Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/58125)

The rewrite relation of the following TRS is considered.

0(1(1(1(2(0(1(x1))))))) 2(2(2(1(1(2(1(0(1(1(x1)))))))))) (1)
1(0(0(2(0(0(0(x1))))))) 2(2(1(1(2(0(2(2(2(1(x1)))))))))) (2)
0(0(2(2(2(0(1(2(0(0(x1)))))))))) 1(2(1(1(0(2(2(1(2(2(2(x1))))))))))) (3)
2(0(0(0(1(1(1(2(0(2(x1)))))))))) 0(2(2(1(1(2(2(2(2(1(0(1(2(x1))))))))))))) (4)
2(0(0(0(1(0(2(1(0(1(2(x1))))))))))) 0(1(1(1(0(2(1(2(2(2(1(1(x1)))))))))))) (5)
1(0(2(0(1(2(2(1(0(1(2(0(x1)))))))))))) 1(1(2(2(1(1(0(2(2(2(1(0(2(1(x1)))))))))))))) (6)
2(0(0(0(0(0(1(1(1(1(2(2(x1)))))))))))) 2(2(2(2(1(1(0(2(0(2(0(0(2(x1))))))))))))) (7)
2(0(0(2(0(1(0(1(1(0(1(0(x1)))))))))))) 0(2(1(1(1(2(2(1(2(1(0(1(2(0(x1)))))))))))))) (8)
0(0(1(0(0(2(0(1(1(2(2(0(1(x1))))))))))))) 2(0(1(2(2(1(0(0(0(1(0(0(1(x1))))))))))))) (9)
1(0(1(2(1(1(2(0(1(1(1(0(2(0(x1)))))))))))))) 1(2(0(2(1(0(0(2(1(2(2(2(1(1(1(2(0(x1))))))))))))))))) (10)
2(0(0(0(1(1(2(0(1(0(2(1(0(0(x1)))))))))))))) 1(0(2(1(2(1(0(2(2(0(2(2(1(0(1(2(1(x1))))))))))))))))) (11)
2(0(1(2(0(0(2(1(1(2(2(0(0(2(0(0(x1)))))))))))))))) 1(0(0(2(0(0(0(2(2(0(1(2(1(2(0(2(x1)))))))))))))))) (12)
2(0(1(2(1(0(0(1(2(0(2(2(2(0(2(1(x1)))))))))))))))) 1(2(1(1(0(2(2(2(2(2(1(0(0(1(1(2(2(1(2(1(0(2(x1)))))))))))))))))))))) (13)
1(0(1(2(1(1(2(0(0(1(0(1(2(2(2(0(2(x1))))))))))))))))) 2(2(1(0(0(2(1(1(2(1(2(0(2(1(2(2(1(2(2(1(x1)))))))))))))))))))) (14)
1(0(2(1(1(0(0(1(0(0(2(1(1(1(0(0(1(1(0(x1))))))))))))))))))) 1(1(0(2(0(1(0(1(2(1(0(1(1(0(0(2(2(1(0(1(x1)))))))))))))))))))) (15)
0(0(1(0(0(1(1(0(2(2(2(1(2(0(2(1(1(0(2(0(x1)))))))))))))))))))) 1(0(0(2(1(2(2(1(1(1(2(2(2(2(1(1(2(0(2(1(1(2(x1)))))))))))))))))))))) (16)
1(0(0(0(0(1(2(2(0(2(1(0(2(1(0(1(2(0(0(2(x1)))))))))))))))))))) 1(0(2(2(0(2(0(2(1(2(1(1(2(2(1(2(2(2(2(1(2(0(1(1(x1)))))))))))))))))))))))) (17)
1(2(1(2(0(1(2(1(1(2(1(1(1(2(0(1(1(1(1(1(x1)))))))))))))))))))) 1(2(2(1(1(1(1(1(1(2(1(2(1(2(0(1(1(1(0(1(x1)))))))))))))))))))) (18)
