Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/132957)

The rewrite relation of the following TRS is considered.

0(0(0(2(3(0(2(2(0(3(0(1(2(3(3(0(2(0(x1)))))))))))))))))) 0(1(3(2(3(2(2(2(0(0(3(3(2(0(0(0(0(0(x1)))))))))))))))))) (1)
0(0(0(3(0(1(3(0(2(0(3(0(3(0(3(1(0(3(x1)))))))))))))))))) 0(0(1(0(0(1(0(3(3(0(0(3(2(0(3(0(3(3(x1)))))))))))))))))) (2)
0(0(2(0(3(0(3(1(1(0(0(1(3(0(3(0(0(2(x1)))))))))))))))))) 0(0(1(1(1(0(3(0(3(3(0(0(2(0(3(0(0(2(x1)))))))))))))))))) (3)
0(0(2(0(3(1(3(2(1(1(2(3(3(0(2(2(2(2(x1)))))))))))))))))) 3(2(3(1(2(0(1(3(2(0(2(0(2(3(0(1(2(2(x1)))))))))))))))))) (4)
0(0(2(3(0(2(1(2(2(3(0(3(3(1(1(0(2(0(x1)))))))))))))))))) 0(0(1(2(2(3(3(2(0(3(1(0(2(1(0(3(2(0(x1)))))))))))))))))) (5)
0(0(3(1(2(3(1(0(2(3(3(0(2(1(3(0(2(2(x1)))))))))))))))))) 0(3(2(0(3(3(1(2(2(0(1(3(0(0(2(1(3(2(x1)))))))))))))))))) (6)
0(1(0(0(2(2(1(1(3(0(0(1(2(0(1(2(2(0(x1)))))))))))))))))) 0(1(1(0(0(0(2(2(1(2(0(1(1(0(3(2(2(0(x1)))))))))))))))))) (7)
0(1(0(2(3(0(2(1(2(2(1(1(3(3(2(0(3(3(x1)))))))))))))))))) 0(1(2(0(2(2(3(3(2(0(1(3(2(3(0(1(1(3(x1)))))))))))))))))) (8)
0(1(1(3(0(2(0(3(0(1(2(3(0(2(0(3(0(3(x1)))))))))))))))))) 0(0(0(2(3(3(1(0(1(2(0(0(0(1(3(3(2(3(x1)))))))))))))))))) (9)
0(1(2(3(2(0(2(3(1(0(3(0(2(2(1(1(3(3(x1)))))))))))))))))) 0(1(2(2(3(2(3(1(1(2(3(3(2(0(0(1(0(3(x1)))))))))))))))))) (10)
0(1(2(3(2(2(1(3(0(2(1(3(3(1(0(0(2(1(x1)))))))))))))))))) 0(3(2(1(0(1(0(2(3(0(1(3(2(1(3(2(2(1(x1)))))))))))))))))) (11)
0(2(1(3(0(3(3(3(3(1(1(1(3(3(3(2(1(2(x1)))))))))))))))))) 1(3(2(3(3(3(1(0(1(3(1(3(3(3(2(0(1(2(x1)))))))))))))))))) (12)
0(2(2(0(3(1(3(3(0(1(0(3(3(1(1(0(1(2(x1)))))))))))))))))) 0(3(1(2(0(3(2(3(1(0(0(3(1(0(1(3(1(2(x1)))))))))))))))))) (13)
0(3(0(0(1(3(0(0(1(3(0(3(3(1(1(1(1(0(x1)))))))))))))))))) 0(3(0(3(0(0(3(1(0(1(3(1(1(0(3(1(1(0(x1)))))))))))))))))) (14)
0(3(0(0(3(1(0(3(0(0(0(1(2(1(2(0(2(0(x1)))))))))))))))))) 0(3(0(0(1(1(0(2(2(3(0(0(1(0(0(3(2(0(x1)))))))))))))))))) (15)
0(3(0(2(0(0(0(0(2(2(0(2(1(0(2(2(2(0(x1)))))))))))))))))) 0(2(2(2(1(2(0(0(3(2(2(0(0(2(0(0(0(0(x1)))))))))))))))))) (16)
0(3(0(3(0(3(0(1(3(0(0(3(2(0(2(1(0(3(x1)))))))))))))))))) 1(3(2(3(0(0(1(0(0(3(2(0(3(0(0(3(0(3(x1)))))))))))))))))) (17)
0(3(0(3(1(3(0(1(3(0(2(2(3(1(2(0(3(1(x1)))))))))))))))))) 1(0(3(0(3(0(0(3(2(3(0(1(2(3(1(2(3(1(x1)))))))))))))))))) (18)
0(3(0(3(2(2(0(0(2(3(2(1(3(3(0(2(0(2(x1)))))))))))))))))) 0(3(3(1(0(0(2(2(0(0(0(2(3(2(3(2(3(2(x1)))))))))))))))))) (19)
0(3(1(2(3(2(1(2(3(3(2(1(2(3(3(2(2(2(x1)))))))))))))))))) 1(2(3(2(3(1(2(0(3(3(1(3(2(2(3(2(2(2(x1)))))))))))))))))) (20)
0(3(2(0(1(0(1(1(1(0(0(2(1(1(2(2(1(1(x1)))))))))))))))))) 0(3(2(1(0(1(2(1(2(0(0(1(1(0(1(2(1(1(x1)))))))))))))))))) (21)
1(0(1(1(1(2(2(3(0(2(0(3(2(3(0(3(0(0(x1)))))))))))))))))) 1(3(2(0(3(1(1(0(3(2(0(3(2(0(2(1(0(0(x1)))))))))))))))))) (22)
1(0(1(2(2(2(0(3(3(2(1(2(0(2(0(1(2(2(x1)))))))))))))))))) 1(0(2(2(1(2(0(2(2(1(1(0(0(2(3(2(3(2(x1)))))))))))))))))) (23)
1(0(3(0(3(3(0(2(1(2(3(3(1(0(2(2(3(3(x1)))))))))))))))))) 1(0(3(1(2(3(3(1(0(2(2(3(0(0(3(2(3(3(x1)))))))))))))))))) (24)
1(1(0(1(3(0(3(1(3(1(1(3(3(1(2(2(3(3(x1)))))))))))))))))) 1(3(1(3(1(0(3(1(3(1(3(1(3(2(3(2(1(0(x1)))))))))))))))))) (25)
1(1(1(0(2(1(3(2(2(2(1(3(3(1(0(0(2(0(x1)))))))))))))))))) 1(0(1(3(2(1(2(1(1(3(2(2(3(0(0(1(2(0(x1)))))))))))))))))) (26)
1(1(1(1(1(1(2(1(2(2(2(2(2(0(3(3(1(0(x1)))))))))))))))))) 1(1(3(2(2(3(1(2(1(1(2(0(1(0(2(1(1(2(x1)))))))))))))))))) (27)
1(1(1(2(0(1(2(1(3(1(0(3(3(0(0(2(1(3(x1)))))))))))))))))) 1(1(1(1(2(2(0(3(1(0(3(2(0(0(1(3(1(3(x1)))))))))))))))))) (28)
1(1(1(2(3(0(3(0(2(2(1(0(1(3(3(3(3(1(x1)))))))))))))))))) 1(2(3(0(1(2(3(1(3(3(2(0(1(3(1(3(0(1(x1)))))))))))))))))) (29)
1(1(1(3(0(1(0(1(3(1(1(0(2(3(1(1(1(3(x1)))))))))))))))))) 1(1(3(1(3(0(1(1(0(1(0(1(3(1(2(1(1(3(x1)))))))))))))))))) (30)
1(1(1(3(0(2(0(3(3(3(0(0(0(1(2(0(2(1(x1)))))))))))))))))) 1(2(3(2(0(1(0(3(0(0(1(3(0(1(0(3(2(1(x1)))))))))))))))))) (31)
1(1(2(2(2(2(3(0(2(1(3(0(0(0(2(2(2(1(x1)))))))))))))))))) 1(2(2(3(0(1(2(0(0(2(3(1(0(2(2(2(2(1(x1)))))))))))))))))) (32)
1(1(3(0(2(1(2(1(0(3(1(0(3(2(3(0(2(1(x1)))))))))))))))))) 1(1(0(2(3(3(3(3(0(1(1(0(1(2(2(0(2(1(x1)))))))))))))))))) (33)
1(1(3(1(1(2(0(2(1(3(0(2(3(3(3(2(1(3(x1)))))))))))))))))) 1(0(3(2(1(3(3(1(2(1(1(3(2(2(3(0(1(3(x1)))))))))))))))))) (34)
1(3(0(2(0(1(1(1(1(3(0(0(1(1(2(3(1(1(x1)))))))))))))))))) 1(0(1(1(2(1(3(2(3(1(3(0(1(1(0(0(1(1(x1)))))))))))))))))) (35)
