Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/135601)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Split

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

0(0(0(0(0(1(0(0(0(0(1(1(0(0(0(1(0(0(1(1(x1)))))))))))))))))))) → 0(1(0(0(1(0(0(0(0(1(1(1(0(1(0(0(1(1(1(1(x1)))))))))))))))))))) (3)
0(0(0(0(1(0(0(0(1(0(0(1(1(1(0(0(0(1(0(0(x1)))))))))))))))))))) → 0(1(0(1(1(0(0(0(1(1(1(1(0(1(1(1(0(1(0(0(x1)))))))))))))))))))) (6)
0(0(0(1(0(0(1(0(1(1(1(1(1(1(1(0(0(0(1(1(x1)))))))))))))))))))) → 0(0(0(1(1(0(1(1(1(1(0(0(1(0(1(1(0(1(1(1(x1)))))))))))))))))))) (7)
0(0(1(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(0(0(x1)))))))))))))))))))) → 0(0(0(0(1(1(0(1(0(1(1(0(1(1(1(0(1(1(1(0(x1)))))))))))))))))))) (16)
0(0(1(0(0(1(0(0(0(0(1(1(0(1(1(0(1(1(1(1(x1)))))))))))))))))))) → 0(1(1(0(1(0(1(0(0(0(0(0(1(1(0(0(0(1(0(1(x1)))))))))))))))))))) (18)
0(0(1(0(0(1(1(0(0(0(0(1(1(0(0(0(0(0(0(1(x1)))))))))))))))))))) → 0(1(0(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(1(1(x1)))))))))))))))))))) (21)
0(0(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(0(1(0(x1)))))))))))))))))))) → 0(0(1(1(1(0(1(0(1(0(1(0(1(1(0(0(1(1(1(0(x1)))))))))))))))))))) (22)
0(0(1(1(0(1(1(0(0(1(1(1(0(0(1(1(0(1(1(1(x1)))))))))))))))))))) → 0(0(1(1(0(0(1(0(1(1(1(0(1(1(0(0(1(0(0(1(x1)))))))))))))))))))) (28)
0(1(0(0(0(0(0(0(0(1(1(1(1(0(1(1(0(1(0(0(x1)))))))))))))))))))) → 0(1(1(1(0(1(0(1(1(1(1(1(1(1(0(1(0(1(0(0(x1)))))))))))))))))))) (32)
0(1(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(1(1(1(x1)))))))))))))))))))) → 0(1(1(0(0(0(1(0(1(1(1(0(0(1(1(0(0(1(1(1(x1)))))))))))))))))))) (33)
0(1(0(0(1(1(0(1(0(0(0(0(0(0(0(0(1(0(0(0(x1)))))))))))))))))))) → 0(0(1(0(0(1(0(1(1(1(0(1(1(0(1(1(0(0(1(0(x1)))))))))))))))))))) (36)
0(1(0(1(1(0(1(1(0(1(0(0(0(0(0(0(0(1(1(0(x1)))))))))))))))))))) → 0(1(1(1(0(1(0(1(1(0(1(1(0(1(1(0(0(0(1(0(x1)))))))))))))))))))) (38)
0(1(0(1(1(0(1(1(1(0(0(0(1(1(0(0(0(0(1(0(x1)))))))))))))))))))) → 0(0(1(0(1(0(0(0(0(1(0(1(0(1(0(0(0(1(1(0(x1)))))))))))))))))))) (39)
0(1(0(1(1(1(1(1(0(0(0(0(0(1(0(0(1(1(1(1(x1)))))))))))))))))))) → 0(1(1(1(0(1(1(1(0(0(1(0(1(1(0(0(1(1(1(1(x1)))))))))))))))))))) (40)
0(1(1(0(0(0(0(0(0(1(1(1(0(1(0(1(1(1(0(0(x1)))))))))))))))))))) → 0(1(0(0(0(1(1(0(1(1(0(1(1(0(0(1(1(0(0(0(x1)))))))))))))))))))) (41)
0(1(1(0(0(1(0(0(0(0(0(0(0(0(0(1(0(1(1(1(x1)))))))))))))))))))) → 0(0(1(1(0(1(0(1(1(0(0(1(0(0(0(0(0(0(1(1(x1)))))))))))))))))))) (44)
0(1(1(1(0(1(1(1(0(1(0(0(1(0(1(1(1(0(0(1(x1)))))))))))))))))))) → 0(0(1(0(1(0(1(1(0(1(0(1(1(1(0(1(1(1(0(1(x1)))))))))))))))))))) (47)
0(1(1(1(1(0(1(1(1(0(0(0(1(0(0(1(0(0(1(0(x1)))))))))))))))))))) → 0(0(1(1(0(0(1(0(1(1(1(1(0(1(0(1(0(0(1(0(x1)))))))))))))))))))) (49)
1(0(0(0(0(0(1(1(0(1(1(0(0(0(0(0(1(0(1(1(x1)))))))))))))))))))) → 1(0(1(0(1(0(0(1(1(1(1(1(0(1(1(0(1(1(0(1(x1)))))))))))))))))))) (53)