0(1(0(2(2(2(2(0(2(2(0(1(2(0(1(1(0(1(2(0(0(x1))))))))))))))))))))) 0(0(2(2(1(2(0(2(2(2(2(1(0(2(1(1(2(2(0(2(1(0(2(0(1(2(2(2(2(2(2(1(2(2(1(x1))))))))))))))))))))))))))))))))))) (19)
1(0(0(2(1(1(1(0(0(0(1(0(1(0(2(0(2(1(0(0(2(x1))))))))))))))))))))) 1(0(2(1(0(1(2(2(1(2(1(1(2(1(0(2(1(1(2(0(2(1(x1)))))))))))))))))))))) (20)
2(0(2(0(1(2(2(0(0(2(1(1(0(1(0(0(1(1(2(0(1(x1))))))))))))))))))))) 2(2(1(2(2(2(1(2(1(2(0(0(1(0(2(2(1(1(0(0(0(1(x1)))))))))))))))))))))) (21)
0(0(0(0(0(2(1(2(0(0(0(2(0(1(2(1(2(1(1(2(0(0(1(0(x1)))))))))))))))))))))))) 2(0(1(2(2(1(0(1(1(2(2(2(2(1(1(1(2(0(0(0(2(1(0(0(0(2(2(1(x1)))))))))))))))))))))))))))) (22)
2(0(0(0(2(0(2(2(2(2(2(2(0(0(0(1(2(0(2(2(2(0(0(1(1(x1))))))))))))))))))))))))) 0(1(2(2(0(1(2(1(1(0(2(2(0(2(0(0(1(0(0(2(1(2(1(2(2(1(1(2(x1)))))))))))))))))))))))))))) (23)
2(1(2(1(0(1(2(0(1(2(0(0(1(2(0(1(2(0(1(0(1(0(0(2(2(x1))))))))))))))))))))))))) 1(0(0(0(2(0(1(1(2(1(1(0(0(2(0(0(2(2(2(1(2(1(2(1(2(2(x1)))))))))))))))))))))))))) (24)
0(0(2(2(2(0(0(1(1(1(0(0(1(1(0(0(0(2(1(2(0(1(0(0(1(1(1(0(x1)))))))))))))))))))))))))))) 1(0(1(1(2(0(2(1(0(0(1(2(1(0(0(2(1(0(0(1(2(0(1(1(1(2(2(0(0(x1))))))))))))))))))))))))))))) (25)
2(0(2(1(1(0(2(1(0(1(0(1(1(1(0(1(1(2(0(0(1(0(1(0(0(0(2(0(x1)))))))))))))))))))))))))))) 2(2(0(2(2(2(0(0(2(1(0(1(1(1(2(0(2(1(1(2(2(1(2(0(1(2(1(2(2(2(2(1(2(2(x1)))))))))))))))))))))))))))))))))) (26)
2(1(0(1(2(2(1(2(2(2(2(2(2(2(0(0(0(1(1(0(1(1(0(0(0(0(2(1(x1)))))))))))))))))))))))))))) 1(1(0(2(0(2(0(0(1(2(2(1(2(2(2(1(0(1(2(2(0(2(1(1(1(2(2(1(1(x1))))))))))))))))))))))))))))) (27)
0(0(2(0(1(2(1(1(1(2(0(0(0(1(1(0(2(2(0(2(2(0(0(2(1(0(0(2(1(x1))))))))))))))))))))))))))))) 0(2(2(2(1(2(0(2(1(0(2(1(0(0(2(2(2(1(2(0(2(1(1(0(1(1(2(2(0(1(2(1(x1)))))))))))))))))))))))))))))))) (28)
2(0(1(0(0(1(0(2(2(0(0(1(1(2(1(2(1(1(1(1(2(1(1(0(0(1(1(2(0(x1))))))))))))))))))))))))))))) 2(1(2(1(2(1(1(2(1(2(1(2(0(1(2(1(1(0(0(2(1(2(0(0(2(0(2(2(2(2(1(2(0(2(x1)))))))))))))))))))))))))))))))))) (29)
0(0(0(2(2(0(0(1(0(2(2(2(2(2(0(1(0(2(0(0(0(0(2(0(1(2(1(2(0(0(x1)))))))))))))))))))))))))))))) 0(2(0(1(2(0(2(2(1(1(0(2(0(2(2(0(1(2(0(2(1(0(1(1(0(0(1(2(1(0(0(1(x1)))))))))))))))))))))))))))))))) (30)
