Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/158620)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[2(x1)] = x1 +
0
[1(x1)] = x1 +
1
[0(x1)] = x1 +
0
all of the following rules can be deleted.
0(0(0(0(1(1(2(0(0(2(1(2(0(1(1(0(1(0(2(1(x1)))))))))))))))))))) → 2(2(0(1(0(1(2(0(2(1(2(0(0(2(2(2(1(2(0(1(x1)))))))))))))))))))) (1)
0(0(0(1(0(1(2(2(2(2(2(1(2(2(1(0(1(0(2(1(x1)))))))))))))))))))) → 1(0(2(0(2(2(1(0(2(2(2(0(0(2(0(0(1(0(1(1(x1)))))))))))))))))))) (2)
0(0(0(1(1(1(1(0(1(0(0(2(0(2(1(2(0(0(1(1(x1)))))))))))))))))))) → 0(2(2(2(0(1(2(2(2(1(2(0(0(1(1(0(1(0(1(1(x1)))))))))))))))))))) (3)
0(0(0(2(0(2(1(0(2(0(1(2(0(1(2(1(2(0(1(0(x1)))))))))))))))))))) → 2(2(0(0(2(1(2(0(0(1(0(2(2(0(0(0(0(2(1(0(x1)))))))))))))))))))) (4)
0(0(0(2(1(1(2(2(0(2(0(2(0(2(1(1(1(2(1(1(x1)))))))))))))))))))) → 2(1(2(1(2(2(0(0(0(1(0(0(2(2(2(2(2(0(1(1(x1)))))))))))))))))))) (5)
0(0(0(2(2(2(1(1(1(2(2(0(2(0(1(2(1(1(2(1(x1)))))))))))))))))))) → 2(2(0(0(2(2(2(0(0(2(1(0(1(1(0(1(2(2(0(1(x1)))))))))))))))))))) (6)
0(0(1(0(0(2(1(1(0(0(1(0(2(2(2(0(1(0(2(1(x1)))))))))))))))))))) → 0(2(0(0(1(1(2(0(0(1(2(0(2(2(2(0(1(0(0(1(x1)))))))))))))))))))) (7)
0(0(1(1(1(2(1(2(1(2(0(2(0(1(0(0(2(2(1(1(x1)))))))))))))))))))) → 1(1(1(0(0(0(0(1(0(2(2(0(2(0(0(2(2(1(0(1(x1)))))))))))))))))))) (8)
0(0(1(2(0(1(2(0(0(0(2(1(2(2(1(1(1(2(1(1(x1)))))))))))))))))))) → 0(0(2(2(1(1(0(0(1(2(0(2(2(0(1(2(0(1(0(1(x1)))))))))))))))))))) (10)
0(0(1(2(0(2(1(2(0(1(1(0(0(0(2(0(2(1(1(2(x1)))))))))))))))))))) → 1(1(0(0(0(0(0(0(2(0(2(0(2(1(0(1(1(2(2(0(x1)))))))))))))))))))) (11)
0(0(1(2(2(2(1(2(1(2(0(2(2(0(0(1(0(1(2(1(x1)))))))))))))))))))) → 0(2(0(0(2(2(0(0(2(1(2(1(0(1(2(0(1(2(2(1(x1)))))))))))))))))))) (12)
0(0(2(0(0(2(2(1(0(2(0(2(0(1(2(0(1(1(0(1(x1)))))))))))))))))))) → 0(2(2(2(0(2(1(0(0(0(1(0(1(2(2(2(0(2(2(1(x1)))))))))))))))))))) (13)
0(0(2(0(1(0(1(1(2(1(2(0(0(2(0(1(0(2(0(0(x1)))))))))))))))))))) → 0(2(1(2(0(2(1(0(1(0(0(2(0(2(0(0(1(2(2(2(x1)))))))))))))))))))) (14)
0(0(2(0(1(2(2(0(2(2(0(2(1(1(0(0(1(2(2(0(x1)))))))))))))))))))) → 2(2(1(0(2(0(2(0(2(1(0(2(2(0(2(0(2(0(0(0(x1)))))))))))))))))))) (15)
0(0(2(1(1(2(2(2(0(1(1(2(2(0(2(2(1(2(2(1(x1)))))))))))))))))))) → 0(0(2(2(1(2(1(0(2(0(0(1(1(0(2(2(2(2(2(1(x1)))))))))))))))))))) (17)
0(0(2(2(1(0(2(0(0(2(1(1(1(0(0(2(0(2(0(1(x1)))))))))))))))))))) → 2(0(0(1(2(0(2(2(0(0(0(2(0(2(0(1(0(2(0(1(x1)))))))))))))))))))) (18)
0(0(2(2(1(0(2(2(2(1(1(2(0(2(2(2(1(0(2(1(x1)))))))))))))))))))) → 2(0(2(0(2(2(0(0(0(1(2(1(0(2(0(0(2(2(1(1(x1)))))))))))))))))))) (20)
0(1(0(0(0(1(0(0(0(1(1(2(0(0(1(2(2(1(0(1(x1)))))))))))))))))))) → 2(0(2(0(1(1(0(0(1(2(2(0(0(0(2(2(2(1(2(1(x1)))))))))))))))))))) (22)