1(0(0(0(0(1(1(1(0(1(1(1(0(0(0(1(0(1(0(0(x1)))))))))))))))))))) → 1(1(0(1(1(0(1(1(0(1(0(1(0(1(0(1(0(1(1(0(x1)))))))))))))))))))) (55)
1(0(0(0(1(1(1(1(0(1(0(0(1(1(0(1(1(1(1(0(x1)))))))))))))))))))) → 1(1(0(0(1(1(0(0(1(0(1(0(1(0(1(0(1(1(1(0(x1)))))))))))))))))))) (59)
1(0(0(0(1(1(1(1(0(1(1(0(0(0(1(1(1(0(1(1(x1)))))))))))))))))))) → 1(0(0(0(0(1(1(1(0(0(0(0(0(1(0(1(0(1(0(1(x1)))))))))))))))))))) (60)
1(0(0(1(0(0(1(0(1(0(1(0(0(0(0(0(0(0(0(1(x1)))))))))))))))))))) → 1(0(1(1(1(0(1(0(0(1(0(0(1(0(0(0(1(1(0(1(x1)))))))))))))))))))) (62)
1(0(0(1(1(0(1(1(1(0(0(0(0(1(0(0(0(0(1(0(x1)))))))))))))))))))) → 1(0(1(0(1(1(0(1(1(1(1(1(1(0(1(1(0(1(1(0(x1)))))))))))))))))))) (64)
1(0(0(1(1(1(1(0(0(0(1(1(1(1(1(0(0(0(0(1(x1)))))))))))))))))))) → 1(1(0(1(0(1(0(0(0(1(0(1(1(0(0(0(0(0(0(1(x1)))))))))))))))))))) (67)
1(0(0(1(1(1(1(0(0(0(1(1(1(1(1(1(0(0(0(1(x1)))))))))))))))))))) → 1(1(1(0(1(0(1(0(0(1(0(1(1(1(1(1(0(0(0(1(x1)))))))))))))))))))) (68)
1(0(1(1(0(0(0(0(0(0(0(0(0(0(1(1(1(0(0(0(x1)))))))))))))))))))) → 1(0(1(1(1(0(1(1(0(1(1(1(1(1(0(0(0(0(0(0(x1)))))))))))))))))))) (72)
1(0(1(1(0(0(0(0(0(0(1(1(1(1(1(0(1(1(1(1(x1)))))))))))))))))))) → 1(1(0(1(0(1(1(1(1(0(0(0(1(1(0(1(0(0(1(1(x1)))))))))))))))))))) (73)
1(0(1(1(1(0(0(0(0(1(1(1(1(0(0(0(0(1(0(1(x1)))))))))))))))))))) → 1(1(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(0(1(1(x1)))))))))))))))))))) (77)
1(0(1(1(1(0(1(1(1(1(1(1(1(0(1(1(1(0(1(0(x1)))))))))))))))))))) → 1(1(1(0(1(1(0(1(1(0(1(0(1(0(1(0(1(1(1(0(x1)))))))))))))))))))) (79)
1(1(0(0(0(0(0(1(0(0(0(1(1(1(1(1(0(1(1(0(x1)))))))))))))))))))) → 0(1(0(1(0(0(0(0(1(1(1(0(1(0(0(0(1(0(1(0(x1)))))))))))))))))))) (82)
1(1(0(0(0(0(0(1(1(1(0(1(0(0(0(1(0(1(1(0(x1)))))))))))))))))))) → 0(0(1(0(1(0(1(0(1(0(1(0(0(1(0(1(0(1(1(0(x1)))))))))))))))))))) (83)
1(1(0(0(1(1(1(0(0(0(0(0(1(0(0(0(0(1(1(0(x1)))))))))))))))))))) → 0(1(0(1(0(1(0(0(0(1(1(1(0(1(0(0(0(0(1(0(x1)))))))))))))))))))) (88)
1(1(0(0(1(1(1(1(0(1(0(1(0(1(1(0(0(1(1(1(x1)))))))))))))))))))) → 1(1(0(1(1(0(0(0(0(1(0(1(0(1(1(1(0(1(0(1(x1)))))))))))))))))))) (89)
1(1(0(1(0(0(1(1(1(0(0(1(1(0(0(0(1(0(0(0(x1)))))))))))))))))))) → 1(0(1(1(0(0(0(0(0(0(1(1(1(0(1(0(1(0(1(0(x1)))))))))))))))))))) (92)
1(1(0(1(0(0(1(1(1(1(1(1(0(0(1(1(0(0(0(0(x1)))))))))))))))))))) → 1(0(0(0(0(1(0(1(1(1(0(1(1(1(0(1(1(1(1(0(x1)))))))))))))))))))) (93)
1(1(0(1(1(0(1(0(0(0(1(1(1(1(0(0(1(1(1(1(x1)))))))))))))))))))) → 1(1(0(1(1(0(0(0(0(1(1(1(0(1(0(0(1(1(0(1(x1)))))))))))))))))))) (94)
1(1(1(0(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(x1)))))))))))))))))))) → 1(0(1(1(1(0(1(1(1(1(1(1(0(1(0(1(1(1(0(1(x1)))))))))))))))))))) (96)
1(1(1(0(1(1(1(0(1(0(1(1(0(0(0(0(1(1(1(0(x1)))))))))))))))))))) → 1(1(0(1(0(1(0(0(0(1(0(1(0(0(1(0(1(1(0(0(x1)))))))))))))))))))) (99)
are deleted.