0(0(1(0(1(2(2(1(0(0(1(0(2(0(0(0(1(1(0(0(2(0(1(0(0(0(2(0(1(0(x1)))))))))))))))))))))))))))))) 0(2(0(0(1(2(1(1(2(2(2(0(2(2(0(2(0(0(0(1(1(2(2(2(2(1(1(1(1(1(1(1(1(x1))))))))))))))))))))))))))))))))) (31)
0(2(0(0(0(0(0(0(0(1(1(0(2(1(1(0(1(2(0(2(0(2(1(2(0(1(2(1(1(0(x1)))))))))))))))))))))))))))))) 1(1(0(1(2(2(0(0(0(0(2(2(1(2(0(0(1(2(0(1(0(2(1(2(1(2(1(0(2(1(0(x1))))))))))))))))))))))))))))))) (32)
2(0(1(1(1(1(1(0(2(0(2(1(0(1(0(2(0(2(1(0(2(2(0(0(1(2(2(0(0(0(x1)))))))))))))))))))))))))))))) 1(2(1(1(2(1(2(2(2(1(1(0(0(2(0(1(2(0(2(2(2(2(2(0(2(2(1(1(0(0(0(1(0(1(x1)))))))))))))))))))))))))))))))))) (33)
2(1(1(1(2(1(0(1(0(1(1(0(1(2(0(2(0(0(0(0(1(2(1(1(0(0(0(0(1(2(x1)))))))))))))))))))))))))))))) 1(0(0(1(1(1(2(2(1(2(2(1(1(0(2(2(1(2(1(1(0(1(2(1(1(2(2(2(0(1(2(2(x1)))))))))))))))))))))))))))))))) (34)
2(0(0(1(0(0(0(1(1(0(0(0(1(0(2(0(2(2(0(0(1(1(2(0(0(0(2(0(0(1(2(x1))))))))))))))))))))))))))))))) 0(0(1(0(2(1(2(2(2(2(1(2(2(2(1(2(0(1(2(0(1(1(2(2(1(2(1(0(0(2(0(1(1(1(2(2(1(1(x1)))))))))))))))))))))))))))))))))))))) (35)
0(2(0(2(1(0(1(2(2(2(0(0(0(0(1(0(1(2(2(0(2(2(0(0(2(2(2(0(1(0(1(1(x1)))))))))))))))))))))))))))))))) 1(0(0(2(1(0(0(0(2(0(0(0(0(0(0(0(1(2(1(1(2(1(2(1(0(1(1(1(0(0(1(2(2(x1))))))))))))))))))))))))))))))))) (36)
2(0(1(2(1(2(0(0(0(1(2(0(1(1(2(0(1(1(0(1(1(2(2(0(2(1(0(1(0(2(0(2(x1)))))))))))))))))))))))))))))))) 1(1(2(0(2(1(2(2(0(1(1(0(2(0(1(2(0(0(1(1(1(0(2(2(2(1(1(1(0(1(2(2(2(x1))))))))))))))))))))))))))))))))) (37)
0(1(0(1(0(1(1(2(1(1(2(0(1(1(1(0(1(1(2(2(2(0(1(2(2(0(2(0(1(2(0(2(0(x1))))))))))))))))))))))))))))))))) 1(1(1(2(2(2(0(1(1(0(1(1(0(2(2(2(2(1(0(1(0(1(1(0(2(1(1(0(1(1(2(0(2(2(0(x1))))))))))))))))))))))))))))))))))) (38)
1(1(0(1(0(1(0(2(2(0(0(2(1(0(0(2(1(0(0(0(0(0(0(0(1(0(2(1(1(0(2(0(0(0(x1)))))))))))))))))))))))))))))))))) 1(1(0(0(1(0(0(1(2(2(1(0(0(1(2(0(2(2(0(2(0(0(2(1(1(2(1(0(1(2(1(0(0(0(2(x1))))))))))))))))))))))))))))))))))) (39)
2(2(0(0(2(2(1(1(1(2(0(2(1(1(2(2(0(0(2(2(2(1(1(2(2(2(2(2(1(0(2(1(2(0(x1)))))))))))))))))))))))))))))))))) 2(0(1(2(2(2(1(0(1(2(0(2(1(2(1(2(2(0(2(1(2(2(1(0(2(2(2(2(1(0(1(2(2(0(x1)))))))))))))))))))))))))))))))))) (40)
