Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/127538)

The rewrite relation of the following TRS is considered.

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

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
2(1(0(2(3(2(2(1(1(3(1(3(3(2(1(0(0(0(x1)))))))))))))))))) → 2(1(2(3(1(3(1(1(3(2(2(0(1(0(2(3(0(0(x1)))))))))))))))))) (81)
2(0(0(0(3(1(1(2(1(3(0(1(0(2(1(1(0(0(x1)))))))))))))))))) → 1(1(3(0(0(3(2(0(1(1(1(0(1(0(0(2(2(0(x1)))))))))))))))))) (82)
3(1(0(0(2(0(0(1(3(3(0(2(1(3(1(1(0(0(x1)))))))))))))))))) → 3(1(0(1(0(0(3(1(3(0(2(3(0(1(0(2(1(0(x1)))))))))))))))))) (83)
3(1(1(0(2(1(1(3(1(3(2(3(1(0(3(1(0(0(x1)))))))))))))))))) → 3(1(2(2(3(0(1(3(1(3(0(1(1(3(0(0(1(1(x1)))))))))))))))))) (84)
0(3(3(1(3(0(3(3(2(1(0(0(0(2(1(3(0(0(x1)))))))))))))))))) → 3(3(3(3(2(2(0(3(1(1(0(0(0(0(3(0(1(0(x1)))))))))))))))))) (85)
1(3(0(3(1(3(0(1(2(0(3(2(0(0(0(2(1(0(x1)))))))))))))))))) → 1(3(2(0(0(2(3(3(0(0(0(3(1(0(2(0(1(1(x1)))))))))))))))))) (86)
3(1(2(1(0(1(0(3(1(3(0(2(1(0(0(2(1(0(x1)))))))))))))))))) → 2(1(0(3(0(1(1(0(2(0(3(0(1(3(2(0(1(1(x1)))))))))))))))))) (87)
3(1(2(2(0(3(2(1(0(3(0(2(0(2(1(2(1(0(x1)))))))))))))))))) → 3(1(2(2(2(0(2(3(3(0(0(1(0(0(1(1(2(2(x1)))))))))))))))))) (88)
2(0(2(2(1(0(3(2(1(0(0(3(3(0(0(0(2(0(x1)))))))))))))))))) → 2(3(2(3(2(2(3(0(0(1(0(0(0(0(2(0(1(0(x1)))))))))))))))))) (89)
0(3(3(2(2(1(3(3(0(2(1(0(2(0(1(0(2(0(x1)))))))))))))))))) → 0(3(2(1(0(1(2(3(1(0(2(0(0(3(2(3(2(0(x1)))))))))))))))))) (90)
2(2(3(3(3(1(0(0(3(2(1(2(1(0(2(0(2(0(x1)))))))))))))))))) → 3(0(3(1(0(1(0(2(2(2(2(0(1(3(3(2(2(0(x1)))))))))))))))))) (91)
2(3(0(3(1(0(3(0(2(3(1(0(3(1(2(0(2(0(x1)))))))))))))))))) → 2(0(2(2(3(0(2(0(1(0(1(0(3(3(3(0(3(1(x1)))))))))))))))))) (92)
3(2(3(0(2(0(2(1(0(1(3(3(3(2(1(0(3(0(x1)))))))))))))))))) → 3(2(3(3(0(3(0(1(1(2(3(3(0(1(2(0(2(0(x1)))))))))))))))))) (93)
3(0(2(1(0(2(0(2(1(1(1(2(2(3(3(0(3(0(x1)))))))))))))))))) → 2(2(2(0(0(3(3(0(2(0(1(1(1(0(3(2(1(3(x1)))))))))))))))))) (94)
0(3(1(0(1(1(0(2(1(0(0(3(2(1(2(1(3(0(x1)))))))))))))))))) → 0(0(0(1(1(1(3(3(1(1(2(0(3(2(1(0(2(0(x1)))))))))))))))))) (95)
2(1(3(2(3(0(3(0(3(0(0(1(3(1(3(1(3(0(x1)))))))))))))))))) → 1(3(0(1(1(2(3(3(1(3(0(0(3(3(3(2(0(0(x1)))))))))))))))))) (96)
0(2(2(2(3(3(0(2(3(0(3(1(0(0(1(2(3(0(x1)))))))))))))))))) → 3(0(3(2(3(2(0(2(1(1(0(3(0(0(2(3(2(0(x1)))))))))))))))))) (97)
3(0(1(2(1(2(2(0(2(1(0(2(0(0(1(2(3(0(x1)))))))))))))))))) → 1(1(0(3(2(3(2(2(2(2(0(0(2(0(0(0(1(1(x1)))))))))))))))))) (98)
0(3(3(0(3(1(1(3(3(1(1(0(2(1(1(2(3(0(x1)))))))))))))))))) → 0(3(1(0(3(1(2(3(0(1(1(1(1(0(3(3(3(2(x1)))))))))))))))))) (99)
3(0(2(0(0(3(3(3(1(2(1(0(0(1(0(3(3(0(x1)))))))))))))))))) → 3(0(2(0(1(3(2(0(1(0(0(3(1(3(3(0(3(0(x1)))))))))))))))))) (100)
2(1(2(0(0(1(0(3(2(1(3(2(3(1(0(3(3(0(x1)))))))))))))))))) → 3(2(3(3(3(2(1(0(1(1(0(0(2(0(3(2(0(1(x1)))))))))))))))))) (101)
0(3(0(2(0(3(0(3(2(1(3(0(2(0(1(3(3(0(x1)))))))))))))))))) → 2(2(0(1(2(3(3(3(0(1(0(0(0(3(0(3(3(0(x1)))))))))))))))))) (102)
3(3(1(2(2(1(2(1(3(2(0(2(3(3(1(3(3(0(x1)))))))))))))))))) → 3(3(1(2(1(1(0(0(2(3(2(1(3(3(3(2(2(3(x1)))))))))))))))))) (103)
2(2(2(0(0(0(2(1(3(0(1(1(1(2(3(3(3(0(x1)))))))))))))))))) → 2(3(3(0(0(1(2(3(2(0(1(1(1(0(3(2(2(0(x1)))))))))))))))))) (104)
2(2(0(2(0(2(1(2(1(1(0(1(1(1(0(3(0(1(x1)))))))))))))))))) → 1(1(2(0(1(0(1(1(2(2(2(0(1(0(1(2(3(0(x1)))))))))))))))))) (105)
2(1(0(3(3(1(0(2(2(2(1(2(0(2(2(3(0(1(x1)))))))))))))))))) → 2(3(2(3(2(0(2(1(2(1(3(2(2(0(0(1(1(0(x1)))))))))))))))))) (106)
