Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/150258)

The rewrite relation of the following TRS is considered.

0(1(1(0(0(2(1(1(x1)))))))) 1(1(1(2(1(1(2(1(2(1(x1)))))))))) (1)
0(1(1(1(0(2(1(0(x1)))))))) 1(1(0(0(1(2(0(1(x1)))))))) (2)
0(2(2(0(1(0(1(1(x1)))))))) 1(2(1(1(2(0(1(2(1(x1))))))))) (3)
2(1(2(0(2(0(1(0(0(2(0(x1))))))))))) 1(0(1(2(1(2(0(1(2(1(2(2(x1)))))))))))) (4)
1(1(1(1(0(0(1(1(1(1(1(2(2(1(x1)))))))))))))) 1(2(0(2(0(2(1(1(2(1(2(1(1(2(0(1(x1)))))))))))))))) (5)
2(1(0(1(0(0(2(2(1(2(2(0(2(2(2(0(x1)))))))))))))))) 2(1(2(2(0(1(2(1(1(2(1(2(0(1(1(1(0(1(x1)))))))))))))))))) (6)
2(2(0(0(2(0(0(2(2(0(1(0(0(0(1(2(x1)))))))))))))))) 1(0(0(1(2(1(2(1(2(2(1(1(1(2(1(1(1(x1))))))))))))))))) (7)
0(2(1(1(1(2(0(0(1(2(2(0(1(1(0(1(1(x1))))))))))))))))) 1(1(2(1(2(1(0(0(2(2(0(1(0(1(1(1(0(1(x1)))))))))))))))))) (8)
2(0(1(0(0(0(2(1(2(0(2(2(0(0(0(1(2(x1))))))))))))))))) 1(1(2(0(0(1(0(1(1(1(2(1(2(2(2(1(2(1(x1)))))))))))))))))) (9)
0(0(2(0(0(0(2(2(1(0(1(1(0(2(0(1(0(0(0(x1))))))))))))))))))) 0(2(2(0(0(2(2(2(1(2(2(2(2(0(2(1(1(2(1(0(x1)))))))))))))))))))) (10)
0(1(0(2(0(1(0(2(1(1(1(0(1(1(0(1(2(2(2(x1))))))))))))))))))) 1(2(2(1(2(1(2(1(0(0(2(1(1(2(2(1(2(1(2(1(0(2(1(x1))))))))))))))))))))))) (11)
1(0(1(1(1(0(2(0(2(0(0(2(0(0(0(0(1(2(1(1(1(x1))))))))))))))))))))) 1(2(1(2(1(1(1(1(1(2(0(0(2(0(2(0(1(1(2(2(1(2(1(x1))))))))))))))))))))))) (12)
2(0(2(0(1(0(0(0(0(2(0(2(0(0(1(1(2(0(0(0(2(x1))))))))))))))))))))) 0(2(0(1(0(1(2(1(2(1(2(2(0(0(1(2(0(0(2(1(2(2(0(x1))))))))))))))))))))))) (13)
2(2(2(1(0(0(2(0(2(2(2(2(0(0(0(2(2(0(1(2(0(2(x1)))))))))))))))))))))) 2(2(0(2(0(2(2(2(2(2(1(1(1(1(2(1(2(1(1(2(1(2(0(x1))))))))))))))))))))))) (14)
0(1(0(0(1(0(0(1(0(2(1(2(2(0(1(1(2(2(2(2(2(2(2(x1))))))))))))))))))))))) 2(2(0(2(0(0(2(1(1(2(1(1(2(1(2(1(2(2(0(1(0(0(1(1(2(1(x1)))))))))))))))))))))))))) (15)
2(1(2(0(2(0(0(2(0(1(1(0(2(1(0(1(2(2(0(1(1(0(0(0(x1)))))))))))))))))))))))) 2(0(1(2(1(0(1(2(2(1(0(2(0(0(2(2(1(2(2(1(2(1(2(2(2(x1))))))))))))))))))))))))) (16)