1.1 Closure Under Flat Contexts

Using the flat contexts

{1(☐), 0(☐)}

We obtain the transformed TRS

There are 198 ruless (increase limit for explicit display).

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 396 ruless (increase limit for explicit display).

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 +
1
[11(x1)] = x1 +
0
[00(x1)] = x1 +
0
[01(x1)] = x1 +
1
all of the following rules can be deleted.

There are 156 ruless (increase limit for explicit display).

1.1.1.1.1 R is empty

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

1.2 Split

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

0(0(0(0(0(0(1(0(1(0(1(0(1(1(0(1(1(0(1(0(x1)))))))))))))))))))) → 0(0(1(1(1(0(0(1(1(0(0(1(0(1(0(1(0(0(1(0(x1)))))))))))))))))))) (1)
0(0(0(0(0(0(1(0(1(1(0(0(1(1(1(1(0(1(1(1(x1)))))))))))))))))))) → 0(0(0(1(0(0(0(0(0(0(1(1(1(0(1(1(0(0(1(1(x1)))))))))))))))))))) (2)
0(0(0(0(0(1(1(0(0(1(1(0(0(1(1(1(0(1(0(1(x1)))))))))))))))))))) → 0(1(0(0(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(x1)))))))))))))))))))) (4)
0(0(0(0(0(1(1(0(0(1(1(1(0(1(0(0(0(0(1(0(x1)))))))))))))))))))) → 0(0(0(1(1(1(0(0(0(1(1(0(0(0(0(1(0(0(1(0(x1)))))))))))))))))))) (5)
0(0(0(1(0(0(1(1(1(0(1(0(1(1(0(1(1(0(1(1(x1)))))))))))))))))))) → 0(1(1(0(0(0(1(1(1(0(0(0(1(0(1(0(1(0(1(1(x1)))))))))))))))))))) (8)
0(0(0(1(0(1(0(0(0(0(1(0(1(0(1(1(1(0(1(0(x1)))))))))))))))))))) → 0(1(1(0(0(1(0(0(1(0(0(1(0(1(1(0(0(0(1(0(x1)))))))))))))))))))) (9)
0(0(0(1(0(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(x1)))))))))))))))))))) → 0(0(1(0(0(1(0(0(1(1(0(0(1(0(0(1(0(1(1(0(x1)))))))))))))))))))) (10)
0(0(0(1(0(1(0(0(1(1(0(0(1(1(1(0(0(0(1(1(x1)))))))))))))))))))) → 0(0(0(1(0(1(1(1(1(0(0(1(0(1(0(0(0(0(1(1(x1)))))))))))))))))))) (11)
0(0(0(1(1(0(0(1(0(0(0(0(1(1(0(1(0(0(1(0(x1)))))))))))))))))))) → 0(0(0(1(0(0(1(1(1(1(0(0(0(1(0(1(0(0(1(0(x1)))))))))))))))))))) (12)
0(0(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(1(0(1(x1)))))))))))))))))))) → 0(0(1(0(0(0(1(1(0(0(1(0(0(0(1(1(1(1(1(1(x1)))))))))))))))))))) (13)
0(0(0(1(1(0(1(1(0(1(0(0(1(1(1(1(1(1(0(1(x1)))))))))))))))))))) → 0(0(1(1(1(1(0(0(1(0(1(1(0(0(0(0(1(1(0(1(x1)))))))))))))))))))) (14)