0(2(2(1(1(1(0(0(0(3(2(1(2(3(3(3(0(1(x1)))))))))))))))))) → 3(0(2(2(0(0(1(3(2(0(3(1(3(2(0(1(1(1(x1)))))))))))))))))) (107)
2(0(2(1(2(0(0(2(1(0(3(1(3(1(3(0(1(1(x1)))))))))))))))))) → 3(2(0(2(0(3(0(1(0(2(2(0(1(1(1(1(3(1(x1)))))))))))))))))) (108)
3(1(0(0(0(2(0(0(0(2(0(2(1(1(2(1(1(1(x1)))))))))))))))))) → 2(1(0(0(1(0(3(1(0(2(2(0(0(2(0(1(1(1(x1)))))))))))))))))) (109)
1(1(3(2(0(3(3(1(2(0(2(0(2(1(0(2(1(1(x1)))))))))))))))))) → 1(1(2(2(0(1(0(3(1(1(2(3(0(3(2(0(2(1(x1)))))))))))))))))) (110)
2(0(3(1(0(2(2(2(2(0(0(2(1(3(0(2(1(1(x1)))))))))))))))))) → 2(2(2(0(1(2(1(1(2(2(3(0(3(2(0(0(1(0(x1)))))))))))))))))) (111)
3(0(0(1(3(0(1(2(1(3(3(0(3(3(1(2(1(1(x1)))))))))))))))))) → 3(2(3(3(0(3(1(0(1(2(1(3(0(1(1(1(3(0(x1)))))))))))))))))) (112)
3(2(1(3(3(1(0(2(1(2(1(0(0(1(3(2(1(1(x1)))))))))))))))))) → 3(2(2(2(2(0(1(0(3(3(1(1(1(1(3(1(0(1(x1)))))))))))))))))) (113)
3(2(2(1(1(3(0(3(0(1(2(1(1(2(0(3(1(1(x1)))))))))))))))))) → 3(2(2(1(0(1(1(3(3(3(0(0(2(1(1(2(1(1(x1)))))))))))))))))) (114)
3(2(3(0(3(2(1(3(1(0(2(2(1(1(2(3(1(1(x1)))))))))))))))))) → 3(2(1(2(2(3(3(2(1(3(3(1(1(2(0(1(0(1(x1)))))))))))))))))) (115)
1(1(3(0(0(1(1(1(2(3(1(3(1(0(0(0(2(1(x1)))))))))))))))))) → 1(1(1(0(0(3(3(0(0(1(1(1(1(1(2(3(2(0(x1)))))))))))))))))) (116)
2(1(2(1(2(0(1(0(3(0(1(3(3(0(2(0(2(1(x1)))))))))))))))))) → 2(2(3(1(2(0(3(3(1(1(2(0(0(1(2(0(0(1(x1)))))))))))))))))) (117)
2(2(0(0(1(3(1(0(1(3(1(3(1(1(2(0(2(1(x1)))))))))))))))))) → 1(1(3(2(2(0(1(1(0(3(2(3(1(0(1(0(1(2(x1)))))))))))))))))) (118)
1(0(1(2(2(0(0(0(2(1(0(0(1(3(2(0(2(1(x1)))))))))))))))))) → 1(1(1(2(0(1(2(2(2(2(0(3(0(0(1(0(0(0(x1)))))))))))))))))) (119)
2(1(0(1(3(1(3(2(1(2(1(1(3(1(3(0(2(1(x1)))))))))))))))))) → 2(1(1(3(1(1(3(1(2(0(1(3(1(0(1(2(3(2(x1)))))))))))))))))) (120)
1(2(1(3(2(0(1(2(0(0(1(3(0(2(3(0(2(1(x1)))))))))))))))))) → 0(1(1(2(2(2(0(0(1(1(2(3(0(3(2(0(1(3(x1)))))))))))))))))) (121)
2(1(0(2(3(1(0(3(3(1(2(0(3(2(0(1(2(1(x1)))))))))))))))))) → 3(0(2(2(2(0(3(0(1(1(1(1(2(2(1(0(3(3(x1)))))))))))))))))) (122)
3(3(3(2(2(0(2(1(0(0(0(0(1(3(1(1(2(1(x1)))))))))))))))))) → 3(2(2(1(1(0(1(1(0(3(3(0(1(3(2(0(2(0(x1)))))))))))))))))) (123)
3(1(1(0(3(0(2(1(3(0(3(1(3(2(3(1(2(1(x1)))))))))))))))))) → 3(2(2(3(3(1(0(3(0(0(1(1(1(2(3(3(1(1(x1)))))))))))))))))) (124)
3(0(2(2(1(2(3(1(0(1(3(2(0(2(1(2(2(1(x1)))))))))))))))))) → 2(1(1(3(2(0(0(1(0(3(2(2(1(3(2(2(1(2(x1)))))))))))))))))) (125)
0(2(1(0(0(0(2(2(1(1(3(2(1(2(0(3(2(1(x1)))))))))))))))))) → 0(2(3(1(2(0(1(0(1(2(2(0(3(2(2(1(0(1(x1)))))))))))))))))) (126)
0(3(0(2(1(1(0(0(1(1(1(2(3(3(1(3(2(1(x1)))))))))))))))))) → 0(1(0(1(0(0(2(2(1(3(1(1(1(3(3(2(3(1(x1)))))))))))))))))) (127)
3(3(1(3(1(2(0(1(2(3(0(1(2(3(3(0(3(1(x1)))))))))))))))))) → 3(3(1(0(3(1(2(2(0(1(1(0(3(3(3(2(3(1(x1)))))))))))))))))) (128)
2(1(1(3(1(2(0(3(3(1(2(1(2(3(3(1(3(1(x1)))))))))))))))))) → 1(2(2(3(3(2(3(3(1(0(1(1(1(1(2(3(1(3(x1)))))))))))))))))) (129)
2(1(2(0(2(2(1(1(3(2(3(0(3(0(2(2(3(1(x1)))))))))))))))))) → 2(2(2(0(2(2(1(3(1(1(3(3(2(0(1(2(0(3(x1)))))))))))))))))) (130)
0(2(1(3(1(1(1(1(2(1(1(1(2(3(3(3(3(1(x1)))))))))))))))))) → 1(1(2(3(3(3(1(1(1(0(1(1(3(3(2(2(1(1(x1)))))))))))))))))) (131)
2(1(3(1(3(1(2(0(3(0(2(1(2(3(0(0(0(2(x1)))))))))))))))))) → 3(0(1(0(1(3(1(3(0(2(2(2(2(0(1(0(3(2(x1)))))))))))))))))) (132)
2(1(1(0(3(3(0(2(1(1(0(3(1(0(3(0(0(2(x1)))))))))))))))))) → 2(3(1(0(0(2(1(3(3(3(1(0(0(1(0(1(0(2(x1)))))))))))))))))) (133)