0(1(0(0(1(0(1(2(0(0(2(0(2(0(0(2(1(1(0(0(x1)))))))))))))))))))) → 2(2(2(1(0(0(1(2(2(2(0(0(2(2(0(2(2(0(2(1(x1)))))))))))))))))))) (23)
0(1(0(1(0(2(2(0(2(2(0(2(0(0(1(2(1(1(1(1(x1)))))))))))))))))))) → 0(1(1(1(2(1(0(0(0(2(2(1(0(2(2(0(0(2(0(1(x1)))))))))))))))))))) (25)
0(1(0(1(2(2(0(0(1(1(0(2(0(1(2(0(0(2(2(1(x1)))))))))))))))))))) → 1(0(2(2(0(2(2(1(2(2(2(0(1(2(1(0(2(2(0(1(x1)))))))))))))))))))) (26)
0(1(0(2(0(1(0(2(1(0(2(1(2(2(1(1(0(2(2(1(x1)))))))))))))))))))) → 2(2(2(0(2(0(1(2(0(2(1(0(0(0(0(2(0(1(2(0(x1)))))))))))))))))))) (27)
0(1(1(0(1(2(0(1(2(0(0(0(2(0(1(2(0(2(1(1(x1)))))))))))))))))))) → 2(2(0(1(0(0(0(2(0(2(1(0(1(0(0(0(0(0(1(1(x1)))))))))))))))))))) (28)
0(1(1(1(2(1(2(0(0(0(1(1(2(2(1(2(2(0(0(1(x1)))))))))))))))))))) → 0(2(1(2(2(1(1(0(2(1(2(0(0(0(0(0(0(2(0(0(x1)))))))))))))))))))) (31)
0(1(1(2(0(0(1(0(2(1(2(2(1(0(1(0(2(0(2(1(x1)))))))))))))))))))) → 0(1(2(0(2(2(0(0(1(0(2(1(2(2(2(2(2(2(2(0(x1)))))))))))))))))))) (32)
0(1(2(0(0(1(1(1(1(0(1(1(1(0(2(0(1(2(2(1(x1)))))))))))))))))))) → 0(1(2(2(0(2(2(1(2(0(1(2(2(1(0(1(2(0(2(0(x1)))))))))))))))))))) (33)
0(1(2(0(2(2(1(0(2(2(1(0(1(0(0(2(0(1(1(1(x1)))))))))))))))))))) → 2(0(2(0(0(2(1(0(1(2(0(0(0(0(2(1(2(1(1(1(x1)))))))))))))))))))) (34)
0(1(2(1(0(1(1(1(0(0(0(2(2(1(0(0(2(0(0(1(x1)))))))))))))))))))) → 0(2(1(0(1(2(0(0(0(1(0(0(2(2(0(1(1(2(2(1(x1)))))))))))))))))))) (35)
0(1(2(1(0(1(2(2(1(2(2(2(1(0(0(2(2(2(1(1(x1)))))))))))))))))))) → 2(2(2(1(2(2(2(2(0(1(0(2(2(1(0(2(2(0(1(1(x1)))))))))))))))))))) (36)
0(1(2(1(0(2(0(0(2(0(1(1(2(0(1(1(2(0(1(1(x1)))))))))))))))))))) → 0(1(2(2(2(0(1(2(2(1(0(1(0(2(1(0(0(2(0(1(x1)))))))))))))))))))) (37)
0(1(2(1(2(0(1(0(0(2(2(0(1(2(2(1(0(0(0(1(x1)))))))))))))))))))) → 2(0(0(2(0(2(0(2(2(0(0(0(1(2(2(0(0(1(1(1(x1)))))))))))))))))))) (38)
0(2(0(0(0(2(0(1(0(1(1(2(2(1(0(2(1(2(0(1(x1)))))))))))))))))))) → 1(0(2(0(2(0(0(0(1(2(2(2(2(0(0(0(0(2(2(1(x1)))))))))))))))))))) (39)
0(2(0(0(2(0(1(2(0(2(0(1(2(1(1(1(1(2(1(1(x1)))))))))))))))))))) → 1(2(1(2(1(2(1(2(2(0(0(2(2(2(1(2(0(0(1(1(x1)))))))))))))))))))) (40)
0(2(0(2(0(1(2(0(1(1(0(0(0(2(1(2(0(2(2(1(x1)))))))))))))))))))) → 0(1(0(0(2(2(2(0(0(0(0(2(0(0(0(1(2(2(0(1(x1)))))))))))))))))))) (42)
0(2(1(0(1(0(2(2(1(1(0(0(0(2(2(1(1(2(0(0(x1)))))))))))))))))))) → 1(0(2(2(1(1(0(2(2(0(2(0(2(2(2(2(1(1(0(0(x1)))))))))))))))))))) (44)
0(2(1(1(2(2(2(0(2(1(0(1(1(2(2(0(2(1(2(1(x1)))))))))))))))))))) → 2(0(1(0(0(0(0(2(0(2(2(2(1(0(0(2(2(0(0(2(x1)))))))))))))))))))) (45)
0(2(1(1(2(2(2(0(2(2(2(2(0(1(2(2(1(2(0(2(x1)))))))))))))))))))) → 2(0(2(1(2(0(0(1(2(0(2(0(0(2(0(2(0(0(0(1(x1)))))))))))))))))))) (46)