0(0(0(1(1(0(1(1(1(1(1(0(1(0(1(0(1(0(0(1(x1)))))))))))))))))))) → 0(1(0(0(0(1(0(1(1(1(0(0(1(0(1(1(1(0(0(1(x1)))))))))))))))))))) (15)
0(0(1(0(0(0(1(1(1(1(1(0(1(1(1(0(1(1(0(0(x1)))))))))))))))))))) → 0(1(1(0(0(0(1(1(1(0(0(1(0(0(1(1(1(1(0(0(x1)))))))))))))))))))) (17)
0(0(1(0(0(1(0(0(0(1(1(1(0(0(0(1(0(0(0(0(x1)))))))))))))))))))) → 0(0(1(0(0(0(0(0(1(0(0(0(0(0(1(0(1(0(0(0(x1)))))))))))))))))))) (19)
0(0(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(x1)))))))))))))))))))) → 0(0(1(0(0(1(0(1(0(0(1(0(1(0(0(0(0(0(1(1(x1)))))))))))))))))))) (20)
0(0(1(1(0(0(1(0(1(1(0(0(0(0(1(0(1(1(0(1(x1)))))))))))))))))))) → 0(0(1(1(0(0(1(0(1(0(0(0(0(1(0(0(1(0(0(1(x1)))))))))))))))))))) (23)
0(0(1(1(0(0(1(1(0(1(0(1(1(1(0(0(0(0(0(0(x1)))))))))))))))))))) → 0(0(1(0(1(1(1(0(1(1(1(1(0(0(1(0(0(0(0(0(x1)))))))))))))))))))) (24)
0(0(1(1(0(1(0(0(0(1(0(1(1(0(0(1(0(1(1(0(x1)))))))))))))))))))) → 0(0(1(0(0(1(0(0(0(1(0(1(0(1(1(0(1(1(1(0(x1)))))))))))))))))))) (25)
0(0(1(1(0(1(1(0(0(0(0(0(0(0(1(1(0(0(1(0(x1)))))))))))))))))))) → 0(0(1(1(0(0(0(0(1(1(1(0(1(0(0(0(0(0(1(0(x1)))))))))))))))))))) (26)
0(0(1(1(0(1(1(0(0(0(1(1(0(0(0(1(0(1(1(1(x1)))))))))))))))))))) → 0(0(1(1(0(1(0(0(0(1(0(1(1(1(0(0(0(1(1(1(x1)))))))))))))))))))) (27)
0(0(1(1(1(1(0(0(0(1(1(0(0(1(1(1(1(0(1(0(x1)))))))))))))))))))) → 0(1(0(0(0(1(0(0(1(1(1(0(0(0(1(1(1(1(1(0(x1)))))))))))))))))))) (29)
0(0(1(1(1(1(0(0(1(1(0(0(1(1(1(0(1(0(1(1(x1)))))))))))))))))))) → 0(1(0(0(0(0(0(1(1(1(1(1(0(1(0(1(0(0(1(1(x1)))))))))))))))))))) (30)
0(0(1(1(1(1(0(1(0(0(1(0(1(1(0(1(1(1(0(0(x1)))))))))))))))))))) → 0(1(0(0(1(0(0(0(0(0(1(1(1(1(0(1(0(1(0(0(x1)))))))))))))))))))) (31)
0(1(0(0(1(0(1(0(0(0(0(1(1(0(1(1(1(1(1(1(x1)))))))))))))))))))) → 0(1(0(0(1(0(0(0(1(1(1(0(1(1(0(0(0(1(1(1(x1)))))))))))))))))))) (34)
0(1(0(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(0(0(x1)))))))))))))))))))) → 0(1(0(1(0(0(0(1(1(0(1(1(1(0(0(0(0(1(0(0(x1)))))))))))))))))))) (35)
0(1(0(0(1(1(1(1(1(1(1(0(1(0(1(0(0(1(1(1(x1)))))))))))))))))))) → 0(1(0(0(1(0(1(1(1(0(0(1(1(1(1(1(0(0(1(1(x1)))))))))))))))))))) (37)
0(1(1(0(0(0(0(0(1(0(1(0(1(1(1(1(1(1(0(1(x1)))))))))))))))))))) → 0(0(1(0(0(0(1(0(0(0(0(1(0(0(0(0(1(0(0(1(x1)))))))))))))))))))) (42)