1(2(0(2(3(2(3(1(0(2(2(1(3(2(1(0(1(2(x1)))))))))))))))))) → 1(2(2(2(0(1(1(2(1(3(3(2(1(0(0(2(3(2(x1)))))))))))))))))) (134)
1(3(2(1(3(0(3(0(3(1(3(1(3(2(2(3(1(2(x1)))))))))))))))))) → 1(1(1(2(3(2(3(0(1(3(3(2(1(3(2(0(3(3(x1)))))))))))))))))) (135)
2(1(3(1(2(1(0(1(1(2(2(1(0(1(0(0(2(2(x1)))))))))))))))))) → 2(1(0(0(1(1(3(1(1(2(2(2(0(1(1(2(0(2(x1)))))))))))))))))) (136)
2(1(1(2(2(2(2(2(0(3(3(3(2(1(0(0(2(2(x1)))))))))))))))))) → 2(2(2(1(1(0(3(2(2(2(0(1(3(0(2(2(3(2(x1)))))))))))))))))) (137)
0(2(3(1(2(0(3(2(2(0(2(1(0(0(3(0(2(2(x1)))))))))))))))))) → 2(2(0(3(0(2(2(2(3(2(2(0(1(0(1(0(0(3(x1)))))))))))))))))) (138)
2(2(2(3(2(2(2(2(3(1(1(3(0(2(3(0(2(2(x1)))))))))))))))))) → 3(2(2(2(3(3(2(3(2(2(0(1(2(0(1(2(2(2(x1)))))))))))))))))) (139)
0(3(3(3(0(3(2(2(2(1(3(1(1(1(0(1(2(2(x1)))))))))))))))))) → 3(1(0(1(1(2(2(3(2(3(2(0(0(3(3(1(1(2(x1)))))))))))))))))) (140)
3(1(2(1(1(1(2(3(0(3(3(3(1(0(3(1(2(2(x1)))))))))))))))))) → 3(1(1(0(3(1(3(2(0(3(2(3(1(1(3(2(1(2(x1)))))))))))))))))) (141)
0(0(1(2(3(0(1(0(2(2(1(3(0(2(1(3(2(2(x1)))))))))))))))))) → 2(0(0(1(0(3(0(1(1(2(0(3(1(2(3(2(2(2(x1)))))))))))))))))) (142)
1(2(3(1(0(0(0(1(0(0(2(3(1(3(0(1(3(2(x1)))))))))))))))))) → 0(0(0(1(1(2(0(1(3(0(3(3(1(2(0(1(3(2(x1)))))))))))))))))) (143)
2(1(0(3(2(0(2(1(1(0(0(0(2(3(0(2(3(2(x1)))))))))))))))))) → 2(0(0(0(0(0(0(2(1(2(3(3(2(3(2(1(1(2(x1)))))))))))))))))) (144)
2(3(3(0(2(1(3(2(1(0(2(0(2(1(3(2(3(2(x1)))))))))))))))))) → 2(3(3(2(2(0(2(0(2(0(3(1(1(3(1(3(2(2(x1)))))))))))))))))) (145)
3(1(2(2(3(0(0(3(0(2(2(1(1(1(3(0(0(3(x1)))))))))))))))))) → 2(0(3(2(3(1(0(0(1(0(3(2(2(0(1(1(3(3(x1)))))))))))))))))) (146)
1(2(2(1(2(3(3(3(1(0(3(3(2(2(1(3(0(3(x1)))))))))))))))))) → 1(2(3(3(2(3(2(0(0(3(1(2(1(3(2(1(3(3(x1)))))))))))))))))) (147)
3(3(0(2(1(3(1(3(3(0(0(3(1(1(2(3(0(3(x1)))))))))))))))))) → 2(3(3(3(3(0(1(0(3(2(0(0(1(3(3(1(1(3(x1)))))))))))))))))) (148)
2(0(2(2(3(0(1(2(3(1(2(3(1(0(3(3(0(3(x1)))))))))))))))))) → 2(3(2(0(0(0(0(1(3(3(3(3(3(2(2(1(2(1(x1)))))))))))))))))) (149)
3(3(3(1(2(1(0(1(3(3(3(0(0(2(3(3(0(3(x1)))))))))))))))))) → 0(2(3(3(3(3(2(3(3(3(3(1(0(0(0(1(1(3(x1)))))))))))))))))) (150)
2(1(3(1(3(1(1(3(2(3(1(0(3(1(3(2(1(3(x1)))))))))))))))))) → 3(0(3(1(1(1(1(1(1(2(3(2(3(2(3(3(3(1(x1)))))))))))))))))) (151)
3(3(2(0(2(2(2(2(1(0(0(0(0(3(3(2(1(3(x1)))))))))))))))))) → 3(3(2(1(0(3(2(0(0(2(2(2(0(3(2(0(1(3(x1)))))))))))))))))) (152)
2(2(1(2(3(2(3(1(3(2(3(0(0(3(0(3(1(3(x1)))))))))))))))))) → 2(2(3(2(2(0(1(1(3(3(0(3(0(3(3(1(2(3(x1)))))))))))))))))) (153)
3(3(3(0(2(1(2(3(0(0(2(1(1(3(2(3(1(3(x1)))))))))))))))))) → 3(3(0(3(0(3(1(0(2(3(2(3(2(1(1(1(2(3(x1)))))))))))))))))) (154)
2(1(1(0(3(0(2(2(0(2(0(1(3(0(0(1(2(3(x1)))))))))))))))))) → 2(3(3(1(0(0(1(3(2(0(0(2(0(1(0(1(2(2(x1)))))))))))))))))) (155)
0(0(0(2(1(0(2(1(3(1(3(0(2(3(2(0(3(3(x1)))))))))))))))))) → 3(1(0(0(0(2(0(1(2(3(0(1(2(2(0(3(3(3(x1)))))))))))))))))) (156)
1(0(3(0(2(0(2(0(3(1(3(0(3(1(0(1(3(3(x1)))))))))))))))))) → 1(1(3(3(0(1(0(0(3(3(1(3(2(0(0(0(3(2(x1)))))))))))))))))) (157)
2(1(0(2(0(3(3(2(3(3(1(3(0(2(2(1(3(3(x1)))))))))))))))))) → 3(0(3(0(2(2(2(3(2(1(1(3(1(0(3(3(2(3(x1)))))))))))))))))) (158)
3(0(2(0(2(2(0(0(2(1(2(3(3(3(0(2(3(3(x1)))))))))))))))))) → 0(0(3(0(0(3(2(3(2(2(1(3(2(2(0(3(2(3(x1)))))))))))))))))) (159)
2(0(2(1(2(3(3(1(2(0(0(1(2(3(0(3(3(3(x1)))))))))))))))))) → 2(0(1(3(0(3(2(1(0(3(1(0(2(2(3(2(3(3(x1)))))))))))))))))) (160)