0(0(0(1(2(0(1(1(1(0(0(0(1(1(1(0(2(2(0(1(0(2(0(2(0(2(2(1(1(2(1(0(0(2(1(x1))))))))))))))))))))))))))))))))))) 2(2(1(1(2(0(0(0(0(2(2(2(2(2(0(1(2(0(0(1(0(0(1(0(2(2(1(0(2(0(0(0(2(2(2(1(x1)))))))))))))))))))))))))))))))))))) (41)
1(0(1(2(0(0(1(1(1(2(1(1(1(0(2(2(2(0(1(1(2(1(0(1(1(0(0(2(2(2(2(0(0(2(0(x1))))))))))))))))))))))))))))))))))) 1(1(1(2(0(0(2(1(2(2(2(2(1(0(2(0(2(1(1(1(1(2(2(1(2(1(0(2(0(0(2(2(2(2(2(0(0(2(2(2(2(2(1(x1))))))))))))))))))))))))))))))))))))))))))) (42)
1(1(2(0(2(2(1(0(1(2(1(1(0(0(2(0(0(1(1(0(1(0(0(0(0(2(0(1(0(2(1(1(1(1(0(x1))))))))))))))))))))))))))))))))))) 1(2(1(0(2(0(2(1(1(2(1(2(2(2(1(2(1(2(2(2(1(1(2(1(1(2(2(0(1(1(1(0(1(1(1(0(2(1(x1)))))))))))))))))))))))))))))))))))))) (43)
1(2(2(2(0(0(0(0(2(2(2(0(2(0(0(2(2(2(0(1(2(2(1(0(1(0(0(2(0(0(0(0(2(1(0(x1))))))))))))))))))))))))))))))))))) 1(2(0(2(2(2(1(2(2(2(2(1(2(2(2(2(0(1(1(1(2(0(0(2(1(0(1(0(0(1(2(2(0(1(1(0(0(2(x1)))))))))))))))))))))))))))))))))))))) (44)
1(2(0(2(0(0(2(1(0(0(0(2(2(0(0(1(0(2(0(0(0(2(0(0(2(0(2(2(2(0(2(2(0(2(1(1(x1)))))))))))))))))))))))))))))))))))) 1(0(0(2(1(1(2(2(1(0(1(2(1(2(0(0(1(2(1(2(2(1(2(1(1(1(0(1(0(2(0(1(0(1(2(1(2(2(2(0(2(x1))))))))))))))))))))))))))))))))))))))))) (45)
2(0(1(2(2(0(1(2(0(2(0(2(1(2(2(2(0(0(0(2(0(1(1(2(0(0(2(1(2(2(1(2(0(0(1(1(0(x1))))))))))))))))))))))))))))))))))))) 2(1(1(2(2(0(1(2(2(1(2(2(2(1(2(1(2(2(0(1(0(1(2(0(2(0(2(2(1(1(0(1(0(1(2(1(2(2(x1)))))))))))))))))))))))))))))))))))))) (46)
0(0(1(2(0(1(2(0(1(2(2(0(0(2(1(1(1(2(0(0(1(1(2(0(0(0(2(1(1(1(2(0(0(1(2(0(0(0(x1)))))))))))))))))))))))))))))))))))))) 1(1(0(2(2(2(2(0(2(1(2(1(0(0(0(1(1(0(1(2(1(1(0(1(1(0(2(2(1(1(1(1(0(2(0(1(2(2(1(1(x1)))))))))))))))))))))))))))))))))))))))) (47)
0(2(0(0(0(0(2(1(2(2(0(2(0(2(1(0(2(2(0(1(2(0(2(1(0(0(1(0(2(2(2(0(1(0(1(2(0(1(x1)))))))))))))))))))))))))))))))))))))) 2(0(0(2(1(0(1(2(0(0(1(2(1(0(1(2(0(1(2(0(1(2(0(1(0(0(0(2(1(1(0(2(1(2(2(2(2(1(1(x1))))))))))))))))))))))))))))))))))))))) (48)