0(1(1(0(0(0(0(1(1(0(0(0(1(1(0(1(0(1(1(0(x1)))))))))))))))))))) → 0(1(0(1(0(0(1(1(1(0(0(1(0(0(0(0(1(1(1(0(x1)))))))))))))))))))) (43)
0(1(1(0(1(1(0(1(0(0(1(0(1(1(1(1(1(0(1(1(x1)))))))))))))))))))) → 0(1(0(0(0(1(0(0(1(0(1(1(0(1(0(0(0(1(1(1(x1)))))))))))))))))))) (45)
0(1(1(1(0(1(1(0(1(1(0(0(0(0(0(0(0(1(0(1(x1)))))))))))))))))))) → 0(1(1(0(0(1(1(0(0(1(1(1(1(1(1(0(0(1(0(1(x1)))))))))))))))))))) (46)
0(1(1(1(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(0(x1)))))))))))))))))))) → 0(1(1(0(0(1(0(0(0(1(0(1(1(1(1(1(1(0(1(0(x1)))))))))))))))))))) (48)
0(1(1(1(1(1(0(0(1(1(1(0(1(1(1(1(0(0(1(1(x1)))))))))))))))))))) → 0(1(1(1(1(1(1(0(1(1(1(1(1(0(0(0(1(0(1(1(x1)))))))))))))))))))) (50)
0(1(1(1(1(1(1(1(1(0(1(0(1(0(0(0(1(1(1(1(x1)))))))))))))))))))) → 0(1(1(1(0(0(0(1(0(1(1(1(1(0(0(0(1(1(1(1(x1)))))))))))))))))))) (51)
1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(x1)))))))))))))))))))) → 1(0(0(0(0(0(1(0(1(0(0(0(1(0(0(1(1(0(0(0(x1)))))))))))))))))))) (52)
1(0(0(0(0(1(0(1(1(1(1(1(0(0(1(0(1(0(1(0(x1)))))))))))))))))))) → 1(0(0(0(1(0(0(1(1(0(0(1(1(0(0(1(0(0(1(0(x1)))))))))))))))))))) (54)
1(0(0(0(0(1(1(1(1(0(1(0(1(0(0(1(0(1(0(0(x1)))))))))))))))))))) → 1(0(0(0(1(1(1(0(1(0(1(0(1(0(0(0(0(1(0(0(x1)))))))))))))))))))) (56)
1(0(0(0(1(0(1(1(1(1(1(1(0(1(0(1(0(1(0(0(x1)))))))))))))))))))) → 1(0(0(1(0(0(1(0(0(0(1(0(1(1(1(1(0(1(0(0(x1)))))))))))))))))))) (57)
1(0(0(0(1(1(1(1(0(0(1(0(0(1(0(1(0(0(0(1(x1)))))))))))))))))))) → 1(0(0(0(0(0(1(0(0(1(1(0(1(0(0(1(0(0(0(1(x1)))))))))))))))))))) (58)
1(0(0(0(1(1(1(1(1(0(1(1(0(0(0(1(0(1(1(1(x1)))))))))))))))))))) → 1(0(1(1(0(1(0(0(0(0(0(0(1(0(0(0(0(0(1(1(x1)))))))))))))))))))) (61)
1(0(0(1(1(0(1(0(0(1(0(1(0(1(0(1(0(1(1(1(x1)))))))))))))))))))) → 1(0(0(0(1(0(1(1(0(0(1(0(1(0(1(0(1(0(1(1(x1)))))))))))))))))))) (63)
1(0(0(1(1(1(0(1(1(0(1(0(0(0(0(1(1(0(0(1(x1)))))))))))))))))))) → 1(0(1(0(0(0(0(1(0(0(0(0(1(1(0(1(1(0(0(1(x1)))))))))))))))))))) (66)
1(0(0(1(1(1(1(0(0(1(1(0(1(1(1(1(0(1(0(1(x1)))))))))))))))))))) → 1(0(1(0(1(0(1(1(0(0(0(0(0(0(0(0(0(1(0(1(x1)))))))))))))))))))) (69)
1(0(1(0(1(0(0(1(1(0(0(1(1(0(0(1(0(0(1(1(x1)))))))))))))))))))) → 1(0(1(0(1(0(0(1(0(1(1(1(0(0(1(0(0(0(1(1(x1)))))))))))))))))))) (70)