1.1 Closure Under Flat Contexts

Using the flat contexts

{2(☐), 1(☐), 0(☐), 3(☐)}

We obtain the transformed TRS

There are 179 ruless (increase limit for explicit display).

1.1.1 Semantic Labeling

Root-labeling is applied.

We obtain the labeled TRS

There are 716 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

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

There are 610 ruless (increase limit for explicit display).

1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[31(x1)] = 1 · x1 + 5
[10(x1)] = 1 · x1 + 11
[00(x1)] = 1 · x1
[02(x1)] = 1 · x1 + 2
[20(x1)] = 1 · x1 + 8
[01(x1)] = 1 · x1
[13(x1)] = 1 · x1
[33(x1)] = 1 · x1 + 2
[30(x1)] = 1 · x1 + 21
[21(x1)] = 1 · x1
[11(x1)] = 1 · x1 + 45
[03(x1)] = 1 · x1 + 12
[23(x1)] = 1 · x1
[32(x1)] = 1 · x1
[22(x1)] = 1 · x1 + 15
[12(x1)] = 1 · x1 + 27
all of the following rules can be deleted.
32(22(21(11(13(30(03(30(01(12(21(11(12(20(03(31(11(12(x1)))))))))))))))))) → 32(22(21(10(01(11(13(33(33(30(00(02(21(11(12(21(11(12(x1)))))))))))))))))) (369)
32(22(21(11(13(30(03(30(01(12(21(11(12(20(03(31(11(11(x1)))))))))))))))))) → 32(22(21(10(01(11(13(33(33(30(00(02(21(11(12(21(11(11(x1)))))))))))))))))) (370)
32(22(21(11(13(30(03(30(01(12(21(11(12(20(03(31(11(10(x1)))))))))))))))))) → 32(22(21(10(01(11(13(33(33(30(00(02(21(11(12(21(11(10(x1)))))))))))))))))) (371)
32(22(21(11(13(30(03(30(01(12(21(11(12(20(03(31(11(13(x1)))))))))))))))))) → 32(22(21(10(01(11(13(33(33(30(00(02(21(11(12(21(11(13(x1)))))))))))))))))) (372)
03(30(02(21(11(10(00(01(11(11(12(23(33(31(13(32(21(12(x1)))))))))))))))))) → 01(10(01(10(00(02(22(21(13(31(11(11(13(33(32(23(31(12(x1)))))))))))))))))) (405)
03(30(02(21(11(10(00(01(11(11(12(23(33(31(13(32(21(11(x1)))))))))))))))))) → 01(10(01(10(00(02(22(21(13(31(11(11(13(33(32(23(31(11(x1)))))))))))))))))) (406)
03(30(02(21(11(10(00(01(11(11(12(23(33(31(13(32(21(10(x1)))))))))))))))))) → 01(10(01(10(00(02(22(21(13(31(11(11(13(33(32(23(31(10(x1)))))))))))))))))) (407)
03(30(02(21(11(10(00(01(11(11(12(23(33(31(13(32(21(13(x1)))))))))))))))))) → 01(10(01(10(00(02(22(21(13(31(11(11(13(33(32(23(31(13(x1)))))))))))))))))) (408)
21(12(20(02(22(21(11(13(32(23(30(03(30(02(22(23(31(11(x1)))))))))))))))))) → 22(22(20(02(22(21(13(31(11(13(33(32(20(01(12(20(03(31(x1)))))))))))))))))) (414)
21(11(10(03(33(30(02(21(11(10(03(31(10(03(30(00(02(22(x1)))))))))))))))))) → 23(31(10(00(02(21(13(33(33(31(10(00(01(10(01(10(02(22(x1)))))))))))))))))) (417)
21(11(10(03(33(30(02(21(11(10(03(31(10(03(30(00(02(21(x1)))))))))))))))))) → 23(31(10(00(02(21(13(33(33(31(10(00(01(10(01(10(02(21(x1)))))))))))))))))) (418)
21(11(10(03(33(30(02(21(11(10(03(31(10(03(30(00(02(20(x1)))))))))))))))))) → 23(31(10(00(02(21(13(33(33(31(10(00(01(10(01(10(02(20(x1)))))))))))))))))) (419)
21(11(10(03(33(30(02(21(11(10(03(31(10(03(30(00(02(23(x1)))))))))))))))))) → 23(31(10(00(02(21(13(33(33(31(10(00(01(10(01(10(02(23(x1)))))))))))))))))) (420)
31(12(21(11(11(12(23(30(03(33(33(31(10(03(31(12(22(22(x1)))))))))))))))))) → 31(11(10(03(31(13(32(20(03(32(23(31(11(13(32(21(12(22(x1)))))))))))))))))) (437)
31(12(21(11(11(12(23(30(03(33(33(31(10(03(31(12(22(21(x1)))))))))))))))))) → 31(11(10(03(31(13(32(20(03(32(23(31(11(13(32(21(12(21(x1)))))))))))))))))) (438)
31(12(21(11(11(12(23(30(03(33(33(31(10(03(31(12(22(20(x1)))))))))))))))))) → 31(11(10(03(31(13(32(20(03(32(23(31(11(13(32(21(12(20(x1)))))))))))))))))) (439)
31(12(21(11(11(12(23(30(03(33(33(31(10(03(31(12(22(23(x1)))))))))))))))))) → 31(11(10(03(31(13(32(20(03(32(23(31(11(13(32(21(12(23(x1)))))))))))))))))) (440)
21(10(03(32(20(02(21(11(10(00(00(02(23(30(02(23(32(22(x1)))))))))))))))))) → 20(00(00(00(00(00(02(21(12(23(33(32(23(32(21(11(12(22(x1)))))))))))))))))) (441)
21(10(03(32(20(02(21(11(10(00(00(02(23(30(02(23(32(21(x1)))))))))))))))))) → 20(00(00(00(00(00(02(21(12(23(33(32(23(32(21(11(12(21(x1)))))))))))))))))) (442)
21(10(03(32(20(02(21(11(10(00(00(02(23(30(02(23(32(20(x1)))))))))))))))))) → 20(00(00(00(00(00(02(21(12(23(33(32(23(32(21(11(12(20(x1)))))))))))))))))) (443)
21(10(03(32(20(02(21(11(10(00(00(02(23(30(02(23(32(23(x1)))))))))))))))))) → 20(00(00(00(00(00(02(21(12(23(33(32(23(32(21(11(12(23(x1)))))))))))))))))) (444)
12(22(21(12(23(33(33(31(10(03(33(32(22(21(13(30(03(32(x1)))))))))))))))))) → 12(23(33(32(23(32(20(00(03(31(12(21(13(32(21(13(33(32(x1)))))))))))))))))) (449)
12(22(21(12(23(33(33(31(10(03(33(32(22(21(13(30(03(31(x1)))))))))))))))))) → 12(23(33(32(23(32(20(00(03(31(12(21(13(32(21(13(33(31(x1)))))))))))))))))) (450)
12(22(21(12(23(33(33(31(10(03(33(32(22(21(13(30(03(30(x1)))))))))))))))))) → 12(23(33(32(23(32(20(00(03(31(12(21(13(32(21(13(33(30(x1)))))))))))))))))) (451)
12(22(21(12(23(33(33(31(10(03(33(32(22(21(13(30(03(33(x1)))))))))))))))))) → 12(23(33(32(23(32(20(00(03(31(12(21(13(32(21(13(33(33(x1)))))))))))))))))) (452)
20(02(22(23(30(01(12(23(31(12(23(31(10(03(33(30(03(32(x1)))))))))))))))))) → 23(32(20(00(00(00(01(13(33(33(33(33(32(22(21(12(21(12(x1)))))))))))))))))) (453)