2(2(0(2(2(2(2(2(2(0(2(2(1(2(2(0(2(2(2(1(1(0(2(0(x1)))))))))))))))))))))))) 0(1(2(2(1(0(1(0(0(1(2(1(2(2(1(2(0(1(2(1(0(0(0(1(2(2(x1)))))))))))))))))))))))))) (17)
0(2(0(1(2(1(1(0(0(0(1(2(2(2(2(2(2(0(2(1(2(0(0(0(0(x1))))))))))))))))))))))))) 1(2(0(0(1(2(1(0(0(1(0(1(1(2(2(1(1(1(0(1(2(1(2(1(0(2(x1)))))))))))))))))))))))))) (18)
1(1(0(2(0(2(0(2(2(1(2(1(0(0(2(1(2(2(0(0(1(0(2(1(0(x1))))))))))))))))))))))))) 1(0(2(0(1(2(0(1(2(0(1(1(2(1(0(0(2(0(1(2(1(1(0(0(1(1(x1)))))))))))))))))))))))))) (19)
1(1(2(0(1(2(1(1(2(0(2(0(1(2(2(0(2(1(0(0(1(1(2(0(0(x1))))))))))))))))))))))))) 1(2(1(0(1(2(1(0(2(1(1(2(1(2(0(1(0(2(2(2(0(1(0(2(2(2(x1)))))))))))))))))))))))))) (20)
2(0(1(0(1(2(2(2(0(0(1(2(2(1(2(2(0(0(0(1(0(2(1(0(0(x1))))))))))))))))))))))))) 2(2(2(1(1(0(2(0(0(0(1(0(2(0(1(2(1(2(1(1(0(2(0(1(0(1(x1)))))))))))))))))))))))))) (21)
2(0(2(0(2(2(0(0(1(0(0(1(0(2(0(2(2(2(2(2(0(1(0(2(0(x1))))))))))))))))))))))))) 2(1(2(1(1(1(0(0(0(1(1(1(2(2(1(0(1(2(2(2(2(0(1(1(1(0(x1)))))))))))))))))))))))))) (22)
0(0(1(0(0(2(1(2(0(1(0(0(0(1(0(0(0(2(1(1(0(1(0(2(0(0(x1)))))))))))))))))))))))))) 0(1(2(2(1(0(1(2(1(2(0(0(1(0(1(2(1(2(1(2(0(2(0(0(2(0(2(1(x1)))))))))))))))))))))))))))) (23)
1(1(1(0(2(1(0(2(0(1(2(2(1(1(2(2(0(1(1(0(1(0(2(0(2(2(x1)))))))))))))))))))))))))) 1(0(2(1(2(1(0(0(2(0(2(1(2(1(2(1(2(1(1(1(0(1(2(2(0(0(0(1(x1)))))))))))))))))))))))))))) (24)
0(0(2(2(0(0(1(0(0(0(2(1(1(0(2(0(2(2(1(1(0(2(0(2(0(0(2(x1))))))))))))))))))))))))))) 0(0(0(1(1(2(0(2(2(2(0(2(0(1(0(1(0(0(1(2(1(1(2(2(0(1(1(0(x1)))))))))))))))))))))))))))) (25)
2(0(1(0(0(0(0(1(0(1(0(0(2(0(0(1(1(1(1(2(0(1(1(1(1(0(0(x1))))))))))))))))))))))))))) 1(1(1(1(1(0(0(1(2(1(2(2(1(2(1(1(2(2(2(1(1(1(2(1(1(2(2(0(x1)))))))))))))))))))))))))))) (26)
0(2(2(1(0(0(2(2(0(1(0(1(1(0(2(1(0(1(2(2(2(0(1(1(2(0(1(0(x1)))))))))))))))))))))))))))) 1(0(2(2(0(1(2(1(0(0(2(1(2(2(1(2(1(0(2(1(0(2(0(1(2(0(1(1(1(1(x1)))))))))))))))))))))))))))))) (27)
