Certification Problem

Input (TPDB SRS_Relative/ICFP_2010_relative/138993)

The relative rewrite relation R/S is considered where R is the following TRS

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

and S is the following TRS.

0(1(2(3(x1)))) 0(1(2(3(x1)))) (81)

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(2(0(2(0(0(2(0(1(2(1(0(0(2(1(0(0(x1)))))))))))))))))) 2(0(1(2(2(2(0(1(0(1(0(0(2(2(1(0(0(0(x1)))))))))))))))))) (82)
0(1(0(0(2(0(1(3(0(3(0(3(1(0(1(0(1(0(x1)))))))))))))))))) 0(1(0(1(1(3(0(1(0(3(0(2(0(1(0(3(0(0(x1)))))))))))))))))) (83)
1(1(2(0(1(2(3(3(1(0(1(1(0(0(2(0(1(0(x1)))))))))))))))))) 1(1(2(0(0(1(1(1(1(0(3(0(0(3(1(2(2(0(x1)))))))))))))))))) (84)
3(1(3(3(1(1(3(0(0(3(1(2(0(0(0(2(1(0(x1)))))))))))))))))) 3(1(3(1(1(3(1(3(2(3(1(0(2(0(0(0(0(0(x1)))))))))))))))))) (85)
2(2(1(0(0(3(0(1(0(3(3(0(1(3(1(3(1(0(x1)))))))))))))))))) 2(3(1(3(3(0(2(0(1(1(0(0(3(1(1(0(3(0(x1)))))))))))))))))) (86)
3(2(3(1(2(0(1(0(2(2(3(1(0(1(2(3(1(0(x1)))))))))))))))))) 3(1(3(1(1(2(0(0(2(1(2(3(2(1(2(0(3(0(x1)))))))))))))))))) (87)
0(0(3(0(3(0(0(2(0(2(0(0(0(3(3(0(2(0(x1)))))))))))))))))) 0(3(3(0(0(0(0(2(3(2(0(0(0(2(3(0(0(0(x1)))))))))))))))))) (88)
2(3(1(0(1(0(2(0(2(1(0(3(1(1(0(1(2(0(x1)))))))))))))))))) 1(1(1(0(3(2(2(0(0(0(0(0(3(1(1(1(2(2(x1)))))))))))))))))) (89)
1(3(1(0(3(0(0(3(0(2(1(3(3(0(2(2(2(0(x1)))))))))))))))))) 2(3(0(3(0(3(1(1(1(2(2(3(0(0(0(3(2(0(x1)))))))))))))))))) (90)
1(0(0(3(0(1(1(0(0(1(0(2(3(0(0(3(2(0(x1)))))))))))))))))) 1(0(3(0(0(1(1(2(1(2(0(0(0(0(3(3(0(0(x1)))))))))))))))))) (91)
1(3(3(2(0(1(3(2(1(2(1(3(1(3(1(3(2(0(x1)))))))))))))))))) 1(2(3(3(3(1(1(2(2(0(3(3(1(1(2(3(1(0(x1)))))))))))))))))) (92)
2(1(3(0(3(1(0(3(0(3(0(3(1(0(3(0(3(0(x1)))))))))))))))))) 2(1(3(0(3(0(0(3(0(3(0(1(1(3(3(3(0(0(x1)))))))))))))))))) (93)
3(3(3(1(3(2(1(3(1(2(1(3(2(2(3(1(3(0(x1)))))))))))))))))) 3(3(2(1(1(0(3(2(1(3(1(2(3(3(3(1(3(2(x1)))))))))))))))))) (94)
3(3(2(0(2(1(3(3(0(0(2(1(3(2(0(2(3(0(x1)))))))))))))))))) 3(3(3(0(1(2(0(2(0(2(3(3(1(2(0(2(3(0(x1)))))))))))))))))) (95)