0(2(1(2(0(2(2(0(2(0(2(2(1(0(1(2(2(2(2(0(x1)))))))))))))))))))) → 0(2(0(0(2(0(2(1(0(1(0(0(0(0(2(0(0(2(0(0(x1)))))))))))))))))))) (47)
0(2(1(2(2(0(1(0(1(2(1(0(1(2(0(0(1(2(0(1(x1)))))))))))))))))))) → 2(0(1(2(2(1(0(0(2(0(1(0(0(0(0(2(2(0(2(1(x1)))))))))))))))))))) (48)
0(2(2(0(0(0(1(1(2(1(1(2(2(2(2(0(0(1(1(1(x1)))))))))))))))))))) → 0(2(2(0(2(2(2(0(2(1(1(0(2(0(2(1(1(0(0(1(x1)))))))))))))))))))) (49)
0(2(2(0(1(0(0(1(2(0(2(0(0(2(1(2(1(1(1(1(x1)))))))))))))))))))) → 0(2(2(2(0(1(2(1(0(1(2(0(0(1(2(2(0(0(2(1(x1)))))))))))))))))))) (50)
0(2(2(1(0(0(2(0(0(2(1(1(1(2(0(0(1(0(0(1(x1)))))))))))))))))))) → 2(0(1(0(0(1(2(0(2(0(2(0(0(2(1(0(0(2(0(1(x1)))))))))))))))))))) (52)
0(2(2(1(1(2(2(0(2(0(1(1(1(0(2(0(2(2(1(1(x1)))))))))))))))))))) → 2(0(0(0(2(0(2(0(0(0(1(1(0(0(2(2(2(0(2(0(x1)))))))))))))))))))) (53)
0(2(2(1(2(0(0(1(2(1(0(0(2(2(1(0(2(1(2(1(x1)))))))))))))))))))) → 0(0(1(0(0(2(2(0(2(2(1(2(0(2(1(0(1(2(2(1(x1)))))))))))))))))))) (54)
0(2(2(2(2(0(0(1(2(1(1(2(0(0(1(1(2(2(1(1(x1)))))))))))))))))))) → 1(0(0(0(2(2(0(0(2(1(2(0(2(2(2(1(2(2(1(1(x1)))))))))))))))))))) (55)
1(0(0(0(0(1(2(0(0(0(2(1(1(2(0(1(2(0(1(1(x1)))))))))))))))))))) → 0(2(1(2(1(0(2(0(0(2(0(0(2(1(1(2(0(0(0(1(x1)))))))))))))))))))) (56)
1(0(0(2(1(1(2(2(0(0(2(2(0(2(0(2(1(0(2(1(x1)))))))))))))))))))) → 0(2(1(0(2(0(1(1(2(2(2(2(2(2(0(0(0(2(0(1(x1)))))))))))))))))))) (58)
1(0(2(0(1(2(1(2(0(0(0(0(1(1(2(2(1(2(1(1(x1)))))))))))))))))))) → 1(0(1(2(2(0(2(2(1(2(0(2(2(2(2(2(2(0(0(2(x1)))))))))))))))))))) (59)
1(0(2(1(0(2(2(2(0(1(0(2(0(1(2(0(2(2(1(1(x1)))))))))))))))))))) → 0(0(0(0(0(1(0(2(0(1(0(2(0(2(0(0(2(0(2(0(x1)))))))))))))))))))) (60)
1(0(2(2(0(1(0(1(0(0(0(2(2(0(1(2(2(1(2(1(x1)))))))))))))))))))) → 0(2(2(2(0(0(0(2(2(2(0(2(0(0(2(0(0(0(2(0(x1)))))))))))))))))))) (61)
1(0(2(2(2(1(2(2(0(2(2(2(2(0(1(0(1(1(1(1(x1)))))))))))))))))))) → 1(1(2(0(0(0(0(0(2(2(2(1(0(0(1(2(0(0(2(0(x1)))))))))))))))))))) (62)
1(1(0(2(0(2(1(2(2(0(0(0(1(0(2(2(1(2(2(1(x1)))))))))))))))))))) → 0(2(1(2(1(2(2(2(1(2(0(0(2(2(2(1(2(0(2(1(x1)))))))))))))))))))) (63)
1(1(1(0(2(0(2(2(2(2(0(0(1(1(0(0(0(0(1(1(x1)))))))))))))))))))) → 1(0(2(0(1(1(1(0(0(0(2(2(2(0(2(1(0(0(2(1(x1)))))))))))))))))))) (66)
1(1(1(0(2(1(1(2(2(2(0(2(0(2(0(1(0(1(0(1(x1)))))))))))))))))))) → 1(2(0(0(2(2(0(2(0(2(0(1(1(0(0(1(2(1(0(0(x1)))))))))))))))))))) (67)
1(1(2(0(2(0(2(0(2(1(0(2(2(0(1(0(1(2(0(1(x1)))))))))))))))))))) → 0(0(0(0(2(1(2(1(2(2(1(0(2(2(0(2(0(1(2(1(x1)))))))))))))))))))) (68)
1(1(2(2(0(0(0(0(2(2(1(1(0(2(2(0(1(2(1(1(x1)))))))))))))))))))) → 0(2(2(0(0(2(0(1(0(2(2(2(2(1(2(1(2(0(0(0(x1)))))))))))))))))))) (69)