1(2(2(1(2(0(0(0(2(1(0(0(1(0(1(1(2(1(1(2(2(1(1(1(0(2(2(0(x1)))))))))))))))))))))))))))) 1(1(2(2(1(2(0(1(0(1(2(0(1(0(1(1(2(1(2(2(0(1(0(1(0(2(2(0(x1)))))))))))))))))))))))))))) (28)
2(0(0(2(1(0(2(0(1(0(2(1(1(2(2(2(0(1(2(2(2(0(2(1(0(2(1(1(x1)))))))))))))))))))))))))))) 1(2(0(0(1(2(1(2(1(0(0(0(0(0(2(2(0(1(1(2(2(2(1(2(2(2(2(1(1(x1))))))))))))))))))))))))))))) (29)
0(1(2(0(1(2(2(0(1(1(0(1(2(2(2(0(2(0(1(2(2(2(1(0(1(1(0(2(2(x1))))))))))))))))))))))))))))) 2(2(0(0(0(1(1(2(1(2(1(2(1(2(0(2(0(2(2(1(0(0(1(0(0(2(2(1(0(0(1(x1))))))))))))))))))))))))))))))) (30)
2(0(0(1(0(0(0(0(0(0(1(1(0(2(2(0(2(1(0(2(2(1(0(2(1(2(2(0(2(x1))))))))))))))))))))))))))))) 0(2(2(2(1(2(2(2(1(1(1(0(0(1(1(2(1(1(1(2(2(2(0(2(1(1(2(0(2(2(x1)))))))))))))))))))))))))))))) (31)
0(0(2(2(0(2(2(0(2(0(2(2(0(2(2(1(1(0(0(2(1(0(0(2(2(2(2(0(2(0(x1)))))))))))))))))))))))))))))) 0(1(1(2(0(1(0(1(2(1(2(0(0(1(1(2(1(1(2(0(1(0(1(0(1(2(1(1(1(2(2(x1))))))))))))))))))))))))))))))) (32)
0(1(1(1(2(0(0(1(2(1(1(2(1(2(2(0(0(2(2(1(0(0(1(0(2(0(1(2(0(1(x1)))))))))))))))))))))))))))))) 2(1(0(1(2(1(0(0(0(0(1(2(1(1(1(2(1(0(1(2(2(1(2(0(1(2(1(1(1(1(2(1(x1)))))))))))))))))))))))))))))))) (33)
1(1(2(0(2(2(2(0(2(2(0(0(1(0(0(1(0(0(0(0(1(2(1(1(0(2(0(0(0(2(x1)))))))))))))))))))))))))))))) 1(1(2(1(1(2(1(1(1(1(1(0(0(2(1(0(2(1(2(1(2(2(2(2(1(1(0(2(2(2(0(x1))))))))))))))))))))))))))))))) (34)
2(2(2(0(1(1(0(0(0(0(0(1(1(2(2(0(2(1(0(0(1(1(0(2(1(2(0(0(2(0(x1)))))))))))))))))))))))))))))) 1(2(1(2(0(1(1(1(2(1(2(1(1(2(0(0(0(1(1(2(1(0(2(2(0(1(2(2(0(0(2(2(x1)))))))))))))))))))))))))))))))) (35)
1(2(2(0(1(0(0(0(0(2(1(2(1(1(0(1(1(0(0(2(0(0(2(1(2(0(1(0(0(1(0(x1))))))))))))))))))))))))))))))) 1(2(1(2(0(0(0(1(0(2(2(1(1(1(1(2(1(2(0(0(0(1(1(2(0(1(0(2(1(2(1(1(x1)))))))))))))))))))))))))))))))) (36)
0(1(0(0(1(1(1(1(0(2(1(0(0(2(0(1(0(2(2(1(1(2(1(2(2(0(0(0(1(1(2(0(x1)))))))))))))))))))))))))))))))) 1(1(2(2(1(2(0(2(1(2(1(2(0(1(1(1(0(1(2(0(0(0(1(2(0(0(1(2(1(2(1(0(1(x1))))))))))))))))))))))))))))))))) (37)