3(2(3(0(2(0(1(2(1(3(3(1(0(0(1(3(3(0(x1)))))))))))))))))) 2(1(3(1(0(2(3(2(3(3(3(3(0(1(1(0(0(0(x1)))))))))))))))))) (96)
1(0(3(0(3(0(2(0(0(0(2(0(3(3(1(3(3(0(x1)))))))))))))))))) 1(0(3(3(0(0(2(1(3(0(3(3(3(2(0(0(0(0(x1)))))))))))))))))) (97)
3(1(1(2(1(1(0(0(3(2(0(1(2(1(1(1(0(1(x1)))))))))))))))))) 3(3(2(1(1(0(1(1(1(1(0(0(1(2(2(1(0(1(x1)))))))))))))))))) (98)
1(3(0(2(3(2(3(0(0(3(3(2(0(1(1(3(0(1(x1)))))))))))))))))) 1(3(3(3(3(0(1(0(0(0(3(2(2(0(3(2(1(1(x1)))))))))))))))))) (99)
1(3(3(3(1(0(1(1(2(1(1(3(1(1(0(2(1(1(x1)))))))))))))))))) 1(1(2(2(0(3(3(0(1(1(1(3(1(1(3(1(1(1(x1)))))))))))))))))) (100)
1(3(0(0(2(1(2(1(1(2(3(1(2(1(3(2(1(1(x1)))))))))))))))))) 1(2(2(2(2(1(3(3(2(1(0(1(0(1(3(1(1(1(x1)))))))))))))))))) (101)
2(1(1(0(3(1(0(3(3(1(0(0(1(3(0(3(1(1(x1)))))))))))))))))) 3(0(3(2(3(3(0(1(1(1(1(0(0(0(3(1(1(1(x1)))))))))))))))))) (102)
3(0(1(2(0(0(1(3(3(1(1(2(1(2(1(0(2(1(x1)))))))))))))))))) 3(0(0(2(2(2(0(1(3(3(1(1(2(1(1(1(1(0(x1)))))))))))))))))) (103)
0(1(2(2(3(2(3(3(3(3(1(3(1(1(2(0(2(1(x1)))))))))))))))))) 0(1(3(3(3(2(1(1(0(3(2(3(1(2(2(3(2(1(x1)))))))))))))))))) (104)
0(2(2(1(2(2(3(2(0(0(1(2(0(1(3(1(2(1(x1)))))))))))))))))) 0(0(1(2(2(2(2(2(3(3(0(0(1(1(1(2(2(1(x1)))))))))))))))))) (105)
2(1(3(1(0(2(3(1(0(0(1(0(1(2(0(1(3(1(x1)))))))))))))))))) 3(3(2(0(1(3(0(0(1(1(2(0(2(1(1(1(0(1(x1)))))))))))))))))) (106)
1(2(1(2(1(1(2(0(2(1(2(1(0(2(2(1(3(1(x1)))))))))))))))))) 1(1(2(0(2(2(1(3(0(1(2(2(2(1(1(1(2(1(x1)))))))))))))))))) (107)
2(3(2(0(0(1(3(1(0(1(2(1(3(0(2(0(0(2(x1)))))))))))))))))) 3(0(0(2(2(0(3(2(1(2(3(1(0(0(1(1(0(2(x1)))))))))))))))))) (108)
1(1(3(1(0(2(1(3(3(1(1(1(2(3(0(1(0(2(x1)))))))))))))))))) 1(1(0(2(2(3(3(1(1(2(0(1(1(1(1(3(0(3(x1)))))))))))))))))) (109)
3(1(0(3(1(3(2(3(1(3(2(2(3(2(3(1(0(2(x1)))))))))))))))))) 3(2(3(3(3(2(1(3(1(2(0(3(0(3(2(1(1(2(x1)))))))))))))))))) (110)
2(1(3(1(2(1(3(0(2(3(3(2(3(2(0(2(0(2(x1)))))))))))))))))) 2(3(3(2(1(2(2(1(1(2(0(0(2(0(3(2(3(3(x1)))))))))))))))))) (111)