1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(0(0(0(1(1(x1)))))))))))))))))))) → 1(0(0(0(0(1(0(1(1(0(1(0(1(1(1(1(0(0(1(1(x1)))))))))))))))))))) (71)
1(0(1(1(0(0(0(0(1(1(0(1(0(1(1(0(1(0(0(1(x1)))))))))))))))))))) → 1(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(0(0(1(x1)))))))))))))))))))) (74)
1(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(0(1(1(x1)))))))))))))))))))) → 1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(1(1(1(x1)))))))))))))))))))) (75)
1(0(1(1(0(1(0(1(1(1(1(1(1(0(0(0(1(0(0(1(x1)))))))))))))))))))) → 1(0(0(0(0(0(0(0(1(0(1(1(0(1(1(0(1(0(0(1(x1)))))))))))))))))))) (76)
1(0(1(1(1(0(1(1(1(1(1(1(1(0(0(1(0(1(1(0(x1)))))))))))))))))))) → 1(0(0(0(1(1(0(0(1(1(0(1(1(1(0(0(1(1(1(0(x1)))))))))))))))))))) (78)
1(0(1(1(1(1(1(0(1(1(0(0(0(1(0(0(1(0(1(0(x1)))))))))))))))))))) → 1(0(0(0(1(0(1(1(1(1(0(1(0(0(1(1(0(0(1(0(x1)))))))))))))))))))) (81)
1(1(0(0(0(0(1(1(1(1(0(1(0(1(1(0(1(0(0(0(x1)))))))))))))))))))) → 1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(0(0(x1)))))))))))))))))))) (84)
1(1(0(0(0(1(0(0(1(1(0(1(1(1(0(0(0(0(1(0(x1)))))))))))))))))))) → 1(1(0(0(0(1(0(0(1(0(0(0(1(1(1(1(0(0(1(0(x1)))))))))))))))))))) (85)
1(1(0(0(1(0(0(1(1(1(1(0(1(1(1(0(0(1(1(0(x1)))))))))))))))))))) → 1(1(0(0(0(1(1(1(1(1(0(0(0(1(0(1(0(1(1(0(x1)))))))))))))))))))) (86)
1(1(0(0(1(0(1(1(0(1(1(0(1(0(1(1(0(1(1(1(x1)))))))))))))))))))) → 1(1(1(0(0(1(1(0(1(1(0(1(0(1(0(1(0(1(1(1(x1)))))))))))))))))))) (87)
1(1(0(0(1(1(1(1(1(0(0(1(0(1(1(0(1(1(0(1(x1)))))))))))))))))))) → 1(0(0(1(0(0(1(0(0(1(1(1(0(0(0(1(0(0(0(1(x1)))))))))))))))))))) (90)
1(1(0(1(0(0(0(1(1(0(1(1(0(1(1(0(0(0(1(1(x1)))))))))))))))))))) → 1(1(0(1(0(0(1(0(1(1(1(0(0(0(0(0(1(0(1(1(x1)))))))))))))))))))) (91)
1(1(0(1(1(1(0(0(0(0(0(0(0(1(1(1(0(0(1(0(x1)))))))))))))))))))) → 1(1(1(0(0(1(0(1(1(1(1(1(1(1(1(1(0(0(1(0(x1)))))))))))))))))))) (95)
1(1(1(0(0(1(1(1(1(0(1(0(0(1(1(0(0(0(1(1(x1)))))))))))))))))))) → 1(1(0(1(0(0(1(1(1(1(1(1(0(0(0(1(0(0(1(1(x1)))))))))))))))))))) (97)
1(1(1(0(1(1(0(0(1(1(1(0(1(0(1(1(0(0(0(1(x1)))))))))))))))))))) → 1(1(1(0(0(1(0(1(1(0(1(0(1(1(1(0(0(0(0(1(x1)))))))))))))))))))) (98)
are deleted.