1(0(2(2(2(2(2(0(2(0(2(1(2(0(0(1(0(2(1(0(0(0(1(2(1(0(2(2(0(1(0(1(1(2(0(0(2(0(x1)))))))))))))))))))))))))))))))))))))) 2(1(1(2(1(0(2(0(1(2(0(1(1(2(2(1(2(2(2(1(1(0(2(0(2(0(0(1(0(0(2(2(1(2(1(0(0(1(0(x1))))))))))))))))))))))))))))))))))))))) (49)
2(0(0(2(0(0(2(1(1(0(2(0(2(0(1(1(2(1(2(0(1(1(0(1(2(0(0(0(2(0(2(2(0(1(2(0(2(2(x1)))))))))))))))))))))))))))))))))))))) 2(1(2(0(0(1(1(2(2(1(2(1(0(2(2(0(2(2(0(1(2(0(1(0(0(0(0(0(1(0(2(1(2(2(0(2(1(0(2(x1))))))))))))))))))))))))))))))))))))))) (50)
2(1(2(1(2(2(2(2(2(0(1(1(2(2(0(0(1(0(0(0(0(1(0(2(1(1(1(2(2(1(2(0(1(0(1(1(2(0(x1)))))))))))))))))))))))))))))))))))))) 2(1(1(1(1(1(0(1(2(1(2(2(1(2(2(2(2(2(0(1(2(1(2(1(1(1(0(1(1(2(1(0(0(0(1(1(1(2(0(x1))))))))))))))))))))))))))))))))))))))) (51)
2(0(0(2(0(0(1(1(1(1(0(2(0(2(1(2(0(0(0(0(0(2(2(0(2(1(2(2(0(2(0(2(0(1(0(0(1(2(2(x1))))))))))))))))))))))))))))))))))))))) 2(2(1(0(2(0(0(0(2(1(2(2(2(0(0(0(0(2(1(2(2(2(2(1(0(0(2(0(0(1(2(0(1(2(1(1(2(0(2(2(1(x1))))))))))))))))))))))))))))))))))))))))) (52)
0(2(1(2(0(2(0(2(2(1(1(1(1(2(2(0(0(0(1(0(2(0(0(0(2(2(0(2(1(2(2(0(2(0(2(2(1(1(1(0(x1)))))))))))))))))))))))))))))))))))))))) 2(0(1(2(1(1(2(1(2(0(2(2(2(2(2(2(1(0(1(2(0(2(2(1(0(0(0(2(2(0(2(0(1(0(0(0(0(2(0(0(1(1(2(1(0(x1))))))))))))))))))))))))))))))))))))))))))))) (53)
1(0(0(2(1(2(1(2(1(0(1(2(0(2(0(0(2(1(2(0(0(1(0(0(0(1(2(1(2(0(0(1(0(0(0(1(1(2(0(0(x1)))))))))))))))))))))))))))))))))))))))) 1(0(1(2(2(0(1(2(2(1(1(2(1(2(0(2(2(2(0(1(2(1(1(0(1(1(0(1(0(2(2(2(1(1(1(1(0(1(2(2(2(1(1(x1))))))))))))))))))))))))))))))))))))))))))) (54)
1(0(2(1(1(0(0(1(0(1(0(0(1(1(0(0(0(0(0(0(1(1(0(1(0(0(1(0(1(0(2(1(0(2(1(1(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))))) 1(1(2(1(1(1(0(2(1(1(1(2(1(0(0(1(2(2(1(2(2(2(2(1(0(0(2(1(1(1(1(1(1(2(0(0(0(0(1(2(1(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))) (55)
1(1(1(0(2(1(1(0(0(1(1(1(2(1(0(1(2(1(2(2(2(0(2(2(0(1(0(0(2(0(0(2(2(1(0(1(2(1(1(1(x1)))))))))))))))))))))))))))))))))))))))) 1(2(1(2(2(2(1(1(2(0(1(1(1(1(2(1(2(0(2(1(2(2(2(0(1(2(0(2(2(1(1(0(2(1(1(1(0(2(1(1(2(2(x1)))))))))))))))))))))))))))))))))))))))))) (56)