1(3(0(0(3(1(3(1(0(3(0(2(1(3(0(2(0(2(x1)))))))))))))))))) 1(0(1(3(1(0(0(1(0(2(0(2(3(2(0(3(3(3(x1)))))))))))))))))) (112)
0(2(3(2(0(3(1(0(2(0(1(0(3(3(0(3(0(2(x1)))))))))))))))))) 0(3(0(0(3(0(0(0(3(1(2(2(0(3(2(1(2(3(x1)))))))))))))))))) (113)
2(1(3(0(0(1(3(2(1(1(3(1(3(2(2(3(0(2(x1)))))))))))))))))) 2(0(3(2(3(1(3(3(2(3(2(1(1(1(0(1(0(2(x1)))))))))))))))))) (114)
1(1(1(1(2(1(1(2(2(1(2(1(3(1(1(0(1(2(x1)))))))))))))))))) 1(1(1(2(2(1(1(2(1(1(1(1(1(0(3(1(2(2(x1)))))))))))))))))) (115)
0(1(3(0(1(0(2(2(3(2(3(2(1(0(0(2(1(2(x1)))))))))))))))))) 0(1(0(0(0(3(2(1(0(3(2(2(3(1(1(2(2(2(x1)))))))))))))))))) (116)
3(0(2(2(0(0(3(1(3(0(1(2(1(2(1(3(1(2(x1)))))))))))))))))) 3(2(1(1(1(2(0(2(2(1(0(1(3(3(2(0(0(3(x1)))))))))))))))))) (117)
2(3(3(2(1(3(2(3(2(1(3(3(1(3(1(3(1(2(x1)))))))))))))))))) 3(3(1(1(3(3(1(3(2(1(2(3(2(3(2(3(1(2(x1)))))))))))))))))) (118)
3(2(0(1(3(1(1(0(0(1(1(2(1(2(2(3(1(2(x1)))))))))))))))))) 3(1(1(1(0(0(0(2(1(2(2(2(1(2(1(1(3(3(x1)))))))))))))))))) (119)
3(2(3(2(0(0(2(2(0(2(0(3(2(1(3(3(1(2(x1)))))))))))))))))) 3(3(2(3(0(2(2(1(1(2(0(3(0(0(2(3(2(2(x1)))))))))))))))))) (120)
1(2(2(3(3(1(0(0(2(2(3(0(1(3(2(0(2(2(x1)))))))))))))))))) 1(3(2(3(0(0(0(3(1(2(2(2(2(1(2(2(0(3(x1)))))))))))))))))) (121)
1(3(1(1(3(0(1(2(2(2(2(2(1(0(3(0(2(2(x1)))))))))))))))))) 1(2(2(3(1(2(2(2(1(1(1(0(0(3(2(0(3(2(x1)))))))))))))))))) (122)
2(0(2(1(3(3(2(3(2(0(2(2(0(2(0(1(2(2(x1)))))))))))))))))) 2(0(2(2(0(2(2(1(2(0(2(3(3(1(0(3(2(2(x1)))))))))))))))))) (123)
2(0(3(0(3(3(0(1(2(0(2(2(0(2(1(1(2(2(x1)))))))))))))))))) 2(0(3(3(0(2(1(1(0(2(2(2(0(0(3(1(2(2(x1)))))))))))))))))) (124)
1(3(3(2(3(0(3(0(0(3(0(1(3(2(2(1(2(2(x1)))))))))))))))))) 1(2(0(0(3(0(1(3(3(1(2(0(3(3(3(2(2(2(x1)))))))))))))))))) (125)
3(1(3(0(3(2(2(0(0(0(1(2(1(1(2(1(3(2(x1)))))))))))))))))) 3(1(3(3(1(2(0(1(3(2(1(1(0(2(0(0(2(2(x1)))))))))))))))))) (126)
3(2(3(1(2(3(0(1(3(2(0(3(1(1(3(1(3(2(x1)))))))))))))))))) 3(1(1(1(3(3(2(2(1(1(3(0(2(3(3(0(3(2(x1)))))))))))))))))) (127)
2(2(1(0(0(3(1(1(2(1(1(0(2(1(3(1(3(2(x1)))))))))))))))))) 3(1(2(2(0(1(1(1(1(0(0(3(2(2(1(1(2(3(x1)))))))))))))))))) (128)
