Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/150877)

The rewrite relation of the following TRS is considered.

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

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 225 ruless (increase limit for explicit display).

1.1 Closure Under Flat Contexts

Using the flat contexts

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

We obtain the transformed TRS

There are 675 ruless (increase limit for explicit display).

1.1.1 Semantic Labeling

The following interpretations form a model of the rules.

As carrier we take the set {0,...,8}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 9):

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

We obtain the labeled TRS

There are 6075 ruless (increase limit for explicit display).

1.1.1.1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[20(x1)] = x1 +
0
[23(x1)] = x1 +
0
[26(x1)] = x1 +
0
[21(x1)] = x1 +
775616/1419
[24(x1)] = x1 +
351691/1419
[27(x1)] = x1 +
308256/473
[22(x1)] = x1 +
810743/1419
[25(x1)] = x1 +
9824/11
[28(x1)] = x1 +
191677/473
[10(x1)] = x1 +
0
[13(x1)] = x1 +
156293/129
[16(x1)] = x1 +
155777/129
[11(x1)] = x1 +
992800/1419
[14(x1)] = x1 +
155648/129
[17(x1)] = x1 +
155648/129
[12(x1)] = x1 +
1
[15(x1)] = x1 +
155648/129
[18(x1)] = x1 +
155777/129
[00(x1)] = x1 +
1
[03(x1)] = x1 +
159260/129
[06(x1)] = x1 +
156293/129
[01(x1)] = x1 +
125120/473
[04(x1)] = x1 +
155648/129
[07(x1)] = x1 +
143393/129
[02(x1)] = x1 +
125821/473
[05(x1)] = x1 +
835435/1419
[08(x1)] = x1 +
151744/129
all of the following rules can be deleted.

There are 6075 ruless (increase limit for explicit display).

1.1.1.1.1 R is empty

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