1(3(0(2(1(1(3(1(1(0(3(2(3(3(1(1(2(2(x1)))))))))))))))))) 1(2(3(0(3(3(3(2(1(1(0(1(1(1(3(1(2(2(x1)))))))))))))))))) (36)
1(3(0(2(1(3(0(1(2(2(1(1(0(2(3(3(3(2(x1)))))))))))))))))) 3(2(1(1(3(2(1(3(2(3(1(0(0(1(0(2(3(2(x1)))))))))))))))))) (37)
1(3(0(2(1(3(1(2(1(1(0(2(1(1(1(1(1(1(x1)))))))))))))))))) 1(3(1(1(1(1(0(1(2(1(1(0(1(2(3(2(1(1(x1)))))))))))))))))) (38)
1(3(0(2(1(3(2(0(0(3(0(1(2(3(3(2(2(2(x1)))))))))))))))))) 1(3(1(0(0(2(0(1(3(3(2(2(3(2(0(2(3(2(x1)))))))))))))))))) (39)
1(3(1(3(0(1(3(0(0(0(3(3(0(1(2(2(2(3(x1)))))))))))))))))) 1(0(0(2(3(1(0(3(1(3(2(3(2(0(1(3(0(3(x1)))))))))))))))))) (40)
1(3(1(3(0(2(1(0(1(3(0(2(1(2(1(1(3(1(x1)))))))))))))))))) 1(0(1(0(1(3(2(2(0(3(1(2(1(1(1(3(3(1(x1)))))))))))))))))) (41)
1(3(3(1(3(3(1(0(2(1(1(3(1(2(2(3(2(3(x1)))))))))))))))))) 1(3(1(2(1(1(0(3(1(2(3(3(1(2(3(3(2(3(x1)))))))))))))))))) (42)
2(0(0(3(0(3(2(0(2(0(1(2(0(1(3(1(0(3(x1)))))))))))))))))) 2(0(0(3(0(3(2(2(3(0(1(2(0(0(1(1(0(3(x1)))))))))))))))))) (43)
2(0(1(3(1(3(0(2(1(3(0(2(1(1(0(2(3(2(x1)))))))))))))))))) 3(0(1(1(2(1(3(2(3(1(2(0(0(1(2(0(3(2(x1)))))))))))))))))) (44)
2(0(2(1(3(0(0(0(3(1(0(2(2(3(0(2(0(0(x1)))))))))))))))))) 2(0(3(2(0(2(1(2(0(3(0(0(3(0(1(2(0(0(x1)))))))))))))))))) (45)
2(0(2(2(1(0(2(0(2(2(2(1(3(0(2(0(0(0(x1)))))))))))))))))) 2(0(0(1(0(0(0(2(3(0(1(2(2(2(2(2(2(0(x1)))))))))))))))))) (46)
2(0(2(2(2(2(1(3(1(2(3(0(3(0(3(3(3(3(x1)))))))))))))))))) 2(0(3(0(2(1(3(3(0(1(3(2(2(2(2(3(3(3(x1)))))))))))))))))) (47)
2(1(1(3(0(0(3(2(1(2(1(2(3(3(0(3(1(0(x1)))))))))))))))))) 2(1(1(3(2(3(0(1(1(2(0(0(3(3(0(3(1(2(x1)))))))))))))))))) (48)
2(1(2(2(1(0(2(1(2(2(1(3(0(2(2(1(1(1(x1)))))))))))))))))) 2(0(2(1(2(2(3(2(2(1(0(2(1(1(1(2(1(1(x1)))))))))))))))))) (49)
2(1(2(2(2(0(2(0(2(1(3(3(2(2(3(1(3(3(x1)))))))))))))))))) 2(1(3(2(3(2(3(3(2(0(2(2(0(1(1(3(2(2(x1)))))))))))))))))) (50)
2(1(2(2(2(2(0(3(0(3(2(0(1(0(0(2(0(2(x1)))))))))))))))))) 2(2(3(2(2(0(0(1(0(2(0(2(2(1(0(3(0(2(x1)))))))))))))))))) (51)
2(1(3(2(3(2(1(2(2(1(3(0(0(0(3(1(1(2(x1)))))))))))))))))) 2(3(2(0(0(1(1(3(2(2(1(3(1(2(0(1(3(2(x1)))))))))))))))))) (52)
2(2(0(1(0(2(3(3(2(0(1(3(2(1(2(2(3(2(x1)))))))))))))))))) 2(2(1(3(2(2(2(3(2(3(1(2(0(0(0(1(3(2(x1)))))))))))))))))) (53)
2(2(1(0(1(3(0(2(1(0(2(1(0(2(1(1(0(1(x1)))))))))))))))))) 2(2(0(1(1(0(1(3(0(1(1(2(1(2(0(2(0(1(x1)))))))))))))))))) (54)
2(2(1(2(1(3(0(1(0(2(2(0(1(3(3(0(2(1(x1)))))))))))))))))) 2(2(2(1(3(2(2(1(1(2(3(0(0(1(3(0(0(1(x1)))))))))))))))))) (55)
2(2(3(0(0(3(1(3(0(2(3(0(3(3(1(2(3(2(x1)))))))))))))))))) 1(0(2(3(2(3(0(0(3(0(3(3(1(3(2(2(3(2(x1)))))))))))))))))) (56)
2(3(0(1(1(0(2(1(2(0(3(1(0(3(2(1(3(1(x1)))))))))))))))))) 2(0(1(1(1(3(3(1(2(3(2(0(0(1(2(0(3(1(x1)))))))))))))))))) (57)
2(3(0(2(1(2(0(0(3(0(0(2(0(2(3(1(2(0(x1)))))))))))))))))) 3(2(0(1(0(2(2(0(0(0(3(1(0(2(3(2(2(0(x1)))))))))))))))))) (58)
2(3(1(1(1(1(2(0(0(2(0(2(2(1(3(3(1(2(x1)))))))))))))))))) 2(3(2(3(0(2(1(3(1(2(1(2(1(0(0(1(1(2(x1)))))))))))))))))) (59)
3(0(0(0(0(1(2(2(3(0(3(0(3(1(3(3(3(3(x1)))))))))))))))))) 3(2(3(0(0(0(3(2(3(0(0(0(1(1(3(3(3(3(x1)))))))))))))))))) (60)
3(0(1(1(2(3(0(0(3(0(3(1(2(1(3(1(1(0(x1)))))))))))))))))) 3(0(1(2(3(3(1(0(3(0(1(0(3(2(1(1(1(0(x1)))))))))))))))))) (61)
3(0(2(1(1(1(3(1(3(2(1(3(0(0(3(2(3(2(x1)))))))))))))))))) 3(3(0(1(2(2(0(1(1(1(3(2(3(3(0(1(3(2(x1)))))))))))))))))) (62)
3(0(2(2(0(0(2(1(2(0(2(1(0(1(2(0(1(0(x1)))))))))))))))))) 0(1(0(2(0(2(0(0(1(2(1(2(3(2(2(0(1(0(x1)))))))))))))))))) (63)
3(0(2(3(1(2(3(3(0(0(0(3(2(2(2(1(2(1(x1)))))))))))))))))) 3(0(3(3(2(3(2(3(0(2(0(2(0(1(2(1(2(1(x1)))))))))))))))))) (64)
3(0(2(3(2(1(0(1(3(3(2(2(3(0(3(2(0(0(x1)))))))))))))))))) 3(0(3(2(3(3(1(2(3(2(2(0(1(2(0(0(3(0(x1)))))))))))))))))) (65)
3(0(3(0(3(3(1(0(3(0(3(3(1(3(1(1(0(3(x1)))))))))))))))))) 0(1(3(1(3(3(3(3(1(0(0(1(3(3(3(0(0(3(x1)))))))))))))))))) (66)
3(0(3(1(0(0(3(1(3(0(2(0(2(3(0(0(0(0(x1)))))))))))))))))) 0(0(0(2(3(1(1(0(0(0(0(0(3(3(2(3(3(0(x1)))))))))))))))))) (67)
3(1(0(1(2(2(1(3(3(3(0(2(3(1(0(1(2(3(x1)))))))))))))))))) 3(1(0(1(1(2(2(3(2(2(0(0(3(1(3(3(1(3(x1)))))))))))))))))) (68)
3(1(2(2(3(3(1(0(2(1(3(3(2(1(1(2(0(0(x1)))))))))))))))))) 3(1(3(0(2(2(2(1(1(3(1(3(2(3(1(2(0(0(x1)))))))))))))))))) (69)
3(1(3(0(2(0(2(2(2(2(2(1(3(0(0(3(0(0(x1)))))))))))))))))) 2(1(3(2(0(3(1(3(0(0(3(2(2(0(2(2(0(0(x1)))))))))))))))))) (70)
3(1(3(0(2(1(2(3(2(2(3(2(3(2(3(0(0(3(x1)))))))))))))))))) 0(1(1(3(2(3(3(2(3(2(3(2(2(0(3(0(2(3(x1)))))))))))))))))) (71)