3(2(3(2(0(3(3(0(2(2(0(3(2(3(3(2(3(2(x1)))))))))))))))))) 3(2(0(0(3(0(3(3(2(2(3(2(3(2(3(3(2(2(x1)))))))))))))))))) (129)
3(0(1(2(3(1(0(3(0(3(0(2(3(2(0(3(3(2(x1)))))))))))))))))) 3(3(1(2(2(0(3(3(0(0(0(1(0(3(2(3(3(2(x1)))))))))))))))))) (130)
2(2(0(1(0(3(1(2(0(3(3(1(1(3(1(0(0(3(x1)))))))))))))))))) 2(3(2(0(3(0(1(1(1(0(0(3(2(0(3(1(1(3(x1)))))))))))))))))) (131)
2(1(3(1(0(1(2(2(3(1(0(2(1(0(2(0(0(3(x1)))))))))))))))))) 2(1(1(0(0(1(2(3(1(2(0(3(2(2(0(0(1(3(x1)))))))))))))))))) (132)
2(0(2(1(3(0(2(2(2(2(1(2(0(2(3(0(0(3(x1)))))))))))))))))) 2(3(0(0(0(0(2(2(2(3(2(2(1(2(1(2(0(3(x1)))))))))))))))))) (133)
0(2(0(2(2(1(0(2(1(2(3(3(3(0(3(1(0(3(x1)))))))))))))))))) 0(0(3(1(2(2(2(0(3(0(0(3(1(1(2(3(3(2(x1)))))))))))))))))) (134)
1(0(1(3(0(1(3(2(2(0(2(1(0(1(1(2(0(3(x1)))))))))))))))))) 1(0(0(1(1(0(1(0(2(1(1(3(3(0(2(3(2(2(x1)))))))))))))))))) (135)
1(3(0(0(2(1(3(3(1(0(1(3(3(2(1(2(0(3(x1)))))))))))))))))) 1(0(3(2(0(1(1(3(2(0(1(1(3(2(3(3(0(3(x1)))))))))))))))))) (136)
2(2(2(2(1(0(2(0(0(3(1(0(0(3(2(2(0(3(x1)))))))))))))))))) 2(2(0(1(2(1(2(2(0(0(0(0(0(2(3(3(2(3(x1)))))))))))))))))) (137)
3(1(1(2(1(0(3(1(0(3(3(1(1(3(2(2(0(3(x1)))))))))))))))))) 2(3(3(3(3(1(1(0(0(3(3(1(1(2(1(1(0(2(x1)))))))))))))))))) (138)
2(2(3(1(2(1(2(1(3(3(1(2(1(0(2(3(0(3(x1)))))))))))))))))) 2(2(3(1(3(2(1(1(3(0(3(1(0(2(1(2(2(3(x1)))))))))))))))))) (139)
2(3(1(3(0(2(3(1(3(1(2(3(2(2(3(3(0(3(x1)))))))))))))))))) 3(2(0(3(3(3(1(2(3(3(2(0(1(3(2(1(2(3(x1)))))))))))))))))) (140)
0(1(3(0(1(3(3(1(0(0(0(2(1(1(2(0(1(3(x1)))))))))))))))))) 1(1(0(0(0(1(1(0(0(3(1(3(2(3(2(0(1(3(x1)))))))))))))))))) (141)
2(1(1(3(3(1(1(3(0(0(2(2(0(2(1(1(1(3(x1)))))))))))))))))) 2(2(0(1(3(0(3(2(1(1(3(1(1(1(1(0(2(3(x1)))))))))))))))))) (142)
2(3(3(0(1(0(2(1(3(1(3(0(2(2(1(1(1(3(x1)))))))))))))))))) 2(3(0(0(1(2(2(1(1(1(2(3(3(1(3(1(0(3(x1)))))))))))))))))) (143)
1(3(3(0(2(2(1(3(1(2(1(2(1(3(1(1(1(3(x1)))))))))))))))))) 3(3(2(1(1(1(2(3(3(2(1(1(2(1(0(1(1(3(x1)))))))))))))))))) (144)