1(2(2(0(1(0(0(1(1(1(1(2(0(2(1(1(0(1(2(0(2(0(1(2(1(1(1(2(0(0(1(1(0(0(1(0(1(0(2(2(1(x1))))))))))))))))))))))))))))))))))))))))) 1(2(0(1(2(0(1(2(2(1(1(0(2(2(2(1(0(0(1(1(0(2(1(1(2(2(0(0(0(0(1(0(0(1(1(2(2(2(2(2(2(2(1(2(0(2(1(x1))))))))))))))))))))))))))))))))))))))))))))))) (57)
2(1(2(2(0(1(0(0(1(2(0(1(2(0(2(2(2(0(1(1(2(0(2(2(2(0(1(2(0(1(0(2(1(0(1(2(2(1(2(1(2(x1))))))))))))))))))))))))))))))))))))))))) 2(1(2(0(0(1(0(2(2(2(0(2(2(1(2(1(2(0(2(2(0(0(0(2(2(1(0(2(0(1(0(1(2(1(2(2(2(1(1(1(1(x1))))))))))))))))))))))))))))))))))))))))) (58)
0(1(0(0(1(2(2(0(0(1(0(2(1(2(0(0(1(2(0(1(1(2(0(2(0(0(0(1(0(0(2(1(0(1(0(0(2(0(1(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))) 2(0(0(1(1(1(1(0(2(2(0(1(2(1(2(1(2(0(0(2(1(0(1(0(0(0(1(2(1(0(2(2(1(2(0(1(0(0(0(2(0(0(0(0(2(x1))))))))))))))))))))))))))))))))))))))))))))) (59)
1(2(2(2(0(2(1(0(2(1(0(1(1(2(1(1(0(1(1(2(1(2(1(2(2(0(0(1(0(0(2(2(2(0(0(1(0(0(2(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))) 2(1(2(1(1(0(1(1(1(1(0(0(2(1(2(2(2(2(2(1(2(0(0(2(2(1(1(0(2(1(2(1(0(2(0(0(1(1(0(0(0(1(2(1(2(x1))))))))))))))))))))))))))))))))))))))))))))) (60)
0(1(2(2(2(1(0(0(0(1(1(1(2(0(1(0(1(0(1(0(0(1(2(2(2(2(2(0(0(0(2(1(0(1(1(2(1(1(0(1(2(0(0(x1))))))))))))))))))))))))))))))))))))))))))) 1(2(1(2(2(2(0(2(2(1(0(2(1(0(2(0(1(2(2(2(1(2(0(1(1(1(0(0(1(2(2(2(2(2(2(1(0(0(0(2(2(2(2(2(1(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))) (61)
0(2(1(1(1(1(0(1(2(0(1(1(0(1(0(0(0(1(2(2(1(2(2(0(1(2(0(1(0(1(0(0(2(0(2(0(0(0(1(0(0(1(2(0(x1)))))))))))))))))))))))))))))))))))))))))))) 0(2(2(2(2(2(1(0(0(0(1(1(0(2(2(2(2(1(1(0(1(2(2(1(1(1(1(2(1(0(2(1(1(0(0(2(0(2(2(2(0(2(2(0(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))))))) (62)
2(0(1(2(1(2(2(0(1(2(1(1(0(0(0(0(1(2(2(0(0(2(0(1(1(0(1(0(0(0(1(2(1(1(2(0(1(0(1(0(0(0(2(2(x1)))))))))))))))))))))))))))))))))))))))))))) 1(2(0(0(1(0(1(2(2(1(1(2(0(1(1(1(2(1(0(1(2(1(1(2(2(2(2(2(1(1(2(2(1(0(0(1(1(2(0(0(2(2(2(0(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))) (63)