20(02(22(23(30(01(12(23(31(12(23(31(10(03(33(30(03(30(x1)))))))))))))))))) → 23(32(20(00(00(00(01(13(33(33(33(33(32(22(21(12(21(10(x1)))))))))))))))))) (455)
20(02(22(23(30(01(12(23(31(12(23(31(10(03(33(30(03(33(x1)))))))))))))))))) → 23(32(20(00(00(00(01(13(33(33(33(33(32(22(21(12(21(13(x1)))))))))))))))))) (456)
21(11(10(03(30(02(22(20(02(20(01(13(30(00(01(12(23(32(x1)))))))))))))))))) → 23(33(31(10(00(01(13(32(20(00(02(20(01(10(01(12(22(22(x1)))))))))))))))))) (469)
21(11(10(03(30(02(22(20(02(20(01(13(30(00(01(12(23(31(x1)))))))))))))))))) → 23(33(31(10(00(01(13(32(20(00(02(20(01(10(01(12(22(21(x1)))))))))))))))))) (470)
21(11(10(03(30(02(22(20(02(20(01(13(30(00(01(12(23(30(x1)))))))))))))))))) → 23(33(31(10(00(01(13(32(20(00(02(20(01(10(01(12(22(20(x1)))))))))))))))))) (471)
21(11(10(03(30(02(22(20(02(20(01(13(30(00(01(12(23(33(x1)))))))))))))))))) → 23(33(31(10(00(01(13(32(20(00(02(20(01(10(01(12(22(23(x1)))))))))))))))))) (472)
20(02(21(12(23(33(31(12(20(00(01(12(23(30(03(33(33(32(x1)))))))))))))))))) → 20(01(13(30(03(32(21(10(03(31(10(02(22(23(32(23(33(32(x1)))))))))))))))))) (477)
20(02(21(12(23(33(31(12(20(00(01(12(23(30(03(33(33(31(x1)))))))))))))))))) → 20(01(13(30(03(32(21(10(03(31(10(02(22(23(32(23(33(31(x1)))))))))))))))))) (478)
20(02(21(12(23(33(31(12(20(00(01(12(23(30(03(33(33(30(x1)))))))))))))))))) → 20(01(13(30(03(32(21(10(03(31(10(02(22(23(32(23(33(30(x1)))))))))))))))))) (479)
20(02(21(12(23(33(31(12(20(00(01(12(23(30(03(33(33(33(x1)))))))))))))))))) → 20(01(13(30(03(32(21(10(03(31(10(02(22(23(32(23(33(33(x1)))))))))))))))))) (480)
23(30(02(21(10(02(20(02(21(11(11(12(22(23(33(30(03(30(01(x1))))))))))))))))))) → 22(22(22(20(00(03(33(30(02(20(01(11(11(10(03(32(21(13(31(x1))))))))))))))))))) (546)
13(30(02(21(10(02(20(02(21(11(11(12(22(23(33(30(03(30(01(x1))))))))))))))))))) → 12(22(22(20(00(03(33(30(02(20(01(11(11(10(03(32(21(13(31(x1))))))))))))))))))) (550)
03(30(02(21(10(02(20(02(21(11(11(12(22(23(33(30(03(30(01(x1))))))))))))))))))) → 02(22(22(20(00(03(33(30(02(20(01(11(11(10(03(32(21(13(31(x1))))))))))))))))))) (554)
33(30(02(21(10(02(20(02(21(11(11(12(22(23(33(30(03(30(01(x1))))))))))))))))))) → 32(22(22(20(00(03(33(30(02(20(01(11(11(10(03(32(21(13(31(x1))))))))))))))))))) (558)
20(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(02(x1))))))))))))))))))) → 23(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(02(x1))))))))))))))))))) (577)
20(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(01(x1))))))))))))))))))) → 23(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(01(x1))))))))))))))))))) (578)
20(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(00(x1))))))))))))))))))) → 23(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(00(x1))))))))))))))))))) (579)
20(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(03(x1))))))))))))))))))) → 23(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(03(x1))))))))))))))))))) (580)
10(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(02(x1))))))))))))))))))) → 13(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(02(x1))))))))))))))))))) (581)
10(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(01(x1))))))))))))))))))) → 13(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(01(x1))))))))))))))))))) (582)
10(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(00(x1))))))))))))))))))) → 13(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(00(x1))))))))))))))))))) (583)
10(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(03(x1))))))))))))))))))) → 13(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(03(x1))))))))))))))))))) (584)
30(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(02(x1))))))))))))))))))) → 33(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(02(x1))))))))))))))))))) (589)
30(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(01(x1))))))))))))))))))) → 33(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(01(x1))))))))))))))))))) (590)
30(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(00(x1))))))))))))))))))) → 33(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(00(x1))))))))))))))))))) (591)
30(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(03(x1))))))))))))))))))) → 33(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(03(x1))))))))))))))))))) (592)
23(30(02(22(21(12(23(31(10(01(13(32(20(02(21(12(22(21(11(x1))))))))))))))))))) → 22(21(11(13(32(20(00(01(10(03(32(22(21(13(32(22(21(12(21(x1))))))))))))))))))) (754)
13(30(02(22(21(12(23(31(10(01(13(32(20(02(21(12(22(21(11(x1))))))))))))))))))) → 12(21(11(13(32(20(00(01(10(03(32(22(21(13(32(22(21(12(21(x1))))))))))))))))))) (758)
03(30(02(22(21(12(23(31(10(01(13(32(20(02(21(12(22(21(11(x1))))))))))))))))))) → 02(21(11(13(32(20(00(01(10(03(32(22(21(13(32(22(21(12(21(x1))))))))))))))))))) (762)