2(3(0(3(0(2(0(0(3(2(2(0(3(1(3(1(1(3(x1)))))))))))))))))) 3(3(3(2(3(3(0(1(0(0(0(2(2(3(1(1(0(2(x1)))))))))))))))))) (145)
3(1(0(3(0(1(3(0(3(2(1(2(0(3(0(2(1(3(x1)))))))))))))))))) 3(1(3(1(2(0(3(0(0(1(2(3(3(0(3(1(0(2(x1)))))))))))))))))) (146)
3(3(1(3(0(2(2(2(0(2(2(2(0(3(2(2(1(3(x1)))))))))))))))))) 3(2(2(3(0(2(2(3(2(2(0(3(0(1(1(2(2(3(x1)))))))))))))))))) (147)
3(3(3(3(0(3(1(2(2(0(1(3(2(3(2(3(1(3(x1)))))))))))))))))) 3(2(3(2(3(2(1(1(0(3(3(3(3(0(1(3(2(3(x1)))))))))))))))))) (148)
3(1(0(1(0(3(3(2(3(3(0(3(1(3(0(0(2(3(x1)))))))))))))))))) 3(1(1(0(0(3(0(3(3(3(1(3(3(2(0(2(0(3(x1)))))))))))))))))) (149)
1(2(1(3(1(1(2(1(3(1(3(0(1(0(2(1(2(3(x1)))))))))))))))))) 1(1(1(1(3(1(3(1(2(2(1(3(3(2(0(0(2(1(x1)))))))))))))))))) (150)
3(0(1(0(2(0(3(1(0(0(0(1(3(1(2(1(2(3(x1)))))))))))))))))) 3(0(1(2(1(1(3(0(0(0(0(2(1(0(1(2(3(3(x1)))))))))))))))))) (151)
3(1(3(0(2(1(3(2(1(3(0(1(0(2(2(1(2(3(x1)))))))))))))))))) 3(0(2(2(1(3(3(2(1(0(0(3(3(1(1(1(2(2(x1)))))))))))))))))) (152)
1(3(0(0(3(0(1(2(1(2(2(2(1(3(2(1(2(3(x1)))))))))))))))))) 1(1(0(3(0(3(2(2(1(0(2(3(3(2(1(2(1(2(x1)))))))))))))))))) (153)
2(3(1(3(1(3(1(3(1(3(3(1(3(1(0(2(2(3(x1)))))))))))))))))) 3(3(1(1(3(0(2(1(3(2(2(3(1(1(3(1(3(3(x1)))))))))))))))))) (154)
2(1(2(1(2(3(1(3(2(2(1(2(1(2(1(2(2(3(x1)))))))))))))))))) 2(1(1(3(1(2(1(1(2(3(2(2(2(2(1(2(3(2(x1)))))))))))))))))) (155)
2(0(3(1(0(0(3(1(0(2(2(2(1(0(1(3(2(3(x1)))))))))))))))))) 1(2(0(2(1(3(1(2(1(2(3(3(0(0(0(0(2(3(x1)))))))))))))))))) (156)
2(2(1(3(2(1(0(1(2(2(2(0(1(2(3(3(2(3(x1)))))))))))))))))) 2(2(2(1(2(3(2(2(3(1(2(0(3(2(1(1(0(3(x1)))))))))))))))))) (157)
0(2(2(3(1(2(0(1(2(0(1(2(0(1(2(0(3(3(x1)))))))))))))))))) 0(3(1(1(2(2(1(3(2(3(2(0(0(1(0(0(2(2(x1)))))))))))))))))) (158)
3(2(0(0(2(1(0(0(2(0(3(1(3(3(1(1(3(3(x1)))))))))))))))))) 3(3(1(0(3(0(1(2(3(3(3(2(0(0(0(1(1(2(x1)))))))))))))))))) (159)
3(1(2(0(1(1(3(3(2(3(1(3(1(0(2(1(3(3(x1)))))))))))))))))) 3(2(3(1(1(1(1(0(3(0(1(1(3(3(3(3(2(2(x1)))))))))))))))))) (160)
1(3(0(3(2(3(1(0(3(1(0(2(0(1(3(3(3(3(x1)))))))))))))))))) 1(3(2(2(3(3(0(1(3(3(3(0(1(0(1(0(3(3(x1)))))))))))))))))) (161)