3(1(3(0(2(3(3(0(1(3(2(2(2(3(2(1(0(2(x1)))))))))))))))))) 3(2(1(3(2(3(2(3(0(1(3(3(1(2(0(2(0(2(x1)))))))))))))))))) (72)
3(2(1(3(3(1(3(0(3(0(2(2(2(2(1(1(0(2(x1)))))))))))))))))) 3(3(2(2(1(0(0(3(0(2(1(1(2(1(2(3(3(2(x1)))))))))))))))))) (73)
3(3(0(2(0(2(0(3(1(3(0(2(0(0(2(2(0(3(x1)))))))))))))))))) 0(2(3(0(0(2(0(3(3(2(1(0(2(0(3(2(0(3(x1)))))))))))))))))) (74)
3(3(0(2(1(0(3(2(2(2(3(3(0(1(3(3(0(2(x1)))))))))))))))))) 3(3(2(2(3(3(3(3(0(3(1(2(1(0(2(0(0(2(x1)))))))))))))))))) (75)
3(3(1(0(0(0(3(3(0(3(0(0(3(2(1(2(3(3(x1)))))))))))))))))) 3(0(0(1(0(1(3(2(3(3(3(2(3(0(3(0(0(3(x1)))))))))))))))))) (76)
3(3(1(1(3(3(0(0(2(0(3(1(2(1(2(3(0(0(x1)))))))))))))))))) 3(0(1(1(3(3(0(3(0(1(3(0(1(2(3(2(2(0(x1)))))))))))))))))) (77)
3(3(2(0(0(0(3(0(1(0(3(1(2(1(2(1(2(2(x1)))))))))))))))))) 0(2(2(0(1(1(0(3(1(3(2(0(1(0(3(2(3(2(x1)))))))))))))))))) (78)
3(3(2(0(2(1(3(1(2(2(2(2(1(2(1(0(3(2(x1)))))))))))))))))) 3(0(2(2(3(1(1(2(1(3(2(2(1(2(0(2(3(2(x1)))))))))))))))))) (79)
3(3(3(0(1(2(1(3(1(1(1(3(0(3(0(0(3(0(x1)))))))))))))))))) 3(3(3(1(3(2(1(3(1(1(0(0(3(1(3(0(0(0(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
0(2(0(3(3(2(1(0(3(0(2(2(0(3(2(0(0(0(x1)))))))))))))))))) 0(0(0(0(0(2(3(3(0(0(2(2(2(3(2(3(1(0(x1)))))))))))))))))) (81)
3(0(1(3(0(3(0(3(0(2(0(3(1(0(3(0(0(0(x1)))))))))))))))))) 3(3(0(3(0(2(3(0(0(3(3(0(1(0(0(1(0(0(x1)))))))))))))))))) (82)
2(0(0(3(0(3(1(0(0(1(1(3(0(3(0(2(0(0(x1)))))))))))))))))) 2(0(0(3(0(2(0(0(3(3(0(3(0(1(1(1(0(0(x1)))))))))))))))))) (83)
2(2(2(2(0(3(3(2(1(1(2(3(1(3(0(2(0(0(x1)))))))))))))))))) 2(2(1(0(3(2(0(2(0(2(3(1(0(2(1(3(2(3(x1)))))))))))))))))) (84)
0(2(0(1(1(3(3(0(3(2(2(1(2(0(3(2(0(0(x1)))))))))))))))))) 0(2(3(0(1(2(0(1(3(0(2(3(3(2(2(1(0(0(x1)))))))))))))))))) (85)
2(2(0(3(1(2(0(3(3(2(0(1(3(2(1(3(0(0(x1)))))))))))))))))) 2(3(1(2(0(0(3(1(0(2(2(1(3(3(0(2(3(0(x1)))))))))))))))))) (86)
0(2(2(1(0(2(1(0(0(3(1(1(2(2(0(0(1(0(x1)))))))))))))))))) 0(2(2(3(0(1(1(0(2(1(2(2(0(0(0(1(1(0(x1)))))))))))))))))) (87)
3(3(0(2(3(3(1(1(2(2(1(2(0(3(2(0(1(0(x1)))))))))))))))))) 3(1(1(0(3(2(3(1(0(2(3(3(2(2(0(2(1(0(x1)))))))))))))))))) (88)
3(0(3(0(2(0(3(2(1(0(3(0(2(0(3(1(1(0(x1)))))))))))))))))) 3(2(3(3(1(0(0(0(2(1(0(1(3(3(2(0(0(0(x1)))))))))))))))))) (89)
3(3(1(1(2(2(0(3(0(1(3(2(0(2(3(2(1(0(x1)))))))))))))))))) 3(0(1(0(0(2(3(3(2(1(1(3(2(3(2(2(1(0(x1)))))))))))))))))) (90)
1(2(0(0(1(3(3(1(2(0(3(1(2(2(3(2(1(0(x1)))))))))))))))))) 1(2(2(3(1(2(3(1(0(3(2(0(1(0(1(2(3(0(x1)))))))))))))))))) (91)
2(1(2(3(3(3(1(1(1(3(3(3(3(0(3(1(2(0(x1)))))))))))))))))) 2(1(0(2(3(3(3(1(3(1(0(1(3(3(3(2(3(1(x1)))))))))))))))))) (92)
2(1(0(1(1(3(3(0(1(0(3(3(1(3(0(2(2(0(x1)))))))))))))))))) 2(1(3(1(0(1(3(0(0(1(3(2(3(0(2(1(3(0(x1)))))))))))))))))) (93)
0(1(1(1(1(3(3(0(3(1(0(0(3(1(0(0(3(0(x1)))))))))))))))))) 0(1(1(3(0(1(1(3(1(0(1(3(0(0(3(0(3(0(x1)))))))))))))))))) (94)
0(2(0(2(1(2(1(0(0(0(3(0(1(3(0(0(3(0(x1)))))))))))))))))) 0(2(3(0(0(1(0(0(3(2(2(0(1(1(0(0(3(0(x1)))))))))))))))))) (95)
0(2(2(2(0(1(2(0(2(2(0(0(0(0(2(0(3(0(x1)))))))))))))))))) 0(0(0(0(2(0(0(2(2(3(0(0(2(1(2(2(2(0(x1)))))))))))))))))) (96)
3(0(1(2(0(2(3(0(0(3(1(0(3(0(3(0(3(0(x1)))))))))))))))))) 3(0(3(0(0(3(0(2(3(0(0(1(0(0(3(2(3(1(x1)))))))))))))))))) (97)
1(3(0(2(1(3(2(2(0(3(1(0(3(1(3(0(3(0(x1)))))))))))))))))) 1(3(2(1(3(2(1(0(3(2(3(0(0(3(0(3(0(1(x1)))))))))))))))))) (98)
2(0(2(0(3(3(1(2(3(2(0(0(2(2(3(0(3(0(x1)))))))))))))))))) 2(3(2(3(2(3(2(0(0(0(2(2(0(0(1(3(3(0(x1)))))))))))))))))) (99)
2(2(2(3(3(2(1(2(3(3(2(1(2(3(2(1(3(0(x1)))))))))))))))))) 2(2(2(3(2(2(3(1(3(3(0(2(1(3(2(3(2(1(x1)))))))))))))))))) (100)
1(1(2(2(1(1(2(0(0(1(1(1(0(1(0(2(3(0(x1)))))))))))))))))) 1(1(2(1(0(1(1(0(0(2(1(2(1(0(1(2(3(0(x1)))))))))))))))))) (101)
0(0(3(0(3(2(3(0(2(0(3(2(2(1(1(1(0(1(x1)))))))))))))))))) 0(0(1(2(0(2(3(0(2(3(0(1(1(3(0(2(3(1(x1)))))))))))))))))) (102)
2(2(1(0(2(0(2(1(2(3(3(0(2(2(2(1(0(1(x1)))))))))))))))))) 2(3(2(3(2(0(0(1(1(2(2(0(2(1(2(2(0(1(x1)))))))))))))))))) (103)
3(3(2(2(0(1(3(3(2(1(2(0(3(3(0(3(0(1(x1)))))))))))))))))) 3(3(2(3(0(0(3(2(2(0(1(3(3(2(1(3(0(1(x1)))))))))))))))))) (104)
3(3(2(2(1(3(3(1(1(3(1(3(0(3(1(0(1(1(x1)))))))))))))))))) 0(1(2(3(2(3(1(3(1(3(1(3(0(1(3(1(3(1(x1)))))))))))))))))) (105)
0(2(0(0(1(3(3(1(2(2(2(3(1(2(0(1(1(1(x1)))))))))))))))))) 0(2(1(0(0(3(2(2(3(1(1(2(1(2(3(1(0(1(x1)))))))))))))))))) (106)
0(1(3(3(0(2(2(2(2(2(1(2(1(1(1(1(1(1(x1)))))))))))))))))) 2(1(1(2(0(1(0(2(1(1(2(1(3(2(2(3(1(1(x1)))))))))))))))))) (107)