1.2.1 Closure Under Flat Contexts

Using the flat contexts

{1(☐), 0(☐)}

We obtain the transformed TRS

There are 120 ruless (increase limit for explicit display).

1.2.1.1 Closure Under Flat Contexts

Using the flat contexts

{1(☐), 0(☐)}

We obtain the transformed TRS

There are 240 ruless (increase limit for explicit display).

1.2.1.1.1 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 960 ruless (increase limit for explicit display).

1.2.1.1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[10(x1)] = x1 +
21
[12(x1)] = x1 +
34
[11(x1)] = x1 +
33
[13(x1)] = x1 +
1
[00(x1)] = x1 +
34
[02(x1)] = x1 +
0
[01(x1)] = x1 +
1
[03(x1)] = x1 +
12
all of the following rules can be deleted.

There are 928 ruless (increase limit for explicit display).

1.2.1.1.1.1.1 R is empty

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

1.2.2 Closure Under Flat Contexts

Using the flat contexts

{1(☐), 0(☐)}

We obtain the transformed TRS
1(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(1(1(0(x1))))))))))))))))))))) → 1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(1(1(0(x1))))))))))))))))))))) (218)
1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(x1))))))))))))))))))))) → 1(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(0(0(0(1(1(x1))))))))))))))))))))) (227)
0(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(1(1(0(x1))))))))))))))))))))) → 0(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(1(1(0(x1))))))))))))))))))))) (278)
0(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(x1))))))))))))))))))))) → 0(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(0(0(0(1(1(x1))))))))))))))))))))) (287)

1.2.2.1 Closure Under Flat Contexts

Using the flat contexts

{1(☐), 0(☐)}

We obtain the transformed TRS
1(1(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(1(1(0(x1)))))))))))))))))))))) → 1(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(1(1(0(x1)))))))))))))))))))))) (926)
1(1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(x1)))))))))))))))))))))) → 1(1(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(0(0(0(1(1(x1)))))))))))))))))))))) (927)
1(0(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(1(1(0(x1)))))))))))))))))))))) → 1(0(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(1(1(0(x1)))))))))))))))))))))) (928)
1(0(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(x1)))))))))))))))))))))) → 1(0(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(0(0(0(1(1(x1)))))))))))))))))))))) (929)
0(1(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(1(1(0(x1)))))))))))))))))))))) → 0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(1(1(0(x1)))))))))))))))))))))) (930)
0(1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(x1)))))))))))))))))))))) → 0(1(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(0(0(0(1(1(x1)))))))))))))))))))))) (931)
0(0(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(1(1(0(x1)))))))))))))))))))))) → 0(0(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(1(1(0(x1)))))))))))))))))))))) (932)
0(0(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(x1)))))))))))))))))))))) → 0(0(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(0(0(0(1(1(x1)))))))))))))))))))))) (933)

