(10(00(00(01(10(00(00(00(00(01(10(01(x1)))))))))))))))))))) → 00(01(11(10(01(10(00(01(10(00(01(10(01(10(00(00(00(00(00(01(x1)))))))))))))))))))) (316)
10(01(11(10(00(00(00(00(00(00(01(10(00(01(11(11(10(01(10(00(x1)))))))))))))))))))) → 10(01(10(00(00(01(10(01(11(11(10(01(10(01(10(00(00(00(00(00(x1)))))))))))))))))))) (325)
10(01(11(10(00(00(00(00(00(00(01(10(00(01(11(11(10(01(10(01(x1)))))))))))))))))))) → 10(01(10(00(00(01(10(01(11(11(10(01(10(01(10(00(00(00(00(01(x1)))))))))))))))))))) (326)
00(01(10(00(00(00(01(11(11(11(10(01(10(00(00(00(00(00(01(10(x1)))))))))))))))))))) → 01(10(00(01(10(00(00(01(11(10(00(01(10(00(00(01(10(01(10(00(x1)))))))))))))))))))) (337)
00(01(10(00(00(00(01(11(11(11(10(01(10(00(00(00(00(00(01(11(x1)))))))))))))))))))) → 01(10(00(01(10(00(00(01(11(10(00(01(10(00(00(01(10(01(10(01(x1)))))))))))))))))))) (338)
11(10(00(00(00(00(00(01(10(00(01(11(11(11(10(00(00(00(01(10(x1)))))))))))))))))))) → 10(01(10(01(11(10(00(00(00(01(10(01(11(10(00(00(00(00(01(10(x1)))))))))))))))))))) (341)
11(10(00(00(00(00(00(01(10(00(01(11(11(11(10(00(00(00(01(11(x1)))))))))))))))))))) → 10(01(10(01(11(10(00(00(00(01(10(01(11(10(00(00(00(00(01(11(x1)))))))))))))))))))) (342)
00(00(01(11(10(01(10(01(10(00(00(00(01(11(11(11(10(00(01(10(x1)))))))))))))))))))) → 01(10(01(10(00(00(01(11(10(00(00(01(10(01(10(00(01(11(11(10(x1)))))))))))))))))))) (363)
00(00(01(11(10(01(10(01(10(00(00(00(01(11(11(11(10(00(01(11(x1)))))))))))))))))))) → 01(10(01(10(00(00(01(11(10(00(00(01(10(01(10(00(01(11(11(11(x1)))))))))))))))))))) (364)
01(10(00(01(11(11(10(01(10(00(00(00(00(00(01(11(11(10(01(10(x1)))))))))))))))))))) → 01(10(01(10(01(10(00(00(00(01(11(11(10(01(10(01(10(00(01(10(x1)))))))))))))))))))) (367)
01(10(00(01(11(11(10(01(10(00(00(00(00(00(01(11(11(10(01(11(x1)))))))))))))))))))) → 01(10(01(10(01(10(00(00(00(01(11(11(10(01(10(01(10(00(01(11(x1)))))))))))))))))))) (368)
10(00(00(01(11(11(10(00(00(00(01(10(01(11(10(00(00(01(11(10(x1)))))))))))))))))))) → 10(01(10(00(00(01(10(01(10(00(01(10(01(11(10(00(00(01(11(10(x1)))))))))))))))))))) (377)
10(00(00(01(11(11(10(00(00(00(01(10(01(11(10(00(00(01(11(11(x1)))))))))))))))))))) → 10(01(10(00(00(01(10(01(10(00(01(10(01(11(10(00(00(01(11(11(x1)))))))))))))))))))) (378)
01(11(10(00(01(11(10(00(01(10(00(00(00(01(10(00(01(11(11(10(x1)))))))))))))))))))) → 00(01(10(01(10(01(10(00(00(01(10(01(11(10(00(01(11(10(01(10(x1)))))))))))))))))))) (387)
01(11(10(00(01(11(10(00(01(10(00(00(00(01(10(00(01(11(11(11(x1)))))))))))))))))))) → 00(01(10(01(10(01(10(00(00(01(10(01(11(10(00(01(11(10(01(11(x1)))))))))))))))))))) (388)
00(00(00(00(00(00(00(01(10(00(00(01(11(11(11(10(01(11(11(10(x1)))))))))))))))))))) → 01(10(01(11(10(01(10(00(01(10(00(00(00(01(11(10(00(01(10(00(x1)))))))))))))))))))) (391)
00(00(00(00(00(00(00(01(10(00(00(01(11(11(11(10(01(11(11(11(x1)))))))))))))))))))) → 01(10(01(11(10(01(10(00(01(10(00(00(00(01(11(10(00(01(10(01(x1)))))))))))))))))))) (392)
00(01(10(00(00(01(11(11(10(00(00(00(00(00(01(11(11(11(11(10(x1)))))))))))))))))))) → 01(11(10(00(00(01(10(00(01(10(01(10(01(10(00(01(10(01(11(10(x1)))))))))))))))))))) (393)
00(01(10(00(00(01(11(11(10(00(00(00(00(00(01(11(11(11(11(11(x1)))))))))))))))))))) → 01(11(10(00(00(01(10(00(01(10(01(10(01(10(00(01(10(01(11(11(x1)))))))))))))))))))) (394)

1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 184 ruless (increase limit for explicit display).

1.1.1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.