1(2(0(1(0(1(0(2(1(1(2(2(1(0(2(0(0(0(1(1(x1)))))))))))))))))))) → 2(2(0(1(1(0(0(0(1(0(2(2(1(1(2(2(0(0(1(1(x1)))))))))))))))))))) (70)
1(2(0(2(0(0(0(1(1(1(1(2(2(2(1(2(2(2(2(1(x1)))))))))))))))))))) → 2(2(2(0(0(0(0(0(2(2(1(2(2(2(1(2(1(2(0(0(x1)))))))))))))))))))) (71)
1(2(0(2(0(1(2(1(1(2(2(0(2(1(2(2(1(2(0(1(x1)))))))))))))))))))) → 2(0(0(1(0(0(0(0(2(2(2(0(2(1(2(2(0(2(2(0(x1)))))))))))))))))))) (72)
1(2(1(1(0(0(2(2(2(1(2(0(2(1(0(2(0(0(1(1(x1)))))))))))))))))))) → 2(0(0(2(1(0(2(0(0(2(2(2(2(0(2(0(2(2(2(2(x1)))))))))))))))))))) (73)
1(2(1(2(2(0(1(0(0(2(0(1(1(0(0(1(2(0(1(1(x1)))))))))))))))))))) → 2(2(0(2(0(0(2(0(0(2(0(1(1(2(2(2(2(0(1(2(x1)))))))))))))))))))) (74)
1(2(2(0(1(1(2(2(0(2(2(1(1(1(1(0(2(0(2(0(x1)))))))))))))))))))) → 1(0(2(2(2(1(1(0(2(1(2(0(1(0(1(0(2(2(2(2(x1)))))))))))))))))))) (75)
1(2(2(1(1(0(0(0(1(0(2(2(0(2(2(0(0(1(2(1(x1)))))))))))))))))))) → 0(0(0(1(2(2(2(2(2(2(2(1(0(0(2(2(1(2(1(1(x1)))))))))))))))))))) (76)
1(2(2(1(1(0(2(0(2(2(1(2(0(1(2(0(0(2(2(1(x1)))))))))))))))))))) → 0(2(0(1(1(0(1(0(2(0(2(2(2(2(0(0(2(0(1(1(x1)))))))))))))))))))) (77)
1(2(2(2(2(2(1(0(2(2(2(0(1(0(1(1(2(0(0(1(x1)))))))))))))))))))) → 0(1(2(2(0(1(0(1(2(2(0(0(2(0(0(0(0(0(0(0(x1)))))))))))))))))))) (78)
2(0(0(1(0(0(2(1(2(0(2(0(0(0(0(1(1(1(1(1(x1)))))))))))))))))))) → 2(0(2(0(1(0(0(0(1(1(0(2(2(2(0(1(0(1(2(1(x1)))))))))))))))))))) (79)
2(0(0(2(0(0(1(2(2(2(0(1(1(0(2(2(1(2(1(1(x1)))))))))))))))))))) → 2(2(2(1(2(0(2(1(0(0(0(0(0(0(0(0(0(0(0(0(x1)))))))))))))))))))) (80)
2(0(0(2(0(0(2(1(0(1(2(2(1(1(1(2(1(0(1(2(x1)))))))))))))))))))) → 2(2(2(1(1(0(1(0(2(0(2(2(2(2(0(1(1(1(2(2(x1)))))))))))))))))))) (81)
2(0(1(1(2(1(2(1(0(2(1(1(2(1(2(0(0(0(1(1(x1)))))))))))))))))))) → 1(0(1(2(1(2(2(2(2(0(1(2(2(2(0(1(1(1(2(1(x1)))))))))))))))))))) (86)
2(0(1(1(2(2(0(2(2(1(2(0(0(1(0(0(1(0(2(1(x1)))))))))))))))))))) → 2(1(0(2(2(2(0(2(0(2(2(1(0(0(0(0(0(2(2(0(x1)))))))))))))))))))) (87)
2(0(1(2(0(0(2(2(2(0(1(1(2(2(2(1(2(0(0(0(x1)))))))))))))))))))) → 2(2(1(0(1(0(0(2(2(2(2(2(0(2(1(2(0(2(2(0(x1)))))))))))))))))))) (88)
2(0(1(2(1(1(2(0(0(1(0(1(2(0(0(2(2(0(2(1(x1)))))))))))))))))))) → 0(2(0(1(0(2(0(0(2(2(0(0(0(0(0(2(1(0(0(0(x1)))))))))))))))))))) (90)
2(1(2(1(0(2(2(2(1(1(2(0(0(0(0(0(2(2(2(1(x1)))))))))))))))))))) → 1(2(1(2(0(2(2(0(2(2(0(2(1(0(2(2(2(2(0(1(x1)))))))))))))))))))) (92)
2(2(1(2(2(2(0(2(2(0(1(0(2(0(2(0(1(0(2(1(x1)))))))))))))))))))) → 0(2(2(0(2(0(1(0(2(2(0(0(2(2(2(2(1(2(2(1(x1)))))))))))))))))))) (94)
2(2(2(0(1(1(1(2(2(0(0(0(1(1(0(2(2(2(2(1(x1)))))))))))))))))))) → 2(0(0(0(2(2(0(0(2(0(0(2(0(1(0(1(2(2(1(0(x1)))))))))))))))))))) (98)