3(1(2(0(0(3(3(0(1(3(1(2(1(0(2(1(1(1(x1)))))))))))))))))) 3(1(3(1(0(0(2(3(0(1(3(0(2(2(1(1(1(1(x1)))))))))))))))))) (108)
1(3(3(3(3(1(0(1(2(2(0(3(0(3(2(1(1(1(x1)))))))))))))))))) 1(0(3(1(3(1(0(2(3(3(1(3(2(1(0(3(2(1(x1)))))))))))))))))) (109)
3(1(1(1(3(2(0(1(1(3(1(0(1(0(3(1(1(1(x1)))))))))))))))))) 3(1(1(2(1(3(1(0(1(0(1(1(0(3(1(3(1(1(x1)))))))))))))))))) (110)
1(2(0(2(1(0(0(0(3(3(3(0(2(0(3(1(1(1(x1)))))))))))))))))) 1(2(3(0(1(0(3(1(0(0(3(0(1(0(2(3(2(1(x1)))))))))))))))))) (111)
1(2(2(2(0(0(0(3(1(2(0(3(2(2(2(2(1(1(x1)))))))))))))))))) 1(2(2(2(2(0(1(3(2(0(0(2(1(0(3(2(2(1(x1)))))))))))))))))) (112)
1(2(0(3(2(3(0(1(3(0(1(2(1(2(0(3(1(1(x1)))))))))))))))))) 1(2(0(2(2(1(0(1(1(0(3(3(3(3(2(0(1(1(x1)))))))))))))))))) (113)
3(1(2(3(3(3(2(0(3(1(2(0(2(1(1(3(1(1(x1)))))))))))))))))) 3(1(0(3(2(2(3(1(1(2(1(3(3(1(2(3(0(1(x1)))))))))))))))))) (114)
1(1(3(2(1(1(0(0(3(1(1(1(1(0(2(0(3(1(x1)))))))))))))))))) 1(1(0(0(1(1(0(3(1(3(2(3(1(2(1(1(0(1(x1)))))))))))))))))) (115)
2(2(1(1(3(3(2(3(0(1(1(3(1(1(2(0(3(1(x1)))))))))))))))))) 2(2(1(3(1(1(1(0(1(1(2(3(3(3(0(3(2(1(x1)))))))))))))))))) (116)
2(3(3(3(2(0(1(1(2(2(1(0(3(1(2(0(3(1(x1)))))))))))))))))) 2(3(2(0(1(0(0(1(3(2(3(1(2(3(1(1(2(3(x1)))))))))))))))))) (117)
1(1(1(1(1(1(2(0(1(1(2(1(3(1(2(0(3(1(x1)))))))))))))))))) 1(1(2(3(2(1(0(1(1(2(1(0(1(1(1(1(3(1(x1)))))))))))))))))) (118)
2(2(2(3(3(2(1(0(3(0(0(2(3(1(2(0(3(1(x1)))))))))))))))))) 2(3(2(0(2(3(2(2(3(3(1(0(2(0(0(1(3(1(x1)))))))))))))))))) (119)
3(2(2(2(1(0(3(3(0(0(0(3(1(0(3(1(3(1(x1)))))))))))))))))) 3(0(3(1(0(2(3(2(3(1(3(0(1(3(2(0(0(1(x1)))))))))))))))))) (120)
1(3(1(1(2(1(2(0(3(1(0(1(2(0(3(1(3(1(x1)))))))))))))))))) 1(3(3(1(1(1(2(1(3(0(2(2(3(1(0(1(0(1(x1)))))))))))))))))) (121)
3(2(3(2(2(1(3(1(1(2(0(1(3(3(1(3(3(1(x1)))))))))))))))))) 3(2(3(3(2(1(3(3(2(1(3(0(1(1(2(1(3(1(x1)))))))))))))))))) (122)
3(0(1(3(1(0(2(1(0(2(0(2(3(0(3(0(0(2(x1)))))))))))))))))) 3(0(1(1(0(0(2(1(0(3(2(2(3(0(3(0(0(2(x1)))))))))))))))))) (123)
2(3(2(0(1(1(2(0(3(1(2(0(3(1(3(1(0(2(x1)))))))))))))))))) 2(3(0(2(1(0(0(2(1(3(2(3(1(2(1(1(0(3(x1)))))))))))))))))) (124)
0(0(2(0(3(2(2(0(1(3(0(0(0(3(1(2(0(2(x1)))))))))))))))))) 0(0(2(1(0(3(0(0(3(0(2(1(2(0(2(3(0(2(x1)))))))))))))))))) (125)
0(0(0(2(0(3(1(2(2(2(0(2(0(1(2(2(0(2(x1)))))))))))))))))) 0(2(2(2(2(2(2(1(0(3(2(0(0(0(1(0(0(2(x1)))))))))))))))))) (126)
3(3(3(3(0(3(0(3(2(1(3(1(2(2(2(2(0(2(x1)))))))))))))))))) 3(3(3(2(2(2(2(3(1(0(3(3(1(2(0(3(0(2(x1)))))))))))))))))) (127)
0(1(3(0(3(3(2(1(2(1(2(3(0(0(3(1(1(2(x1)))))))))))))))))) 2(1(3(0(3(3(0(0(2(1(1(0(3(2(3(1(1(2(x1)))))))))))))))))) (128)
1(1(1(2(2(0(3(1(2(2(1(2(0(1(2(2(1(2(x1)))))))))))))))))) 1(1(2(1(1(1(2(0(1(2(2(3(2(2(1(2(0(2(x1)))))))))))))))))) (129)
3(3(1(3(2(2(3(3(1(2(0(2(0(2(2(2(1(2(x1)))))))))))))))))) 2(2(3(1(1(0(2(2(0(2(3(3(2(3(2(3(1(2(x1)))))))))))))))))) (130)
2(0(2(0(0(1(0(2(3(0(3(0(2(2(2(2(1(2(x1)))))))))))))))))) 2(0(3(0(1(2(2(0(2(0(1(0(0(2(2(3(2(2(x1)))))))))))))))))) (131)
2(1(1(3(0(0(0(3(1(2(2(1(2(3(2(3(1(2(x1)))))))))))))))))) 2(3(1(0(2(1(3(1(2(2(3(1(1(0(0(2(3(2(x1)))))))))))))))))) (132)
2(3(2(2(1(2(3(1(0(2(3(3(2(0(1(0(2(2(x1)))))))))))))))))) 2(3(1(0(0(0(2(1(3(2(3(2(2(2(3(1(2(2(x1)))))))))))))))))) (133)
1(0(1(1(2(0(1(2(0(1(2(0(3(1(0(1(2(2(x1)))))))))))))))))) 1(0(2(0(2(1(2(1(1(0(3(1(0(1(1(0(2(2(x1)))))))))))))))))) (134)
1(2(0(3(3(1(0(2(2(0(1(0(3(1(2(1(2(2(x1)))))))))))))))))) 1(0(0(3(1(0(0(3(2(1(1(2(2(3(1(2(2(2(x1)))))))))))))))))) (135)
2(3(2(1(3(3(0(3(2(0(3(1(3(0(0(3(2(2(x1)))))))))))))))))) 2(3(2(2(3(1(3(3(0(3(0(0(3(2(3(2(0(1(x1)))))))))))))))))) (136)
1(3(1(2(3(0(1(3(0(2(1(2(0(1(1(0(3(2(x1)))))))))))))))))) 1(3(0(2(1(0(0(2(3(2(1(3(3(1(1(1(0(2(x1)))))))))))))))))) (137)
0(2(1(3(2(0(2(0(0(3(0(0(2(1(2(0(3(2(x1)))))))))))))))))) 0(2(2(3(2(0(1(3(0(0(0(2(2(0(1(0(2(3(x1)))))))))))))))))) (138)
2(1(3(3(1(2(2(0(2(0(0(2(1(1(1(1(3(2(x1)))))))))))))))))) 2(1(1(0(0(1(2(1(2(1(3(1(2(0(3(2(3(2(x1)))))))))))))))))) (139)
3(3(3(3(1(3(0(3(0(3(2(2(1(0(0(0(0(3(x1)))))))))))))))))) 3(3(3(3(1(1(0(0(0(3(2(3(0(0(0(3(2(3(x1)))))))))))))))))) (140)
0(1(1(3(1(2(1(3(0(3(0(0(3(2(1(1(0(3(x1)))))))))))))))))) 0(1(1(1(2(3(0(1(0(3(0(1(3(3(2(1(0(3(x1)))))))))))))))))) (141)
2(3(2(3(0(0(3(1(2(3(1(3(1(1(1(2(0(3(x1)))))))))))))))))) 2(3(1(0(3(3(2(3(1(1(1(0(2(2(1(0(3(3(x1)))))))))))))))))) (142)
0(1(0(2(1(0(1(2(0(2(1(2(0(0(2(2(0(3(x1)))))))))))))))))) 0(1(0(2(2(3(2(1(2(1(0(0(2(0(2(0(1(0(x1)))))))))))))))))) (143)