2(1(2(2(2(2(0(1(1(0(1(1(2(1(2(2(1(0(0(1(0(2(1(2(1(2(1(0(2(2(1(2(1(2(1(1(2(0(0(1(1(1(2(1(x1)))))))))))))))))))))))))))))))))))))))))))) 1(1(1(1(1(1(2(1(1(2(2(2(2(2(1(2(1(0(2(2(0(2(1(2(1(2(1(0(2(2(1(2(0(1(2(0(2(0(0(1(1(1(0(1(x1)))))))))))))))))))))))))))))))))))))))))))) (64)
0(1(0(2(0(1(1(2(1(1(2(1(0(1(1(2(0(0(0(1(0(0(0(0(0(0(1(1(2(0(2(1(2(0(1(0(1(2(2(2(0(0(0(2(0(x1))))))))))))))))))))))))))))))))))))))))))))) 1(2(1(2(1(2(1(2(1(2(2(1(1(1(0(1(2(0(1(0(2(0(0(1(2(0(1(0(1(2(1(1(2(2(0(2(1(0(0(0(0(1(2(2(1(2(2(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))) (65)
0(2(0(0(0(2(2(2(2(0(2(0(0(1(2(1(1(1(1(0(2(1(1(0(1(1(0(2(2(0(0(0(2(1(0(2(1(0(0(1(0(2(2(0(1(x1))))))))))))))))))))))))))))))))))))))))))))) 1(1(2(0(2(1(1(1(0(1(1(2(0(0(0(0(2(2(2(1(1(2(2(1(2(1(0(2(1(0(2(1(1(1(0(2(1(0(1(0(0(1(1(0(2(2(1(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) (66)
0(2(2(0(1(1(0(0(2(2(1(0(0(1(2(1(0(2(1(2(1(0(2(2(1(2(0(0(1(2(0(2(0(2(1(1(0(0(1(2(0(2(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))) 2(1(2(1(0(1(2(0(1(1(2(2(2(2(1(2(0(1(2(1(0(0(2(1(2(1(0(1(2(2(2(2(0(1(2(1(0(1(2(2(2(1(2(1(1(2(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) (67)
1(1(2(2(0(2(1(2(0(1(0(2(2(2(1(1(2(1(2(0(1(2(1(0(2(1(1(1(2(0(1(0(0(2(1(0(0(2(1(1(1(0(1(1(1(x1))))))))))))))))))))))))))))))))))))))))))))) 1(2(1(2(0(1(0(1(2(0(0(0(0(0(0(2(2(2(0(0(2(2(2(1(1(1(2(0(1(0(2(2(1(1(1(1(2(2(2(1(0(1(0(1(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))) (68)
2(0(2(0(0(1(2(0(1(1(1(2(0(2(1(2(0(2(1(1(2(0(2(0(2(1(2(2(0(1(1(2(2(1(0(1(0(1(1(0(2(1(2(0(0(x1))))))))))))))))))))))))))))))))))))))))))))) 2(1(2(1(1(2(1(2(1(1(0(0(2(2(2(1(0(2(0(1(1(0(1(1(0(2(0(2(0(1(2(1(0(1(2(2(0(2(2(2(2(1(2(1(1(1(1(0(0(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))) (69)
2(0(2(0(1(0(1(0(1(1(2(0(1(1(1(0(0(0(2(2(1(1(1(0(2(1(0(0(1(1(0(0(0(2(0(0(1(0(2(1(2(0(0(2(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(2(2(0(0(1(0(0(1(0(1(1(0(0(1(1(1(1(1(1(2(1(2(0(1(2(2(2(2(1(1(1(0(1(1(2(2(0(2(0(1(1(2(0(2(2(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) (70)