1.1 Closure Under Flat Contexts

Using the flat contexts

{2(☐), 1(☐), 0(☐)}

We obtain the transformed TRS
2(0(0(1(1(2(1(0(0(1(2(2(2(1(0(0(0(0(2(2(2(x1))))))))))))))))))))) → 2(0(1(2(0(0(2(0(0(0(2(1(0(0(1(1(1(0(2(2(0(x1))))))))))))))))))))) (100)
2(0(0(2(1(0(2(0(2(2(1(2(0(0(1(0(2(0(1(0(0(x1))))))))))))))))))))) → 2(0(1(2(0(0(2(2(1(2(0(2(0(2(2(1(0(1(2(2(0(x1))))))))))))))))))))) (101)
2(0(0(2(2(1(0(2(0(2(2(2(2(1(0(1(2(0(1(2(2(x1))))))))))))))))))))) → 2(0(1(2(2(0(1(0(0(2(0(0(0(2(0(0(0(1(0(0(1(x1))))))))))))))))))))) (102)
2(0(0(2(2(2(1(0(1(0(2(2(1(1(2(0(0(0(1(0(0(x1))))))))))))))))))))) → 2(0(2(0(0(2(0(0(1(1(0(0(2(1(1(2(2(2(1(0(0(x1))))))))))))))))))))) (103)
2(0(1(0(1(0(0(2(1(1(0(0(2(0(2(0(0(2(0(2(0(x1))))))))))))))))))))) → 2(0(1(2(2(2(0(2(0(2(0(2(2(1(2(1(0(2(0(1(2(x1))))))))))))))))))))) (104)
2(0(1(1(0(1(2(2(1(1(1(0(2(2(0(0(0(0(0(2(1(x1))))))))))))))))))))) → 2(0(0(2(2(1(1(2(2(2(0(1(2(1(1(2(2(0(2(1(1(x1))))))))))))))))))))) (105)
2(0(1(1(0(2(1(1(2(0(1(2(2(2(2(2(1(0(2(0(0(x1))))))))))))))))))))) → 2(0(2(1(2(1(1(2(0(0(2(2(1(0(2(0(2(2(1(1(2(x1))))))))))))))))))))) (106)
2(0(2(0(1(1(0(2(0(2(0(2(1(2(1(2(0(1(1(0(2(x1))))))))))))))))))))) → 2(0(1(1(1(2(2(2(0(1(2(2(0(2(0(2(0(1(2(1(0(x1))))))))))))))))))))) (107)
2(0(2(0(2(1(0(1(0(2(0(1(0(2(0(0(1(1(0(2(1(x1))))))))))))))))))))) → 2(0(2(1(0(0(0(1(1(2(1(0(2(2(1(0(2(2(0(0(1(x1))))))))))))))))))))) (108)
2(0(2(2(0(1(2(0(0(2(2(1(1(0(2(2(1(0(1(0(1(x1))))))))))))))))))))) → 2(0(2(0(1(2(1(1(0(0(2(1(0(2(2(0(0(1(0(2(1(x1))))))))))))))))))))) (109)
2(1(0(0(0(1(0(2(1(0(1(1(2(2(2(0(0(1(0(2(1(x1))))))))))))))))))))) → 2(1(2(2(0(1(2(0(1(0(1(0(2(2(1(0(1(2(0(2(1(x1))))))))))))))))))))) (110)
2(1(1(0(2(2(2(0(2(0(2(2(2(2(0(1(0(2(1(2(0(x1))))))))))))))))))))) → 2(1(0(0(0(2(1(2(2(0(0(1(2(2(2(0(0(0(1(0(2(x1))))))))))))))))))))) (111)
2(1(1(1(0(2(0(0(0(1(0(0(1(2(1(2(2(1(0(2(1(x1))))))))))))))))))))) → 2(1(1(1(2(2(0(1(0(0(2(1(2(2(2(0(1(1(2(2(1(x1))))))))))))))))))))) (112)
2(2(0(0(2(0(0(2(1(2(0(0(2(2(1(0(1(1(1(0(1(x1))))))))))))))))))))) → 2(2(2(1(2(0(0(0(0(2(1(2(0(1(0(1(1(0(2(0(1(x1))))))))))))))))))))) (113)
2(2(0(0(2(1(1(0(2(2(2(1(0(0(2(2(0(1(1(2(0(x1))))))))))))))))))))) → 2(1(2(2(0(1(2(0(0(2(2(0(2(1(2(2(2(0(1(0(1(x1))))))))))))))))))))) (114)
2(2(0(1(0(1(0(2(1(1(0(2(0(2(2(2(0(1(0(2(1(x1))))))))))))))))))))) → 2(1(0(0(1(1(2(0(1(2(2(2(2(2(0(2(0(1(0(2(1(x1))))))))))))))))))))) (115)
2(2(0(1(0(2(2(0(2(2(1(0(1(2(2(2(0(0(0(2(0(x1))))))))))))))))))))) → 2(2(0(0(1(2(1(2(2(0(1(2(2(2(0(0(2(2(2(0(2(x1))))))))))))))))))))) (116)
2(2(0(1(2(0(1(1(0(2(2(2(1(2(2(1(2(2(2(0(2(x1))))))))))))))))))))) → 2(2(0(0(2(2(0(0(1(0(2(1(1(2(2(1(2(2(1(0(2(x1))))))))))))))))))))) (117)
2(2(0(2(2(2(1(0(0(0(2(1(0(2(0(1(0(2(1(1(0(x1))))))))))))))))))))) → 2(2(2(1(2(1(2(2(2(2(2(0(0(1(0(2(1(1(0(2(0(x1))))))))))))))))))))) (118)
2(2(2(0(1(0(1(2(1(1(2(0(0(2(1(1(2(2(2(2(2(x1))))))))))))))))))))) → 2(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(1(1(2(1(0(x1))))))))))))))))))))) (119)
2(2(2(1(2(2(2(1(1(0(2(2(2(2(1(2(0(2(0(0(1(x1))))))))))))))))))))) → 2(0(0(0(1(2(1(2(0(0(2(0(2(0(1(1(2(0(2(2(1(x1))))))))))))))))))))) (120)
2(2(2(2(0(0(1(2(2(1(1(0(1(1(0(0(0(2(0(2(0(x1))))))))))))))))))))) → 2(2(2(0(2(0(1(1(2(0(2(2(1(2(1(1(2(0(2(0(2(x1))))))))))))))))))))) (121)
2(2(2(2(0(1(1(0(2(0(1(1(0(2(2(0(2(0(0(0(0(x1))))))))))))))))))))) → 2(2(0(0(0(0(2(2(1(1(0(0(0(2(0(1(0(2(1(0(0(x1))))))))))))))))))))) (122)