1(2(1(2(2(2(3(0(0(0(3(3(2(1(3(2(0(3(x1)))))))))))))))))) 1(2(1(2(1(0(2(0(2(0(3(2(3(2(3(3(0(3(x1)))))))))))))))))) (144)
0(0(2(3(0(3(2(2(3(3(1(0(1(2(3(2(0(3(x1)))))))))))))))))) 0(3(0(0(2(1(0(2(2(3(2(1(3(3(2(3(0(3(x1)))))))))))))))))) (145)
3(0(1(1(3(1(3(3(0(3(0(1(3(3(0(3(0(3(x1)))))))))))))))))) 3(0(0(3(3(3(1(0(0(1(3(3(3(3(1(3(1(0(x1)))))))))))))))))) (146)
0(0(0(0(3(2(0(2(0(3(1(3(0(0(1(3(0(3(x1)))))))))))))))))) 0(3(3(2(3(3(0(0(0(0(0(1(1(3(2(0(0(0(x1)))))))))))))))))) (147)
3(2(1(0(1(3(2(0(3(3(3(1(2(2(1(0(1(3(x1)))))))))))))))))) 3(1(3(3(1(3(0(0(2(2(3(2(2(1(1(0(1(3(x1)))))))))))))))))) (148)
0(0(2(1(1(2(3(3(1(2(0(1(3(3(2(2(1(3(x1)))))))))))))))))) 0(0(2(1(3(2(3(1(3(1(1(2(2(2(0(3(1(3(x1)))))))))))))))))) (149)
0(0(3(0(0(3(1(2(2(2(2(2(0(2(0(3(1(3(x1)))))))))))))))))) 0(0(2(2(0(2(2(3(0(0(3(1(3(0(2(3(1(2(x1)))))))))))))))))) (150)
3(0(0(3(2(3(2(3(2(2(3(2(1(2(0(3(1(3(x1)))))))))))))))))) 3(2(0(3(0(2(2(3(2(3(2(3(3(2(3(1(1(0(x1)))))))))))))))))) (151)
2(0(1(2(3(2(2(2(3(1(0(3(3(2(0(3(1(3(x1)))))))))))))))))) 2(0(2(0(2(1(3(3(1(0(3(2(3(2(3(1(2(3(x1)))))))))))))))))) (152)
2(0(1(1(2(2(2(2(0(3(0(3(1(3(3(1(2(3(x1)))))))))))))))))) 2(3(3(2(1(2(1(1(2(0(3(0(0(1(2(2(3(3(x1)))))))))))))))))) (153)
3(0(2(2(0(0(2(0(3(1(3(0(2(0(2(0(3(3(x1)))))))))))))))))) 3(0(2(3(0(2(0(1(2(3(3(0(2(0(0(3(2(0(x1)))))))))))))))))) (154)
2(0(3(3(1(0(3(3(2(2(2(3(0(1(2(0(3(3(x1)))))))))))))))))) 2(0(0(2(0(1(2(1(3(0(3(3(3(3(2(2(3(3(x1)))))))))))))))))) (155)
3(3(2(1(2(3(0(0(3(0(3(3(0(0(0(1(3(3(x1)))))))))))))))))) 3(0(0(3(0(3(2(3(3(3(2(3(1(0(1(0(0(3(x1)))))))))))))))))) (156)
0(0(3(2(1(2(1(3(0(2(0(0(3(3(1(1(3(3(x1)))))))))))))))))) 0(2(2(3(2(1(0(3(1(0(3(0(3(3(1(1(0(3(x1)))))))))))))))))) (157)
2(2(1(2(1(2(1(3(0(1(0(3(0(0(0(2(3(3(x1)))))))))))))))))) 2(3(2(3(0(1(0(2(3(1(3(0(1(1(0(2(2(0(x1)))))))))))))))))) (158)
2(3(0(1(2(1(2(2(2(2(1(3(1(2(0(2(3(3(x1)))))))))))))))))) 2(3(2(0(2(1(2(2(3(1(2(1(1(3(2(2(0(3(x1)))))))))))))))))) (159)
0(3(0(0(3(0(3(1(1(1(3(1(2(1(0(3(3(3(x1)))))))))))))))))) 0(0(0(3(1(3(0(0(1(1(3(1(2(3(1(3(3(3(x1)))))))))))))))))) (160)

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS
0(2(0(3(3(2(1(0(3(0(2(2(0(3(2(0(0(0(x1)))))))))))))))))) 0(0(0(0(0(2(3(3(0(0(2(2(2(3(2(3(1(0(x1)))))))))))))))))) (81)
3(0(1(3(0(3(0(3(0(2(0(3(1(0(3(0(0(0(x1)))))))))))))))))) 3(3(0(3(0(2(3(0(0(3(3(0(1(0(0(1(0(0(x1)))))))))))))))))) (82)
2(0(0(3(0(3(1(0(0(1(1(3(0(3(0(2(0(0(x1)))))))))))))))))) 2(0(0(3(0(2(0(0(3(3(0(3(0(1(1(1(0(0(x1)))))))))))))))))) (83)
2(2(2(2(0(3(3(2(1(1(2(3(1(3(0(2(0(0(x1)))))))))))))))))) 2(2(1(0(3(2(0(2(0(2(3(1(0(2(1(3(2(3(x1)))))))))))))))))) (84)
0(2(0(1(1(3(3(0(3(2(2(1(2(0(3(2(0(0(x1)))))))))))))))))) 0(2(3(0(1(2(0(1(3(0(2(3(3(2(2(1(0(0(x1)))))))))))))))))) (85)
2(2(0(3(1(2(0(3(3(2(0(1(3(2(1(3(0(0(x1)))))))))))))))))) 2(3(1(2(0(0(3(1(0(2(2(1(3(3(0(2(3(0(x1)))))))))))))))))) (86)
0(2(2(1(0(2(1(0(0(3(1(1(2(2(0(0(1(0(x1)))))))))))))))))) 0(2(2(3(0(1(1(0(2(1(2(2(0(0(0(1(1(0(x1)))))))))))))))))) (87)
3(3(0(2(3(3(1(1(2(2(1(2(0(3(2(0(1(0(x1)))))))))))))))))) 3(1(1(0(3(2(3(1(0(2(3(3(2(2(0(2(1(0(x1)))))))))))))))))) (88)
3(0(3(0(2(0(3(2(1(0(3(0(2(0(3(1(1(0(x1)))))))))))))))))) 3(2(3(3(1(0(0(0(2(1(0(1(3(3(2(0(0(0(x1)))))))))))))))))) (89)
3(3(1(1(2(2(0(3(0(1(3(2(0(2(3(2(1(0(x1)))))))))))))))))) 3(0(1(0(0(2(3(3(2(1(1(3(2(3(2(2(1(0(x1)))))))))))))))))) (90)
1(2(0(0(1(3(3(1(2(0(3(1(2(2(3(2(1(0(x1)))))))))))))))))) 1(2(2(3(1(2(3(1(0(3(2(0(1(0(1(2(3(0(x1)))))))))))))))))) (91)
2(1(2(3(3(3(1(1(1(3(3(3(3(0(3(1(2(0(x1)))))))))))))))))) 2(1(0(2(3(3(3(1(3(1(0(1(3(3(3(2(3(1(x1)))))))))))))))))) (92)
2(1(0(1(1(3(3(0(1(0(3(3(1(3(0(2(2(0(x1)))))))))))))))))) 2(1(3(1(0(1(3(0(0(1(3(2(3(0(2(1(3(0(x1)))))))))))))))))) (93)
0(1(1(1(1(3(3(0(3(1(0(0(3(1(0(0(3(0(x1)))))))))))))))))) 0(1(1(3(0(1(1(3(1(0(1(3(0(0(3(0(3(0(x1)))))))))))))))))) (94)
0(2(0(2(1(2(1(0(0(0(3(0(1(3(0(0(3(0(x1)))))))))))))))))) 0(2(3(0(0(1(0(0(3(2(2(0(1(1(0(0(3(0(x1)))))))))))))))))) (95)
0(2(2(2(0(1(2(0(2(2(0(0(0(0(2(0(3(0(x1)))))))))))))))))) 0(0(0(0(2(0(0(2(2(3(0(0(2(1(2(2(2(0(x1)))))))))))))))))) (96)
3(0(1(2(0(2(3(0(0(3(1(0(3(0(3(0(3(0(x1)))))))))))))))))) 3(0(3(0(0(3(0(2(3(0(0(1(0(0(3(2(3(1(x1)))))))))))))))))) (97)
1(3(0(2(1(3(2(2(0(3(1(0(3(1(3(0(3(0(x1)))))))))))))))))) 1(3(2(1(3(2(1(0(3(2(3(0(0(3(0(3(0(1(x1)))))))))))))))))) (98)