2(1(2(2(2(1(2(0(1(2(2(2(0(0(2(1(0(0(2(2(0(0(0(1(0(2(1(2(1(0(0(0(0(1(1(1(1(0(2(0(1(0(0(1(0(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(2(1(0(2(1(2(0(1(1(2(1(2(2(1(1(1(2(1(1(1(2(0(0(2(0(2(0(1(0(0(2(1(2(1(2(1(0(1(2(2(2(1(1(1(1(2(2(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))) (71)
0(2(0(1(2(1(0(1(1(2(0(2(1(0(0(2(0(1(1(0(1(2(2(0(2(0(1(1(0(1(2(0(0(0(1(0(0(1(2(0(1(2(0(0(2(0(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))) 1(2(1(1(0(1(1(1(1(2(1(0(1(1(1(2(2(0(0(1(2(0(0(0(2(0(2(0(1(2(2(0(1(0(2(0(2(0(2(2(1(0(1(2(0(1(1(2(0(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))) (72)
2(1(0(1(1(1(1(2(2(1(2(2(2(0(1(0(0(0(2(2(0(2(1(2(1(0(1(0(0(1(2(0(1(1(0(1(1(2(0(0(2(0(1(1(2(1(1(1(0(x1))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(2(2(0(2(1(1(1(0(1(0(1(0(0(1(2(1(0(2(0(0(2(0(1(0(2(2(1(2(1(2(1(1(0(1(2(2(1(0(2(2(2(2(1(2(1(0(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))) (73)
2(2(2(1(2(2(2(0(1(2(0(1(2(0(1(1(1(2(0(0(2(1(1(2(1(0(1(1(2(0(1(2(0(1(2(2(1(2(2(1(1(1(1(0(2(2(1(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(1(2(1(2(2(1(1(2(1(0(2(0(1(1(2(0(2(0(1(1(2(2(1(0(1(2(1(1(2(0(1(0(1(0(2(1(1(2(2(1(1(2(2(2(0(2(x1))))))))))))))))))))))))))))))))))))))))))))))))) (74)
2(1(0(1(0(0(2(2(1(1(1(0(1(1(0(1(1(2(0(1(0(1(2(2(0(0(1(0(0(1(1(0(1(1(2(1(0(0(0(0(1(1(1(2(1(1(1(0(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(0(0(0(0(2(0(0(1(0(0(2(1(0(1(1(2(1(0(0(1(2(1(0(1(2(0(0(1(2(1(1(1(2(1(0(1(1(1(2(1(1(0(1(2(0(1(1(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 +
8026
[21(x1)] = x1 +
0
[24(x1)] = x1 +
1
[27(x1)] = x1 +
1
[22(x1)] = x1 +
3664
[25(x1)] = x1 +
7927
[28(x1)] = x1 +
7918
[10(x1)] = x1 +
0
[13(x1)] = x1 +
1
[16(x1)] = x1 +
5624
[11(x1)] = x1 +
0
[14(x1)] = x1 +
9
[17(x1)] = x1 +
7587/2
[12(x1)] = x1 +
10325/2
[15(x1)] = x1 +
7067/2
[18(x1)] = x1 +
6735
[00(x1)] = x1 +
0
[03(x1)] = x1 +
7919
[06(x1)] = x1 +
7918
[01(x1)] = x1 +
1711
[04(x1)] = x1 +
7918
[07(x1)] = x1 +
7918
[02(x1)] = x1 +
12173/2
[05(x1)] = x1 +
7964
[08(x1)] = x1 +
14319/2
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.