2(2(2(2(0(2(2(1(0(1(2(0(0(1(2(1(2(1(0(1(0(x1))))))))))))))))))))) → 2(1(1(0(2(2(1(0(1(2(0(1(2(0(1(2(0(2(2(0(0(x1))))))))))))))))))))) (123)
1(0(0(1(1(2(1(0(0(1(2(2(2(1(0(0(0(0(2(2(2(x1))))))))))))))))))))) → 1(0(1(2(0(0(2(0(0(0(2(1(0(0(1(1(1(0(2(2(0(x1))))))))))))))))))))) (124)
1(0(0(2(1(0(2(0(2(2(1(2(0(0(1(0(2(0(1(0(0(x1))))))))))))))))))))) → 1(0(1(2(0(0(2(2(1(2(0(2(0(2(2(1(0(1(2(2(0(x1))))))))))))))))))))) (125)
1(0(0(2(2(1(0(2(0(2(2(2(2(1(0(1(2(0(1(2(2(x1))))))))))))))))))))) → 1(0(1(2(2(0(1(0(0(2(0(0(0(2(0(0(0(1(0(0(1(x1))))))))))))))))))))) (126)
1(0(0(2(2(2(1(0(1(0(2(2(1(1(2(0(0(0(1(0(0(x1))))))))))))))))))))) → 1(0(2(0(0(2(0(0(1(1(0(0(2(1(1(2(2(2(1(0(0(x1))))))))))))))))))))) (127)
1(0(1(0(1(0(0(2(1(1(0(0(2(0(2(0(0(2(0(2(0(x1))))))))))))))))))))) → 1(0(1(2(2(2(0(2(0(2(0(2(2(1(2(1(0(2(0(1(2(x1))))))))))))))))))))) (128)
1(0(1(1(0(1(2(2(1(1(1(0(2(2(0(0(0(0(0(2(1(x1))))))))))))))))))))) → 1(0(0(2(2(1(1(2(2(2(0(1(2(1(1(2(2(0(2(1(1(x1))))))))))))))))))))) (129)
1(0(1(1(0(2(1(1(2(0(1(2(2(2(2(2(1(0(2(0(0(x1))))))))))))))))))))) → 1(0(2(1(2(1(1(2(0(0(2(2(1(0(2(0(2(2(1(1(2(x1))))))))))))))))))))) (130)
1(0(2(0(1(1(0(2(0(2(0(2(1(2(1(2(0(1(1(0(2(x1))))))))))))))))))))) → 1(0(1(1(1(2(2(2(0(1(2(2(0(2(0(2(0(1(2(1(0(x1))))))))))))))))))))) (131)
1(0(2(0(2(1(0(1(0(2(0(1(0(2(0(0(1(1(0(2(1(x1))))))))))))))))))))) → 1(0(2(1(0(0(0(1(1(2(1(0(2(2(1(0(2(2(0(0(1(x1))))))))))))))))))))) (132)
1(0(2(2(0(1(2(0(0(2(2(1(1(0(2(2(1(0(1(0(1(x1))))))))))))))))))))) → 1(0(2(0(1(2(1(1(0(0(2(1(0(2(2(0(0(1(0(2(1(x1))))))))))))))))))))) (133)
1(1(0(0(0(1(0(2(1(0(1(1(2(2(2(0(0(1(0(2(1(x1))))))))))))))))))))) → 1(1(2(2(0(1(2(0(1(0(1(0(2(2(1(0(1(2(0(2(1(x1))))))))))))))))))))) (134)
1(1(1(0(2(2(2(0(2(0(2(2(2(2(0(1(0(2(1(2(0(x1))))))))))))))))))))) → 1(1(0(0(0(2(1(2(2(0(0(1(2(2(2(0(0(0(1(0(2(x1))))))))))))))))))))) (135)
1(1(1(1(0(2(0(0(0(1(0(0(1(2(1(2(2(1(0(2(1(x1))))))))))))))))))))) → 1(1(1(1(2(2(0(1(0(0(2(1(2(2(2(0(1(1(2(2(1(x1))))))))))))))))))))) (136)
1(2(0(0(2(0(0(2(1(2(0(0(2(2(1(0(1(1(1(0(1(x1))))))))))))))))))))) → 1(2(2(1(2(0(0(0(0(2(1(2(0(1(0(1(1(0(2(0(1(x1))))))))))))))))))))) (137)
1(2(0(0(2(1(1(0(2(2(2(1(0(0(2(2(0(1(1(2(0(x1))))))))))))))))))))) → 1(1(2(2(0(1(2(0(0(2(2(0(2(1(2(2(2(0(1(0(1(x1))))))))))))))))))))) (138)
1(2(0(1(0(1(0(2(1(1(0(2(0(2(2(2(0(1(0(2(1(x1))))))))))))))))))))) → 1(1(0(0(1(1(2(0(1(2(2(2(2(2(0(2(0(1(0(2(1(x1))))))))))))))))))))) (139)
1(2(0(1(0(2(2(0(2(2(1(0(1(2(2(2(0(0(0(2(0(x1))))))))))))))))))))) → 1(2(0(0(1(2(1(2(2(0(1(2(2(2(0(0(2(2(2(0(2(x1))))))))))))))))))))) (140)
1(2(0(1(2(0(1(1(0(2(2(2(1(2(2(1(2(2(2(0(2(x1))))))))))))))))))))) → 1(2(0(0(2(2(0(0(1(0(2(1(1(2(2(1(2(2(1(0(2(x1))))))))))))))))))))) (141)
1(2(0(2(2(2(1(0(0(0(2(1(0(2(0(1(0(2(1(1(0(x1))))))))))))))))))))) → 1(2(2(1(2(1(2(2(2(2(2(0(0(1(0(2(1(1(0(2(0(x1))))))))))))))))))))) (142)
1(2(2(0(1(0(1(2(1(1(2(0(0(2(1(1(2(2(2(2(2(x1))))))))))))))))))))) → 1(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(1(1(2(1(0(x1))))))))))))))))))))) (143)
1(2(2(1(2(2(2(1(1(0(2(2(2(2(1(2(0(2(0(0(1(x1))))))))))))))))))))) → 1(0(0(0(1(2(1(2(0(0(2(0(2(0(1(1(2(0(2(2(1(x1))))))))))))))))))))) (144)
1(2(2(2(0(0(1(2(2(1(1(0(1(1(0(0(0(2(0(2(0(x1))))))))))))))))))))) → 1(2(2(0(2(0(1(1(2(0(2(2(1(2(1(1(2(0(2(0(2(x1))))))))))))))))))))) (145)
1(2(2(2(0(1(1(0(2(0(1(1(0(2(2(0(2(0(0(0(0(x1))))))))))))))))))))) → 1(2(0(0(0(0(2(2(1(1(0(0(0(2(0(1(0(2(1(0(0(x1))))))))))))))))))))) (146)
1(2(2(2(0(2(2(1(0(1(2(0(0(1(2(1(2(1(0(1(0(x1))))))))))))))))))))) → 1(1(1(0(2(2(1(0(1(2(0(1(2(0(1(2(0(2(2(0(0(x1))))))))))))))))))))) (147)