1.2.2.1.1 Closure Under Flat Contexts

Using the flat contexts

{1(☐), 0(☐)}

We obtain the transformed TRS
1(1(1(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(1(1(0(x1))))))))))))))))))))))) → 1(1(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(1(1(0(x1))))))))))))))))))))))) (1894)
1(1(1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(x1))))))))))))))))))))))) → 1(1(1(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(0(0(0(1(1(x1))))))))))))))))))))))) (1895)
1(1(0(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(1(1(0(x1))))))))))))))))))))))) → 1(1(0(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(1(1(0(x1))))))))))))))))))))))) (1896)
1(1(0(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(x1))))))))))))))))))))))) → 1(1(0(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(0(0(0(1(1(x1))))))))))))))))))))))) (1897)
1(0(1(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(1(1(0(x1))))))))))))))))))))))) → 1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(1(1(0(x1))))))))))))))))))))))) (1898)
1(0(1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(x1))))))))))))))))))))))) → 1(0(1(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(0(0(0(1(1(x1))))))))))))))))))))))) (1899)
1(0(0(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(1(1(0(x1))))))))))))))))))))))) → 1(0(0(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(1(1(0(x1))))))))))))))))))))))) (1900)
1(0(0(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(x1))))))))))))))))))))))) → 1(0(0(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(0(0(0(1(1(x1))))))))))))))))))))))) (1901)
0(1(1(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(1(1(0(x1))))))))))))))))))))))) → 0(1(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(1(1(0(x1))))))))))))))))))))))) (1902)
0(1(1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(x1))))))))))))))))))))))) → 0(1(1(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(0(0(0(1(1(x1))))))))))))))))))))))) (1903)
0(1(0(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(1(1(0(x1))))))))))))))))))))))) → 0(1(0(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(1(1(0(x1))))))))))))))))))))))) (1904)
0(1(0(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(x1))))))))))))))))))))))) → 0(1(0(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(0(0(0(1(1(x1))))))))))))))))))))))) (1905)
0(0(1(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(1(1(0(x1))))))))))))))))))))))) → 0(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(1(1(0(x1))))))))))))))))))))))) (1906)
0(0(1(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(x1))))))))))))))))))))))) → 0(0(1(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(0(0(0(1(1(x1))))))))))))))))))))))) (1907)
0(0(0(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(1(1(0(x1))))))))))))))))))))))) → 0(0(0(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(1(1(1(0(x1))))))))))))))))))))))) (1908)
0(0(0(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(x1))))))))))))))))))))))) → 0(0(0(1(0(0(1(0(1(1(1(0(0(0(0(1(1(1(0(0(0(1(1(x1))))))))))))))))))))))) (1909)

1.2.2.1.1.1 Semantic Labeling

The following interpretations form a model of the rules.

As carrier we take the set {0,...,7}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 8):

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

We obtain the labeled TRS

There are 128 ruless (increase limit for explicit display).

1.2.2.1.1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[10(x1)] = x1 +
1
[14(x1)] = x1 +
0
[12(x1)] = x1 +
1
[16(x1)] = x1 +
0
[11(x1)] = x1 +
0
[15(x1)] = x1 +
1
[13(x1)] = x1 +
1
[17(x1)] = x1 +
0
[00(x1)] = x1 +
0
[04(x1)] = x1 +
1
[02(x1)] = x1 +
0
[06(x1)] = x1 +
1
[01(x1)] = x1 +
1
[05(x1)] = x1 +
0
[03(x1)] = x1 +
0
[07(x1)] = x1 +
1
all of the following rules can be deleted.

There are 128 ruless (increase limit for explicit display).

1.2.2.1.1.1.1.1 R is empty

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