1.1 Closure Under Flat Contexts

Using the flat contexts

{2(), 1(), 0(), 3()}

We obtain the transformed TRS

There are 125 ruless (increase limit for explicit display).

1.1.1 Semantic Labeling

Root-labeling is applied.

We obtain the labeled TRS

There are 500 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[21(x1)] = 1 · x1
[12(x1)] = 1 · x1 + 9
[20(x1)] = 1 · x1 + 4
[02(x1)] = 1 · x1
[00(x1)] = 1 · x1
[01(x1)] = 1 · x1
[10(x1)] = 1 · x1 + 10
[22(x1)] = 1 · x1
[03(x1)] = 1 · x1 + 1
[13(x1)] = 1 · x1 + 13
[30(x1)] = 1 · x1 + 4
[31(x1)] = 1 · x1
[11(x1)] = 1 · x1
[23(x1)] = 1 · x1 + 1
[33(x1)] = 1 · x1
[32(x1)] = 1 · x1
all of the following rules can be deleted.

There are 477 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 + 2
[13(x1)] = 1 · x1
[33(x1)] = 1 · x1
[11(x1)] = 1 · x1
[30(x1)] = 1 · x1 + 4
[00(x1)] = 1 · x1
[03(x1)] = 1 · x1
[12(x1)] = 1 · x1
[20(x1)] = 1 · x1 + 2
[02(x1)] = 1 · x1 + 1
[21(x1)] = 1 · x1
[10(x1)] = 1 · x1
[32(x1)] = 1 · x1 + 2
[23(x1)] = 1 · x1
[01(x1)] = 1 · x1 + 1
[22(x1)] = 1 · x1
all of the following rules can be deleted.
12(22(23(33(31(10(00(02(22(23(30(01(13(32(20(02(22(22(x1)))))))))))))))))) 13(32(23(30(00(00(03(31(12(22(22(22(21(12(22(20(03(32(x1)))))))))))))))))) (350)
12(22(23(33(31(10(00(02(22(23(30(01(13(32(20(02(22(21(x1)))))))))))))))))) 13(32(23(30(00(00(03(31(12(22(22(22(21(12(22(20(03(31(x1)))))))))))))))))) (351)
12(22(23(33(31(10(00(02(22(23(30(01(13(32(20(02(22(20(x1)))))))))))))))))) 13(32(23(30(00(00(03(31(12(22(22(22(21(12(22(20(03(30(x1)))))))))))))))))) (352)