0(0(0(1(1(2(1(0(0(1(2(2(2(1(0(0(0(0(2(2(2(x1))))))))))))))))))))) → 0(0(1(2(0(0(2(0(0(0(2(1(0(0(1(1(1(0(2(2(0(x1))))))))))))))))))))) (148)
0(0(0(2(1(0(2(0(2(2(1(2(0(0(1(0(2(0(1(0(0(x1))))))))))))))))))))) → 0(0(1(2(0(0(2(2(1(2(0(2(0(2(2(1(0(1(2(2(0(x1))))))))))))))))))))) (149)
0(0(0(2(2(1(0(2(0(2(2(2(2(1(0(1(2(0(1(2(2(x1))))))))))))))))))))) → 0(0(1(2(2(0(1(0(0(2(0(0(0(2(0(0(0(1(0(0(1(x1))))))))))))))))))))) (150)
0(0(0(2(2(2(1(0(1(0(2(2(1(1(2(0(0(0(1(0(0(x1))))))))))))))))))))) → 0(0(2(0(0(2(0(0(1(1(0(0(2(1(1(2(2(2(1(0(0(x1))))))))))))))))))))) (151)
0(0(1(0(1(0(0(2(1(1(0(0(2(0(2(0(0(2(0(2(0(x1))))))))))))))))))))) → 0(0(1(2(2(2(0(2(0(2(0(2(2(1(2(1(0(2(0(1(2(x1))))))))))))))))))))) (152)
0(0(1(1(0(1(2(2(1(1(1(0(2(2(0(0(0(0(0(2(1(x1))))))))))))))))))))) → 0(0(0(2(2(1(1(2(2(2(0(1(2(1(1(2(2(0(2(1(1(x1))))))))))))))))))))) (153)
0(0(1(1(0(2(1(1(2(0(1(2(2(2(2(2(1(0(2(0(0(x1))))))))))))))))))))) → 0(0(2(1(2(1(1(2(0(0(2(2(1(0(2(0(2(2(1(1(2(x1))))))))))))))))))))) (154)
0(0(2(0(1(1(0(2(0(2(0(2(1(2(1(2(0(1(1(0(2(x1))))))))))))))))))))) → 0(0(1(1(1(2(2(2(0(1(2(2(0(2(0(2(0(1(2(1(0(x1))))))))))))))))))))) (155)
0(0(2(0(2(1(0(1(0(2(0(1(0(2(0(0(1(1(0(2(1(x1))))))))))))))))))))) → 0(0(2(1(0(0(0(1(1(2(1(0(2(2(1(0(2(2(0(0(1(x1))))))))))))))))))))) (156)
0(0(2(2(0(1(2(0(0(2(2(1(1(0(2(2(1(0(1(0(1(x1))))))))))))))))))))) → 0(0(2(0(1(2(1(1(0(0(2(1(0(2(2(0(0(1(0(2(1(x1))))))))))))))))))))) (157)
0(1(0(0(0(1(0(2(1(0(1(1(2(2(2(0(0(1(0(2(1(x1))))))))))))))))))))) → 0(1(2(2(0(1(2(0(1(0(1(0(2(2(1(0(1(2(0(2(1(x1))))))))))))))))))))) (158)
0(1(1(0(2(2(2(0(2(0(2(2(2(2(0(1(0(2(1(2(0(x1))))))))))))))))))))) → 0(1(0(0(0(2(1(2(2(0(0(1(2(2(2(0(0(0(1(0(2(x1))))))))))))))))))))) (159)
0(1(1(1(0(2(0(0(0(1(0(0(1(2(1(2(2(1(0(2(1(x1))))))))))))))))))))) → 0(1(1(1(2(2(0(1(0(0(2(1(2(2(2(0(1(1(2(2(1(x1))))))))))))))))))))) (160)
0(2(0(0(2(0(0(2(1(2(0(0(2(2(1(0(1(1(1(0(1(x1))))))))))))))))))))) → 0(2(2(1(2(0(0(0(0(2(1(2(0(1(0(1(1(0(2(0(1(x1))))))))))))))))))))) (161)
0(2(0(0(2(1(1(0(2(2(2(1(0(0(2(2(0(1(1(2(0(x1))))))))))))))))))))) → 0(1(2(2(0(1(2(0(0(2(2(0(2(1(2(2(2(0(1(0(1(x1))))))))))))))))))))) (162)
0(2(0(1(0(1(0(2(1(1(0(2(0(2(2(2(0(1(0(2(1(x1))))))))))))))))))))) → 0(1(0(0(1(1(2(0(1(2(2(2(2(2(0(2(0(1(0(2(1(x1))))))))))))))))))))) (163)
0(2(0(1(0(2(2(0(2(2(1(0(1(2(2(2(0(0(0(2(0(x1))))))))))))))))))))) → 0(2(0(0(1(2(1(2(2(0(1(2(2(2(0(0(2(2(2(0(2(x1))))))))))))))))))))) (164)
0(2(0(1(2(0(1(1(0(2(2(2(1(2(2(1(2(2(2(0(2(x1))))))))))))))))))))) → 0(2(0(0(2(2(0(0(1(0(2(1(1(2(2(1(2(2(1(0(2(x1))))))))))))))))))))) (165)
0(2(0(2(2(2(1(0(0(0(2(1(0(2(0(1(0(2(1(1(0(x1))))))))))))))))))))) → 0(2(2(1(2(1(2(2(2(2(2(0(0(1(0(2(1(1(0(2(0(x1))))))))))))))))))))) (166)
0(2(2(0(1(0(1(2(1(1(2(0(0(2(1(1(2(2(2(2(2(x1))))))))))))))))))))) → 0(0(0(2(2(0(0(1(0(0(0(0(1(2(0(1(1(1(2(1(0(x1))))))))))))))))))))) (167)
0(2(2(1(2(2(2(1(1(0(2(2(2(2(1(2(0(2(0(0(1(x1))))))))))))))))))))) → 0(0(0(0(1(2(1(2(0(0(2(0(2(0(1(1(2(0(2(2(1(x1))))))))))))))))))))) (168)
0(2(2(2(0(0(1(2(2(1(1(0(1(1(0(0(0(2(0(2(0(x1))))))))))))))))))))) → 0(2(2(0(2(0(1(1(2(0(2(2(1(2(1(1(2(0(2(0(2(x1))))))))))))))))))))) (169)
0(2(2(2(0(1(1(0(2(0(1(1(0(2(2(0(2(0(0(0(0(x1))))))))))))))))))))) → 0(2(0(0(0(0(2(2(1(1(0(0(0(2(0(1(0(2(1(0(0(x1))))))))))))))))))))) (170)
0(2(2(2(0(2(2(1(0(1(2(0(0(1(2(1(2(1(0(1(0(x1))))))))))))))))))))) → 0(1(1(0(2(2(1(0(1(2(0(1(2(0(1(2(0(2(2(0(0(x1))))))))))))))))))))) (171)

