Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/29415)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 297 ruless (increase limit for explicit display).

1.1 Semantic Labeling

The following interpretations form a model of the rules.

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

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

We obtain the labeled TRS

There are 891 ruless (increase limit for explicit display).

1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[20(x1)] = x1 +
1104
[21(x1)] = x1 +
1146
[22(x1)] = x1 +
847
[10(x1)] = x1 +
1500
[11(x1)] = x1 +
1561
[12(x1)] = x1 +
1428
[00(x1)] = x1 +
0
[01(x1)] = x1 +
1
[02(x1)] = x1 +
0
all of the following rules can be deleted.

There are 891 ruless (increase limit for explicit display).

1.1.1.1 R is empty

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