2(0(2(0(3(3(1(2(3(2(0(0(2(2(3(0(3(0(x1)))))))))))))))))) 2(3(2(3(2(3(2(0(0(0(2(2(0(0(1(3(3(0(x1)))))))))))))))))) (99)
2(2(2(3(3(2(1(2(3(3(2(1(2(3(2(1(3(0(x1)))))))))))))))))) 2(2(2(3(2(2(3(1(3(3(0(2(1(3(2(3(2(1(x1)))))))))))))))))) (100)
1(1(2(2(1(1(2(0(0(1(1(1(0(1(0(2(3(0(x1)))))))))))))))))) 1(1(2(1(0(1(1(0(0(2(1(2(1(0(1(2(3(0(x1)))))))))))))))))) (101)
0(0(3(0(3(2(3(0(2(0(3(2(2(1(1(1(0(1(x1)))))))))))))))))) 0(0(1(2(0(2(3(0(2(3(0(1(1(3(0(2(3(1(x1)))))))))))))))))) (102)
2(2(1(0(2(0(2(1(2(3(3(0(2(2(2(1(0(1(x1)))))))))))))))))) 2(3(2(3(2(0(0(1(1(2(2(0(2(1(2(2(0(1(x1)))))))))))))))))) (103)
3(3(2(2(0(1(3(3(2(1(2(0(3(3(0(3(0(1(x1)))))))))))))))))) 3(3(2(3(0(0(3(2(2(0(1(3(3(2(1(3(0(1(x1)))))))))))))))))) (104)
0(2(0(0(1(3(3(1(2(2(2(3(1(2(0(1(1(1(x1)))))))))))))))))) 0(2(1(0(0(3(2(2(3(1(1(2(1(2(3(1(0(1(x1)))))))))))))))))) (106)
3(1(2(0(0(3(3(0(1(3(1(2(1(0(2(1(1(1(x1)))))))))))))))))) 3(1(3(1(0(0(2(3(0(1(3(0(2(2(1(1(1(1(x1)))))))))))))))))) (108)
1(3(3(3(3(1(0(1(2(2(0(3(0(3(2(1(1(1(x1)))))))))))))))))) 1(0(3(1(3(1(0(2(3(3(1(3(2(1(0(3(2(1(x1)))))))))))))))))) (109)
3(1(1(1(3(2(0(1(1(3(1(0(1(0(3(1(1(1(x1)))))))))))))))))) 3(1(1(2(1(3(1(0(1(0(1(1(0(3(1(3(1(1(x1)))))))))))))))))) (110)
1(2(0(2(1(0(0(0(3(3(3(0(2(0(3(1(1(1(x1)))))))))))))))))) 1(2(3(0(1(0(3(1(0(0(3(0(1(0(2(3(2(1(x1)))))))))))))))))) (111)
1(2(2(2(0(0(0(3(1(2(0(3(2(2(2(2(1(1(x1)))))))))))))))))) 1(2(2(2(2(0(1(3(2(0(0(2(1(0(3(2(2(1(x1)))))))))))))))))) (112)
1(2(0(3(2(3(0(1(3(0(1(2(1(2(0(3(1(1(x1)))))))))))))))))) 1(2(0(2(2(1(0(1(1(0(3(3(3(3(2(0(1(1(x1)))))))))))))))))) (113)
3(1(2(3(3(3(2(0(3(1(2(0(2(1(1(3(1(1(x1)))))))))))))))))) 3(1(0(3(2(2(3(1(1(2(1(3(3(1(2(3(0(1(x1)))))))))))))))))) (114)
1(1(3(2(1(1(0(0(3(1(1(1(1(0(2(0(3(1(x1)))))))))))))))))) 1(1(0(0(1(1(0(3(1(3(2(3(1(2(1(1(0(1(x1)))))))))))))))))) (115)
2(2(1(1(3(3(2(3(0(1(1(3(1(1(2(0(3(1(x1)))))))))))))))))) 2(2(1(3(1(1(1(0(1(1(2(3(3(3(0(3(2(1(x1)))))))))))))))))) (116)
2(3(3(3(2(0(1(1(2(2(1(0(3(1(2(0(3(1(x1)))))))))))))))))) 2(3(2(0(1(0(0(1(3(2(3(1(2(3(1(1(2(3(x1)))))))))))))))))) (117)
1(1(1(1(1(1(2(0(1(1(2(1(3(1(2(0(3(1(x1)))))))))))))))))) 1(1(2(3(2(1(0(1(1(2(1(0(1(1(1(1(3(1(x1)))))))))))))))))) (118)
2(2(2(3(3(2(1(0(3(0(0(2(3(1(2(0(3(1(x1)))))))))))))))))) 2(3(2(0(2(3(2(2(3(3(1(0(2(0(0(1(3(1(x1)))))))))))))))))) (119)
3(2(2(2(1(0(3(3(0(0(0(3(1(0(3(1(3(1(x1)))))))))))))))))) 3(0(3(1(0(2(3(2(3(1(3(0(1(3(2(0(0(1(x1)))))))))))))))))) (120)
1(3(1(1(2(1(2(0(3(1(0(1(2(0(3(1(3(1(x1)))))))))))))))))) 1(3(3(1(1(1(2(1(3(0(2(2(3(1(0(1(0(1(x1)))))))))))))))))) (121)
3(2(3(2(2(1(3(1(1(2(0(1(3(3(1(3(3(1(x1)))))))))))))))))) 3(2(3(3(2(1(3(3(2(1(3(0(1(1(2(1(3(1(x1)))))))))))))))))) (122)
3(0(1(3(1(0(2(1(0(2(0(2(3(0(3(0(0(2(x1)))))))))))))))))) 3(0(1(1(0(0(2(1(0(3(2(2(3(0(3(0(0(2(x1)))))))))))))))))) (123)
2(3(2(0(1(1(2(0(3(1(2(0(3(1(3(1(0(2(x1)))))))))))))))))) 2(3(0(2(1(0(0(2(1(3(2(3(1(2(1(1(0(3(x1)))))))))))))))))) (124)
0(0(2(0(3(2(2(0(1(3(0(0(0(3(1(2(0(2(x1)))))))))))))))))) 0(0(2(1(0(3(0(0(3(0(2(1(2(0(2(3(0(2(x1)))))))))))))))))) (125)
0(0(0(2(0(3(1(2(2(2(0(2(0(1(2(2(0(2(x1)))))))))))))))))) 0(2(2(2(2(2(2(1(0(3(2(0(0(0(1(0(0(2(x1)))))))))))))))))) (126)
3(3(3(3(0(3(0(3(2(1(3(1(2(2(2(2(0(2(x1)))))))))))))))))) 3(3(3(2(2(2(2(3(1(0(3(3(1(2(0(3(0(2(x1)))))))))))))))))) (127)
1(1(1(2(2(0(3(1(2(2(1(2(0(1(2(2(1(2(x1)))))))))))))))))) 1(1(2(1(1(1(2(0(1(2(2(3(2(2(1(2(0(2(x1)))))))))))))))))) (129)
2(0(2(0(0(1(0(2(3(0(3(0(2(2(2(2(1(2(x1)))))))))))))))))) 2(0(3(0(1(2(2(0(2(0(1(0(0(2(2(3(2(2(x1)))))))))))))))))) (131)
2(1(1(3(0(0(0(3(1(2(2(1(2(3(2(3(1(2(x1)))))))))))))))))) 2(3(1(0(2(1(3(1(2(2(3(1(1(0(0(2(3(2(x1)))))))))))))))))) (132)
2(3(2(2(1(2(3(1(0(2(3(3(2(0(1(0(2(2(x1)))))))))))))))))) 2(3(1(0(0(0(2(1(3(2(3(2(2(2(3(1(2(2(x1)))))))))))))))))) (133)
1(0(1(1(2(0(1(2(0(1(2(0(3(1(0(1(2(2(x1)))))))))))))))))) 1(0(2(0(2(1(2(1(1(0(3(1(0(1(1(0(2(2(x1)))))))))))))))))) (134)
1(2(0(3(3(1(0(2(2(0(1(0(3(1(2(1(2(2(x1)))))))))))))))))) 1(0(0(3(1(0(0(3(2(1(1(2(2(3(1(2(2(2(x1)))))))))))))))))) (135)
2(3(2(1(3(3(0(3(2(0(3(1(3(0(0(3(2(2(x1)))))))))))))))))) 2(3(2(2(3(1(3(3(0(3(0(0(3(2(3(2(0(1(x1)))))))))))))))))) (136)
1(3(1(2(3(0(1(3(0(2(1(2(0(1(1(0(3(2(x1)))))))))))))))))) 1(3(0(2(1(0(0(2(3(2(1(3(3(1(1(1(0(2(x1)))))))))))))))))) (137)
0(2(1(3(2(0(2(0(0(3(0(0(2(1(2(0(3(2(x1)))))))))))))))))) 0(2(2(3(2(0(1(3(0(0(0(2(2(0(1(0(2(3(x1)))))))))))))))))) (138)