1.1.1 Semantic Labeling

The following interpretations form a model of the rules.

As carrier we take the set {0,1,2}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 3):

[2(x1)] = 3x1 + 0
[1(x1)] = 3x1 + 1
[0(x1)] = 3x1 + 2

We obtain the labeled TRS

There are 216 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
[20(x1)] = x1 +
10
[21(x1)] = x1 +
0
[22(x1)] = x1 +
1
[10(x1)] = x1 +
0
[11(x1)] = x1 +
1
[12(x1)] = x1 +
10
[00(x1)] = x1 +
10
[01(x1)] = x1 +
1
[02(x1)] = x1 +
1
all of the following rules can be deleted.

There are 197 ruless (increase limit for explicit display).

1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 266 ruless (increase limit for explicit display).

1.1.1.1.1.1 Monotonic Reduction Pair Processor with Usable Rules

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[20(x1)] = x1 +
2
[21(x1)] = x1 +
2
[22(x1)] = x1 +
2
[10(x1)] = x1 +
2
[11(x1)] = x1 +
2
[12(x1)] = x1 +
2
[00(x1)] = x1 +
2
[01(x1)] = x1 +
2
[02(x1)] = x1 +
2
[20#(x1)] = x1 +
0
[21#(x1)] = x1 +
2
[10#(x1)] = x1 +
3
[11#(x1)] = x1 +
2
[00#(x1)] = x1 +
2
[01#(x1)] = x1 +
2
together with the usable rules
01(11(11(12(00(22(02(02(01(12(02(01(10(21(10(20(21(12(00(21(12(x1))))))))))))))))))))) → 01(11(11(10(20(22(01(12(02(00(21(10(20(20(22(01(11(10(20(21(12(x1))))))))))))))))))))) (280)
01(11(11(12(00(22(02(02(01(12(02(01(10(21(10(20(21(12(00(21(11(x1))))))))))))))))))))) → 01(11(11(10(20(22(01(12(02(00(21(10(20(20(22(01(11(10(20(21(11(x1))))))))))))))))))))) (281)
01(11(11(12(00(22(02(02(01(12(02(01(10(21(10(20(21(12(00(21(10(x1))))))))))))))))))))) → 01(11(11(10(20(22(01(12(02(00(21(10(20(20(22(01(11(10(20(21(10(x1))))))))))))))))))))) (282)
11(11(11(12(00(22(02(02(01(12(02(01(10(21(10(20(21(12(00(21(12(x1))))))))))))))))))))) → 11(11(11(10(20(22(01(12(02(00(21(10(20(20(22(01(11(10(20(21(12(x1))))))))))))))))))))) (283)
11(11(11(12(00(22(02(02(01(12(02(01(10(21(10(20(21(12(00(21(11(x1))))))))))))))))))))) → 11(11(11(10(20(22(01(12(02(00(21(10(20(20(22(01(11(10(20(21(11(x1))))))))))))))))))))) (284)
11(11(11(12(00(22(02(02(01(12(02(01(10(21(10(20(21(12(00(21(10(x1))))))))))))))))))))) → 11(11(11(10(20(22(01(12(02(00(21(10(20(20(22(01(11(10(20(21(10(x1))))))))))))))))))))) (285)
21(11(11(12(00(22(02(02(01(12(02(01(10(21(10(20(21(12(00(21(12(x1))))))))))))))))))))) → 21(11(11(10(20(22(01(12(02(00(21(10(20(20(22(01(11(10(20(21(12(x1))))))))))))))))))))) (286)
21(11(11(12(00(22(02(02(01(12(02(01(10(21(10(20(21(12(00(21(11(x1))))))))))))))))))))) → 21(11(11(10(20(22(01(12(02(00(21(10(20(20(22(01(11(10(20(21(11(x1))))))))))))))))))))) (287)
21(11(11(12(00(22(02(02(01(12(02(01(10(21(10(20(21(12(00(21(10(x1))))))))))))))))))))) → 21(11(11(10(20(22(01(12(02(00(21(10(20(20(22(01(11(10(20(21(10(x1))))))))))))))))))))) (288)
10(22(02(00(21(11(12(00(20(20(21(12(02(00(20(22(01(11(10(22(02(x1))))))))))))))))))))) → 11(10(20(22(01(10(22(02(00(20(22(00(21(10(20(20(22(01(12(01(12(x1))))))))))))))))))))) (301)
00(22(01(10(22(01(11(12(00(20(20(21(10(20(21(10(20(20(22(00(22(x1))))))))))))))))))))) → 00(22(02(00(20(22(02(01(12(00(21(11(10(20(21(10(20(21(12(00(22(x1))))))))))))))))))))) (325)
00(22(01(10(22(01(11(12(00(20(20(21(10(20(21(10(20(20(22(00(21(x1))))))))))))))))))))) → 00(22(02(00(20(22(02(01(12(00(21(11(10(20(21(10(20(21(12(00(21(x1))))))))))))))))))))) (326)
00(22(01(10(22(01(11(12(00(20(20(21(10(20(21(10(20(20(22(00(20(x1))))))))))))))))))))) → 00(22(02(00(20(22(02(01(12(00(21(11(10(20(21(10(20(21(12(00(20(x1))))))))))))))))))))) (327)
10(22(01(10(22(01(11(12(00(20(20(21(10(20(21(10(20(20(22(00(22(x1))))))))))))))))))))) → 10(22(02(00(20(22(02(01(12(00(21(11(10(20(21(10(20(21(12(00(22(x1))))))))))))))))))))) (328)
10(22(01(10(22(01(11(12(00(20(20(21(10(20(21(10(20(20(22(00(21(x1))))))))))))))))))))) → 10(22(02(00(20(22(02(01(12(00(21(11(10(20(21(10(20(21(12(00(21(x1))))))))))))))))))))) (329)
10(22(01(10(22(01(11(12(00(20(20(21(10(20(21(10(20(20(22(00(20(x1))))))))))))))))))))) → 10(22(02(00(20(22(02(01(12(00(21(11(10(20(21(10(20(21(12(00(20(x1))))))))))))))))))))) (330)
20(22(01(10(22(01(11(12(00(20(20(21(10(20(21(10(20(20(22(00(22(x1))))))))))))))))))))) → 20(22(02(00(20(22(02(01(12(00(21(11(10(20(21(10(20(21(12(00(22(x1))))))))))))))))))))) (331)
20(22(01(10(22(01(11(12(00(20(20(21(10(20(21(10(20(20(22(00(21(x1))))))))))))))))))))) → 20(22(02(00(20(22(02(01(12(00(21(11(10(20(21(10(20(21(12(00(21(x1))))))))))))))))))))) (332)
20(22(01(10(22(01(11(12(00(20(20(21(10(20(21(10(20(20(22(00(20(x1))))))))))))))))))))) → 20(22(02(00(20(22(02(01(12(00(21(11(10(20(21(10(20(21(12(00(20(x1))))))))))))))))))))) (333)
(w.r.t. the implicit argument filter of the reduction pair), the pairs

There are 248 ruless (increase limit for explicit display).

and no rules could be deleted.

1.1.1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.