33(30(02(22(21(12(23(31(10(01(13(32(20(02(21(12(22(21(11(x1))))))))))))))))))) → 32(21(11(13(32(20(00(01(10(03(32(22(21(13(32(22(21(12(21(x1))))))))))))))))))) (766)
20(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(22(x1))))))))))))))))))) → 23(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(22(x1))))))))))))))))))) (849)
20(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(21(x1))))))))))))))))))) → 23(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(21(x1))))))))))))))))))) (850)
20(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(20(x1))))))))))))))))))) → 23(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(20(x1))))))))))))))))))) (851)
20(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(23(x1))))))))))))))))))) → 23(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(23(x1))))))))))))))))))) (852)
10(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(22(x1))))))))))))))))))) → 13(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(22(x1))))))))))))))))))) (853)
10(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(21(x1))))))))))))))))))) → 13(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(21(x1))))))))))))))))))) (854)
10(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(20(x1))))))))))))))))))) → 13(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(20(x1))))))))))))))))))) (855)
10(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(23(x1))))))))))))))))))) → 13(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(23(x1))))))))))))))))))) (856)
00(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(22(x1))))))))))))))))))) → 03(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(22(x1))))))))))))))))))) (857)
00(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(21(x1))))))))))))))))))) → 03(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(21(x1))))))))))))))))))) (858)
00(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(20(x1))))))))))))))))))) → 03(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(20(x1))))))))))))))))))) (859)
00(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(23(x1))))))))))))))))))) → 03(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(23(x1))))))))))))))))))) (860)
30(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(22(x1))))))))))))))))))) → 33(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(22(x1))))))))))))))))))) (861)
30(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(21(x1))))))))))))))))))) → 33(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(21(x1))))))))))))))))))) (862)
30(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(20(x1))))))))))))))))))) → 33(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(20(x1))))))))))))))))))) (863)
30(03(33(33(30(03(32(22(22(21(13(31(11(11(10(01(12(22(23(x1))))))))))))))))))) → 33(31(10(01(11(12(22(23(32(23(32(20(00(03(33(31(11(12(23(x1))))))))))))))))))) (864)
23(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(32(x1))))))))))))))))))) → 20(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(32(x1))))))))))))))))))) (993)
23(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(31(x1))))))))))))))))))) → 20(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(31(x1))))))))))))))))))) (994)
23(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(30(x1))))))))))))))))))) → 20(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(30(x1))))))))))))))))))) (995)
23(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(33(x1))))))))))))))))))) → 20(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(33(x1))))))))))))))))))) (996)
13(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(32(x1))))))))))))))))))) → 10(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(32(x1))))))))))))))))))) (997)
13(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(31(x1))))))))))))))))))) → 10(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(31(x1))))))))))))))))))) (998)
13(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(30(x1))))))))))))))))))) → 10(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(30(x1))))))))))))))))))) (999)
13(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(33(x1))))))))))))))))))) → 10(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(33(x1))))))))))))))))))) (1000)
03(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(32(x1))))))))))))))))))) → 00(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(32(x1))))))))))))))))))) (1001)
03(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(31(x1))))))))))))))))))) → 00(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(31(x1))))))))))))))))))) (1002)
03(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(30(x1))))))))))))))))))) → 00(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(30(x1))))))))))))))))))) (1003)
03(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(33(x1))))))))))))))))))) → 00(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(33(x1))))))))))))))))))) (1004)