1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[31(x1)] = 1 · x1
[13(x1)] = 1 · x1
[33(x1)] = 1 · x1
[11(x1)] = 1 · x1
[30(x1)] = 1 · x1
[00(x1)] = 1 · x1 + 1
[03(x1)] = 1 · x1
[12(x1)] = 1 · x1
[20(x1)] = 1 · x1 + 3
[02(x1)] = 1 · x1
[21(x1)] = 1 · x1 + 2
[10(x1)] = 1 · x1
[32(x1)] = 1 · x1
[23(x1)] = 1 · x1
[01(x1)] = 1 · x1
[22(x1)] = 1 · x1 + 2
all of the following rules can be deleted.
31(13(33(31(11(13(30(00(03(31(12(20(00(00(02(21(10(02(x1)))))))))))))))))) 31(13(31(11(13(31(13(32(23(31(10(02(20(00(00(00(00(02(x1)))))))))))))))))) (234)
31(13(33(31(11(13(30(00(03(31(12(20(00(00(02(21(10(01(x1)))))))))))))))))) 31(13(31(11(13(31(13(32(23(31(10(02(20(00(00(00(00(01(x1)))))))))))))))))) (235)
31(13(33(31(11(13(30(00(03(31(12(20(00(00(02(21(10(00(x1)))))))))))))))))) 31(13(31(11(13(31(13(32(23(31(10(02(20(00(00(00(00(00(x1)))))))))))))))))) (236)
31(13(33(31(11(13(30(00(03(31(12(20(00(00(02(21(10(03(x1)))))))))))))))))) 31(13(31(11(13(31(13(32(23(31(10(02(20(00(00(00(00(03(x1)))))))))))))))))) (237)

1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[31(x1)] = 1 · x1
[13(x1)] = 1 · x1
[30(x1)] = 1 · x1
[03(x1)] = 1 · x1
[32(x1)] = 1 · x1
[22(x1)] = 1 · x1 + 1
[20(x1)] = 1 · x1
[00(x1)] = 1 · x1
[01(x1)] = 1 · x1
[12(x1)] = 1 · x1
[21(x1)] = 1 · x1 + 1
[11(x1)] = 1 · x1
[33(x1)] = 1 · x1
[10(x1)] = 1 · x1
[02(x1)] = 1 · x1
[23(x1)] = 1 · x1 + 1
all of the following rules can be deleted.
31(13(30(03(32(22(20(00(00(01(12(21(11(12(21(13(32(22(x1)))))))))))))))))) 31(13(33(31(12(20(01(13(32(21(11(10(02(20(00(02(22(22(x1)))))))))))))))))) (370)
31(13(30(03(32(22(20(00(00(01(12(21(11(12(21(13(32(21(x1)))))))))))))))))) 31(13(33(31(12(20(01(13(32(21(11(10(02(20(00(02(22(21(x1)))))))))))))))))) (371)
31(13(30(03(32(22(20(00(00(01(12(21(11(12(21(13(32(20(x1)))))))))))))))))) 31(13(33(31(12(20(01(13(32(21(11(10(02(20(00(02(22(20(x1)))))))))))))))))) (372)
31(13(30(03(32(22(20(00(00(01(12(21(11(12(21(13(32(23(x1)))))))))))))))))) 31(13(33(31(12(20(01(13(32(21(11(10(02(20(00(02(22(23(x1)))))))))))))))))) (373)

1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[22(x1)] = 1 · x1 + 1
[20(x1)] = 1 · x1
[03(x1)] = 1 · x1
[31(x1)] = 1 · x1
[10(x1)] = 1 · x1
[00(x1)] = 1 · x1
[02(x1)] = 1 · x1
[21(x1)] = 1 · x1
[01(x1)] = 1 · x1
[13(x1)] = 1 · x1
[32(x1)] = 1 · x1
[23(x1)] = 1 · x1
[12(x1)] = 1 · x1
[33(x1)] = 1 · x1 + 2
[30(x1)] = 1 · x1
all of the following rules can be deleted.
22(20(03(31(10(00(03(31(10(02(22(22(21(10(01(13(32(23(32(x1))))))))))))))))))) 21(12(20(02(21(13(31(12(21(12(23(33(30(00(00(00(02(23(32(x1))))))))))))))))))) (706)
22(20(03(31(10(00(03(31(10(02(22(22(21(10(01(13(32(23(31(x1))))))))))))))))))) 21(12(20(02(21(13(31(12(21(12(23(33(30(00(00(00(02(23(31(x1))))))))))))))))))) (707)
22(20(03(31(10(00(03(31(10(02(22(22(21(10(01(13(32(23(30(x1))))))))))))))))))) 21(12(20(02(21(13(31(12(21(12(23(33(30(00(00(00(02(23(30(x1))))))))))))))))))) (708)
22(20(03(31(10(00(03(31(10(02(22(22(21(10(01(13(32(23(33(x1))))))))))))))))))) 21(12(20(02(21(13(31(12(21(12(23(33(30(00(00(00(02(23(33(x1))))))))))))))))))) (709)