2(1(3(3(1(2(2(0(2(0(0(2(1(1(1(1(3(2(x1)))))))))))))))))) 2(1(1(0(0(1(2(1(2(1(3(1(2(0(3(2(3(2(x1)))))))))))))))))) (139)
3(3(3(3(1(3(0(3(0(3(2(2(1(0(0(0(0(3(x1)))))))))))))))))) 3(3(3(3(1(1(0(0(0(3(2(3(0(0(0(3(2(3(x1)))))))))))))))))) (140)
0(1(1(3(1(2(1(3(0(3(0(0(3(2(1(1(0(3(x1)))))))))))))))))) 0(1(1(1(2(3(0(1(0(3(0(1(3(3(2(1(0(3(x1)))))))))))))))))) (141)
2(3(2(3(0(0(3(1(2(3(1(3(1(1(1(2(0(3(x1)))))))))))))))))) 2(3(1(0(3(3(2(3(1(1(1(0(2(2(1(0(3(3(x1)))))))))))))))))) (142)
0(1(0(2(1(0(1(2(0(2(1(2(0(0(2(2(0(3(x1)))))))))))))))))) 0(1(0(2(2(3(2(1(2(1(0(0(2(0(2(0(1(0(x1)))))))))))))))))) (143)
1(2(1(2(2(2(3(0(0(0(3(3(2(1(3(2(0(3(x1)))))))))))))))))) 1(2(1(2(1(0(2(0(2(0(3(2(3(2(3(3(0(3(x1)))))))))))))))))) (144)
0(0(2(3(0(3(2(2(3(3(1(0(1(2(3(2(0(3(x1)))))))))))))))))) 0(3(0(0(2(1(0(2(2(3(2(1(3(3(2(3(0(3(x1)))))))))))))))))) (145)
3(0(1(1(3(1(3(3(0(3(0(1(3(3(0(3(0(3(x1)))))))))))))))))) 3(0(0(3(3(3(1(0(0(1(3(3(3(3(1(3(1(0(x1)))))))))))))))))) (146)
0(0(0(0(3(2(0(2(0(3(1(3(0(0(1(3(0(3(x1)))))))))))))))))) 0(3(3(2(3(3(0(0(0(0(0(1(1(3(2(0(0(0(x1)))))))))))))))))) (147)
3(2(1(0(1(3(2(0(3(3(3(1(2(2(1(0(1(3(x1)))))))))))))))))) 3(1(3(3(1(3(0(0(2(2(3(2(2(1(1(0(1(3(x1)))))))))))))))))) (148)
0(0(2(1(1(2(3(3(1(2(0(1(3(3(2(2(1(3(x1)))))))))))))))))) 0(0(2(1(3(2(3(1(3(1(1(2(2(2(0(3(1(3(x1)))))))))))))))))) (149)
0(0(3(0(0(3(1(2(2(2(2(2(0(2(0(3(1(3(x1)))))))))))))))))) 0(0(2(2(0(2(2(3(0(0(3(1(3(0(2(3(1(2(x1)))))))))))))))))) (150)
3(0(0(3(2(3(2(3(2(2(3(2(1(2(0(3(1(3(x1)))))))))))))))))) 3(2(0(3(0(2(2(3(2(3(2(3(3(2(3(1(1(0(x1)))))))))))))))))) (151)
2(0(1(2(3(2(2(2(3(1(0(3(3(2(0(3(1(3(x1)))))))))))))))))) 2(0(2(0(2(1(3(3(1(0(3(2(3(2(3(1(2(3(x1)))))))))))))))))) (152)
2(0(1(1(2(2(2(2(0(3(0(3(1(3(3(1(2(3(x1)))))))))))))))))) 2(3(3(2(1(2(1(1(2(0(3(0(0(1(2(2(3(3(x1)))))))))))))))))) (153)
3(0(2(2(0(0(2(0(3(1(3(0(2(0(2(0(3(3(x1)))))))))))))))))) 3(0(2(3(0(2(0(1(2(3(3(0(2(0(0(3(2(0(x1)))))))))))))))))) (154)
2(0(3(3(1(0(3(3(2(2(2(3(0(1(2(0(3(3(x1)))))))))))))))))) 2(0(0(2(0(1(2(1(3(0(3(3(3(3(2(2(3(3(x1)))))))))))))))))) (155)
3(3(2(1(2(3(0(0(3(0(3(3(0(0(0(1(3(3(x1)))))))))))))))))) 3(0(0(3(0(3(2(3(3(3(2(3(1(0(1(0(0(3(x1)))))))))))))))))) (156)
0(0(3(2(1(2(1(3(0(2(0(0(3(3(1(1(3(3(x1)))))))))))))))))) 0(2(2(3(2(1(0(3(1(0(3(0(3(3(1(1(0(3(x1)))))))))))))))))) (157)
2(2(1(2(1(2(1(3(0(1(0(3(0(0(0(2(3(3(x1)))))))))))))))))) 2(3(2(3(0(1(0(2(3(1(3(0(1(1(0(2(2(0(x1)))))))))))))))))) (158)
2(3(0(1(2(1(2(2(2(2(1(3(1(2(0(2(3(3(x1)))))))))))))))))) 2(3(2(0(2(1(2(2(3(1(2(1(1(3(2(2(0(3(x1)))))))))))))))))) (159)
0(3(0(0(3(0(3(1(1(1(3(1(2(1(0(3(3(3(x1)))))))))))))))))) 0(0(0(3(1(3(0(0(1(1(3(1(2(3(1(3(3(3(x1)))))))))))))))))) (160)
0(3(3(2(2(1(3(3(1(1(3(1(3(0(3(1(0(1(1(x1))))))))))))))))))) 0(0(1(2(3(2(3(1(3(1(3(1(3(0(1(3(1(3(1(x1))))))))))))))))))) (161)
2(3(3(2(2(1(3(3(1(1(3(1(3(0(3(1(0(1(1(x1))))))))))))))))))) 2(0(1(2(3(2(3(1(3(1(3(1(3(0(1(3(1(3(1(x1))))))))))))))))))) (162)
3(3(3(2(2(1(3(3(1(1(3(1(3(0(3(1(0(1(1(x1))))))))))))))))))) 3(0(1(2(3(2(3(1(3(1(3(1(3(0(1(3(1(3(1(x1))))))))))))))))))) (163)
1(3(3(2(2(1(3(3(1(1(3(1(3(0(3(1(0(1(1(x1))))))))))))))))))) 1(0(1(2(3(2(3(1(3(1(3(1(3(0(1(3(1(3(1(x1))))))))))))))))))) (164)
0(0(1(3(3(0(2(2(2(2(2(1(2(1(1(1(1(1(1(x1))))))))))))))))))) 0(2(1(1(2(0(1(0(2(1(1(2(1(3(2(2(3(1(1(x1))))))))))))))))))) (165)
2(0(1(3(3(0(2(2(2(2(2(1(2(1(1(1(1(1(1(x1))))))))))))))))))) 2(2(1(1(2(0(1(0(2(1(1(2(1(3(2(2(3(1(1(x1))))))))))))))))))) (166)
3(0(1(3(3(0(2(2(2(2(2(1(2(1(1(1(1(1(1(x1))))))))))))))))))) 3(2(1(1(2(0(1(0(2(1(1(2(1(3(2(2(3(1(1(x1))))))))))))))))))) (167)
1(0(1(3(3(0(2(2(2(2(2(1(2(1(1(1(1(1(1(x1))))))))))))))))))) 1(2(1(1(2(0(1(0(2(1(1(2(1(3(2(2(3(1(1(x1))))))))))))))))))) (168)
0(0(1(3(0(3(3(2(1(2(1(2(3(0(0(3(1(1(2(x1))))))))))))))))))) 0(2(1(3(0(3(3(0(0(2(1(1(0(3(2(3(1(1(2(x1))))))))))))))))))) (169)
2(0(1(3(0(3(3(2(1(2(1(2(3(0(0(3(1(1(2(x1))))))))))))))))))) 2(2(1(3(0(3(3(0(0(2(1(1(0(3(2(3(1(1(2(x1))))))))))))))))))) (170)
3(0(1(3(0(3(3(2(1(2(1(2(3(0(0(3(1(1(2(x1))))))))))))))))))) 3(2(1(3(0(3(3(0(0(2(1(1(0(3(2(3(1(1(2(x1))))))))))))))))))) (171)
1(0(1(3(0(3(3(2(1(2(1(2(3(0(0(3(1(1(2(x1))))))))))))))))))) 1(2(1(3(0(3(3(0(0(2(1(1(0(3(2(3(1(1(2(x1))))))))))))))))))) (172)
0(3(3(1(3(2(2(3(3(1(2(0(2(0(2(2(2(1(2(x1))))))))))))))))))) 0(2(2(3(1(1(0(2(2(0(2(3(3(2(3(2(3(1(2(x1))))))))))))))))))) (173)