1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[31(x1)] = 1 · x1 + 3
[10(x1)] = 1 · x1
[00(x1)] = 1 · x1
[02(x1)] = 1 · x1 + 1
[20(x1)] = 1 · x1
[01(x1)] = 1 · x1
[13(x1)] = 1 · x1 + 1
[33(x1)] = 1 · x1 + 1
[30(x1)] = 1 · x1 + 1
[21(x1)] = 1 · x1
[11(x1)] = 1 · x1
[03(x1)] = 1 · x1 + 1
[23(x1)] = 1 · x1
[32(x1)] = 1 · x1 + 1
[22(x1)] = 1 · x1
[12(x1)] = 1 · x1
all of the following rules can be deleted.
03(33(30(03(31(11(13(33(31(11(10(02(21(11(12(23(30(01(x1)))))))))))))))))) → 03(31(10(03(31(12(23(30(01(11(11(11(10(03(33(33(32(21(x1)))))))))))))))))) (334)
33(31(12(22(21(12(21(13(32(20(02(23(33(31(13(33(30(01(x1)))))))))))))))))) → 33(31(12(21(11(10(00(02(23(32(21(13(33(33(32(22(23(31(x1)))))))))))))))))) (342)

1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[31(x1)] = 1 · x1 + 1
[10(x1)] = 1 · x1
[00(x1)] = 1 · x1
[02(x1)] = 1 · x1
[20(x1)] = 1 · x1
[01(x1)] = 1 · x1
[13(x1)] = 1 · x1
[33(x1)] = 1 · x1
[30(x1)] = 1 · x1 + 1
[21(x1)] = 1 · x1
[11(x1)] = 1 · x1 + 2
[03(x1)] = 1 · x1
[23(x1)] = 1 · x1
[32(x1)] = 1 · x1
[22(x1)] = 1 · x1
[12(x1)] = 1 · x1
all of the following rules can be deleted.
31(10(00(02(20(00(01(13(33(30(02(21(13(31(11(10(00(02(x1)))))))))))))))))) → 31(10(01(10(00(03(31(13(30(02(23(30(01(10(02(21(10(02(x1)))))))))))))))))) (297)
31(10(00(02(20(00(01(13(33(30(02(21(13(31(11(10(00(01(x1)))))))))))))))))) → 31(10(01(10(00(03(31(13(30(02(23(30(01(10(02(21(10(01(x1)))))))))))))))))) (298)
31(10(00(02(20(00(01(13(33(30(02(21(13(31(11(10(00(00(x1)))))))))))))))))) → 31(10(01(10(00(03(31(13(30(02(23(30(01(10(02(21(10(00(x1)))))))))))))))))) (299)
31(10(00(02(20(00(01(13(33(30(02(21(13(31(11(10(00(03(x1)))))))))))))))))) → 31(10(01(10(00(03(31(13(30(02(23(30(01(10(02(21(10(03(x1)))))))))))))))))) (300)