1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[02(x1)] = 1 · x1
[20(x1)] = 1 · x1
[03(x1)] = 1 · x1
[31(x1)] = 1 · x1 + 1
[10(x1)] = 1 · x1
[00(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[01(x1)] = 1 · x1
[13(x1)] = 1 · x1
[32(x1)] = 1 · x1
[23(x1)] = 1 · x1
[12(x1)] = 1 · x1
[33(x1)] = 1 · x1
[30(x1)] = 1 · x1
all of the following rules can be deleted.
02(20(03(31(10(00(03(31(10(02(22(22(21(10(01(13(32(23(32(x1))))))))))))))))))) 01(12(20(02(21(13(31(12(21(12(23(33(30(00(00(00(02(23(32(x1))))))))))))))))))) (714)
02(20(03(31(10(00(03(31(10(02(22(22(21(10(01(13(32(23(31(x1))))))))))))))))))) 01(12(20(02(21(13(31(12(21(12(23(33(30(00(00(00(02(23(31(x1))))))))))))))))))) (715)
02(20(03(31(10(00(03(31(10(02(22(22(21(10(01(13(32(23(30(x1))))))))))))))))))) 01(12(20(02(21(13(31(12(21(12(23(33(30(00(00(00(02(23(30(x1))))))))))))))))))) (716)
02(20(03(31(10(00(03(31(10(02(22(22(21(10(01(13(32(23(33(x1))))))))))))))))))) 01(12(20(02(21(13(31(12(21(12(23(33(30(00(00(00(02(23(33(x1))))))))))))))))))) (717)

1.1.1.1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[32(x1)] = 1 · x1
[20(x1)] = 1 · x1
[03(x1)] = 1 · x1
[31(x1)] = 1 · x1
[10(x1)] = 1 · x1
[00(x1)] = 1 · x1
[02(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[01(x1)] = 1 · x1 + 1
[13(x1)] = 1 · x1
[23(x1)] = 1 · x1
[12(x1)] = 1 · x1
[33(x1)] = 1 · x1
[30(x1)] = 1 · x1
all of the following rules can be deleted.
32(20(03(31(10(00(03(31(10(02(22(22(21(10(01(13(32(23(32(x1))))))))))))))))))) 31(12(20(02(21(13(31(12(21(12(23(33(30(00(00(00(02(23(32(x1))))))))))))))))))) (718)
32(20(03(31(10(00(03(31(10(02(22(22(21(10(01(13(32(23(31(x1))))))))))))))))))) 31(12(20(02(21(13(31(12(21(12(23(33(30(00(00(00(02(23(31(x1))))))))))))))))))) (719)
32(20(03(31(10(00(03(31(10(02(22(22(21(10(01(13(32(23(30(x1))))))))))))))))))) 31(12(20(02(21(13(31(12(21(12(23(33(30(00(00(00(02(23(30(x1))))))))))))))))))) (720)
32(20(03(31(10(00(03(31(10(02(22(22(21(10(01(13(32(23(33(x1))))))))))))))))))) 31(12(20(02(21(13(31(12(21(12(23(33(30(00(00(00(02(23(33(x1))))))))))))))))))) (721)

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.