2(3(3(1(3(2(2(3(3(1(2(0(2(0(2(2(2(1(2(x1))))))))))))))))))) 2(2(2(3(1(1(0(2(2(0(2(3(3(2(3(2(3(1(2(x1))))))))))))))))))) (174)
3(3(3(1(3(2(2(3(3(1(2(0(2(0(2(2(2(1(2(x1))))))))))))))))))) 3(2(2(3(1(1(0(2(2(0(2(3(3(2(3(2(3(1(2(x1))))))))))))))))))) (175)
1(3(3(1(3(2(2(3(3(1(2(0(2(0(2(2(2(1(2(x1))))))))))))))))))) 1(2(2(3(1(1(0(2(2(0(2(3(3(2(3(2(3(1(2(x1))))))))))))))))))) (176)

1.1.1 Semantic Labeling

Root-labeling is applied.

We obtain the labeled TRS

There are 368 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[02(x1)] = 1 · x1 + 3
[20(x1)] = 1 · x1 + 6
[03(x1)] = 1 · x1 + 14
[33(x1)] = 1 · x1 + 13
[32(x1)] = 1 · x1
[21(x1)] = 1 · x1
[10(x1)] = 1 · x1
[30(x1)] = 1 · x1 + 4
[22(x1)] = 1 · x1 + 1
[00(x1)] = 1 · x1
[23(x1)] = 1 · x1
[31(x1)] = 1 · x1 + 4
[01(x1)] = 1 · x1 + 1
[13(x1)] = 1 · x1 + 12
[11(x1)] = 1 · x1 + 3
[12(x1)] = 1 · x1 + 8
all of the following rules can be deleted.

There are 332 ruless (increase limit for explicit display).

1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[20(x1)] = 1 · x1 + 2
[00(x1)] = 1 · x1 + 2
[03(x1)] = 1 · x1
[30(x1)] = 1 · x1
[31(x1)] = 1 · x1 + 1
[10(x1)] = 1 · x1
[01(x1)] = 1 · x1
[11(x1)] = 1 · x1
[13(x1)] = 1 · x1
[02(x1)] = 1 · x1 + 1
[33(x1)] = 1 · x1 + 1
[22(x1)] = 1 · x1 + 1
[21(x1)] = 1 · x1 + 1
[12(x1)] = 1 · x1
[23(x1)] = 1 · x1
[32(x1)] = 1 · x1
all of the following rules can be deleted.
01(11(11(11(13(33(30(03(31(10(00(03(31(10(00(03(30(00(x1)))))))))))))))))) 01(11(13(30(01(11(13(31(10(01(13(30(00(03(30(03(30(00(x1)))))))))))))))))) (229)
01(11(11(11(13(33(30(03(31(10(00(03(31(10(00(03(30(02(x1)))))))))))))))))) 01(11(13(30(01(11(13(31(10(01(13(30(00(03(30(03(30(02(x1)))))))))))))))))) (230)
01(11(11(11(13(33(30(03(31(10(00(03(31(10(00(03(30(03(x1)))))))))))))))))) 01(11(13(30(01(11(13(31(10(01(13(30(00(03(30(03(30(03(x1)))))))))))))))))) (231)
01(11(11(11(13(33(30(03(31(10(00(03(31(10(00(03(30(01(x1)))))))))))))))))) 01(11(13(30(01(11(13(31(10(01(13(30(00(03(30(03(30(01(x1)))))))))))))))))) (232)

1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[20(x1)] = 1 · x1 + 1
[00(x1)] = 1 · x1
[03(x1)] = 1 · x1
[30(x1)] = 1 · x1 + 1
[31(x1)] = 1 · x1
[10(x1)] = 1 · x1 + 1
[01(x1)] = 1 · x1
[11(x1)] = 1 · x1
[13(x1)] = 1 · x1
[02(x1)] = 1 · x1
[33(x1)] = 1 · x1
[22(x1)] = 1 · x1
[21(x1)] = 1 · x1
[12(x1)] = 1 · x1
[23(x1)] = 1 · x1
[32(x1)] = 1 · x1
all of the following rules can be deleted.
22(21(10(02(20(02(21(12(23(33(30(02(22(22(21(10(01(10(x1)))))))))))))))))) 23(32(23(32(20(00(01(11(12(22(20(02(21(12(22(20(01(10(x1)))))))))))))))))) (265)
22(21(10(02(20(02(21(12(23(33(30(02(22(22(21(10(01(12(x1)))))))))))))))))) 23(32(23(32(20(00(01(11(12(22(20(02(21(12(22(20(01(12(x1)))))))))))))))))) (266)
22(21(10(02(20(02(21(12(23(33(30(02(22(22(21(10(01(13(x1)))))))))))))))))) 23(32(23(32(20(00(01(11(12(22(20(02(21(12(22(20(01(13(x1)))))))))))))))))) (267)
22(21(10(02(20(02(21(12(23(33(30(02(22(22(21(10(01(11(x1)))))))))))))))))) 23(32(23(32(20(00(01(11(12(22(20(02(21(12(22(20(01(11(x1)))))))))))))))))) (268)

1.1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[20(x1)] = 1 · x1
[00(x1)] = 1 · x1
[03(x1)] = 1 · x1
[30(x1)] = 1 · x1
[31(x1)] = 1 · x1 + 1
[10(x1)] = 1 · x1 + 1
[01(x1)] = 1 · x1 + 1
[11(x1)] = 1 · x1 + 1
[13(x1)] = 1 · x1 + 1
[02(x1)] = 1 · x1 + 1
[33(x1)] = 1 · x1 + 1
[32(x1)] = 1 · x1
[12(x1)] = 1 · x1
[21(x1)] = 1 · x1
[23(x1)] = 1 · x1
[22(x1)] = 1 · x1
all of the following rules can be deleted.
10(01(13(33(30(02(22(22(22(22(21(12(21(11(11(11(11(11(10(x1))))))))))))))))))) 12(21(11(12(20(01(10(02(21(11(12(21(13(32(22(23(31(11(10(x1))))))))))))))))))) (509)
10(01(13(33(30(02(22(22(22(22(21(12(21(11(11(11(11(11(12(x1))))))))))))))))))) 12(21(11(12(20(01(10(02(21(11(12(21(13(32(22(23(31(11(12(x1))))))))))))))))))) (510)
10(01(13(33(30(02(22(22(22(22(21(12(21(11(11(11(11(11(13(x1))))))))))))))))))) 12(21(11(12(20(01(10(02(21(11(12(21(13(32(22(23(31(11(13(x1))))))))))))))))))) (511)
10(01(13(33(30(02(22(22(22(22(21(12(21(11(11(11(11(11(11(x1))))))))))))))))))) 12(21(11(12(20(01(10(02(21(11(12(21(13(32(22(23(31(11(11(x1))))))))))))))))))) (512)

1.1.1.1.1.1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

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

1.1.1.1.1.1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.