1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[03(x1)] = 1 · x1
[33(x1)] = 1 · x1
[32(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[13(x1)] = 1 · x1 + 4
[30(x1)] = 1 · x1
[02(x1)] = 1 · x1 + 1
[10(x1)] = 1 · x1
[20(x1)] = 1 · x1
[01(x1)] = 1 · x1
[12(x1)] = 1 · x1
[23(x1)] = 1 · x1
[31(x1)] = 1 · x1 + 4
[00(x1)] = 1 · x1
[11(x1)] = 1 · x1 + 4
all of the following rules can be deleted.
03(33(32(22(21(13(33(30(02(21(10(02(20(01(10(02(20(02(x1)))))))))))))))))) → 03(32(21(10(01(12(23(31(10(02(20(00(03(32(23(32(20(02(x1)))))))))))))))))) (317)
03(33(32(22(21(13(33(30(02(21(10(02(20(01(10(02(20(01(x1)))))))))))))))))) → 03(32(21(10(01(12(23(31(10(02(20(00(03(32(23(32(20(01(x1)))))))))))))))))) (318)
03(33(32(22(21(13(33(30(02(21(10(02(20(01(10(02(20(00(x1)))))))))))))))))) → 03(32(21(10(01(12(23(31(10(02(20(00(03(32(23(32(20(00(x1)))))))))))))))))) (319)
03(33(32(22(21(13(33(30(02(21(10(02(20(01(10(02(20(03(x1)))))))))))))))))) → 03(32(21(10(01(12(23(31(10(02(20(00(03(32(23(32(20(03(x1)))))))))))))))))) (320)

1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[33(x1)] = 1 · x1
[31(x1)] = 1 · x1
[13(x1)] = 1 · x1
[12(x1)] = 1 · x1
[20(x1)] = 1 · x1
[01(x1)] = 1 · x1 + 1
[23(x1)] = 1 · x1
[30(x1)] = 1 · x1
[03(x1)] = 1 · x1
[10(x1)] = 1 · x1
[22(x1)] = 1 · x1
[11(x1)] = 1 · x1
[32(x1)] = 1 · x1
[00(x1)] = 1 · x1
[02(x1)] = 1 · x1
[21(x1)] = 1 · x1 + 1
all of the following rules can be deleted.
33(31(13(31(12(20(01(12(23(30(01(12(23(33(30(03(31(12(x1)))))))))))))))))) → 33(31(10(03(31(12(22(20(01(11(10(03(33(33(32(23(31(12(x1)))))))))))))))))) (409)
33(31(13(31(12(20(01(12(23(30(01(12(23(33(30(03(31(11(x1)))))))))))))))))) → 33(31(10(03(31(12(22(20(01(11(10(03(33(33(32(23(31(11(x1)))))))))))))))))) (410)
33(31(13(31(12(20(01(12(23(30(01(12(23(33(30(03(31(10(x1)))))))))))))))))) → 33(31(10(03(31(12(22(20(01(11(10(03(33(33(32(23(31(10(x1)))))))))))))))))) (411)
33(31(13(31(12(20(01(12(23(30(01(12(23(33(30(03(31(13(x1)))))))))))))))))) → 33(31(10(03(31(12(22(20(01(11(10(03(33(33(32(23(31(13(x1)))))))))))))))))) (412)

1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[00(x1)] = 1 · x1
[02(x1)] = 1 · x1
[22(x1)] = 1 · x1
[23(x1)] = 1 · x1 + 1
[33(x1)] = 1 · x1
[30(x1)] = 1 · x1
[03(x1)] = 1 · x1
[31(x1)] = 1 · x1
[10(x1)] = 1 · x1
[01(x1)] = 1 · x1
[12(x1)] = 1 · x1
[32(x1)] = 1 · x1
[20(x1)] = 1 · x1
[21(x1)] = 1 · x1
[11(x1)] = 1 · x1
[13(x1)] = 1 · x1
all of the following rules can be deleted.
00(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(02(x1))))))))))))))))))) → 03(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(02(x1))))))))))))))))))) (585)
00(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(01(x1))))))))))))))))))) → 03(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(01(x1))))))))))))))))))) (586)
00(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(00(x1))))))))))))))))))) → 03(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(00(x1))))))))))))))))))) (587)
00(02(22(22(23(33(30(02(23(30(03(31(10(00(01(12(23(30(03(x1))))))))))))))))))) → 03(30(03(32(23(32(20(02(21(11(10(03(30(00(02(23(32(20(03(x1))))))))))))))))))) (588)

1.1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[33(x1)] = 1 · x1
[30(x1)] = 1 · x1
[02(x1)] = 1 · x1
[20(x1)] = 1 · x1
[22(x1)] = 1 · x1
[00(x1)] = 1 · x1
[21(x1)] = 1 · x1
[12(x1)] = 1 · x1 + 1
[23(x1)] = 1 · x1
[32(x1)] = 1 · x1
[03(x1)] = 1 · x1
[13(x1)] = 1 · x1
[31(x1)] = 1 · x1
all of the following rules can be deleted.
33(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(32(x1))))))))))))))))))) → 30(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(32(x1))))))))))))))))))) (1005)
33(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(31(x1))))))))))))))))))) → 30(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(31(x1))))))))))))))))))) (1006)
33(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(30(x1))))))))))))))))))) → 30(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(30(x1))))))))))))))))))) (1007)
33(30(02(20(02(22(20(00(02(21(12(23(33(33(30(02(23(33(33(x1))))))))))))))))))) → 30(00(03(30(00(03(32(23(32(22(21(13(32(22(20(03(32(23(33(x1))))))))))))))))))) (1008)

1.1.1.1.1.1.1.1.1.1.1.1 R is empty

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