1(0(1(0(0(1(1(1(2(1(0(2(0(1(2(0(2(1(1(0(1(1(1(0(2(2(2(1(0(1(2(0(1(x1))))))))))))))))))))))))))))))))) 1(2(1(0(1(0(1(0(1(0(0(0(2(0(0(0(1(2(1(2(0(0(2(0(2(2(1(1(0(1(2(0(0(1(x1)))))))))))))))))))))))))))))))))) (38)
2(2(0(0(2(0(1(1(2(2(2(2(0(2(0(2(1(2(1(0(0(0(0(2(1(1(1(1(2(2(0(2(2(x1))))))))))))))))))))))))))))))))) 2(2(0(0(2(0(2(1(2(1(2(2(1(0(2(2(2(0(1(0(2(0(0(2(1(0(1(1(2(2(1(2(0(x1))))))))))))))))))))))))))))))))) (39)
0(0(0(2(2(0(2(0(0(1(2(0(0(0(1(2(2(1(0(0(0(2(2(2(2(1(2(2(2(0(2(1(2(2(x1)))))))))))))))))))))))))))))))))) 0(0(2(2(1(0(0(0(1(0(1(2(1(2(1(2(1(1(2(1(1(1(0(2(0(1(2(1(1(1(2(0(2(0(1(x1))))))))))))))))))))))))))))))))))) (40)
2(0(0(0(2(1(2(2(2(0(1(1(1(0(2(1(1(0(0(1(0(0(0(0(2(1(0(1(1(2(2(0(2(0(x1)))))))))))))))))))))))))))))))))) 2(0(2(2(0(1(1(1(2(0(0(2(1(2(1(2(0(1(1(1(2(2(2(1(0(0(2(2(2(1(2(1(1(0(0(2(x1)))))))))))))))))))))))))))))))))))) (41)
2(0(1(1(2(2(0(0(0(0(0(0(0(2(2(2(2(2(2(2(1(2(0(0(0(1(0(0(2(0(0(2(1(0(2(x1))))))))))))))))))))))))))))))))))) 1(1(2(0(0(1(1(2(0(2(1(1(1(2(0(0(0(0(1(1(2(1(1(1(2(1(0(2(1(0(2(2(1(2(0(1(2(x1))))))))))))))))))))))))))))))))))))) (42)
2(2(0(2(2(0(1(0(1(1(1(2(0(2(2(1(0(0(0(0(2(0(0(1(1(2(2(1(0(2(0(0(2(2(2(x1))))))))))))))))))))))))))))))))))) 0(2(1(2(0(2(0(2(1(1(1(2(1(0(0(1(1(1(2(1(2(0(1(2(0(2(2(1(2(0(1(0(1(2(1(2(0(2(x1)))))))))))))))))))))))))))))))))))))) (43)
1(2(0(2(1(0(2(2(2(2(1(1(1(1(0(0(2(2(0(0(2(2(0(1(1(0(2(2(1(0(2(2(0(1(1(1(x1)))))))))))))))))))))))))))))))))))) 1(2(1(0(1(2(2(2(2(2(0(1(0(2(1(0(2(1(1(1(0(2(1(2(2(2(2(0(2(1(1(0(0(1(0(0(1(x1))))))))))))))))))))))))))))))))))))) (44)
2(1(1(1(1(1(1(0(0(1(0(2(1(0(1(1(2(2(1(2(1(1(0(2(2(2(2(0(1(1(0(2(2(2(0(2(x1)))))))))))))))))))))))))))))))))))) 1(1(2(1(1(2(0(2(1(2(0(0(1(1(0(2(1(2(2(1(2(1(0(1(1(2(1(0(0(2(1(0(1(2(2(0(2(x1))))))))))))))))))))))))))))))))))))) (45)
2(0(2(0(0(2(2(2(1(0(2(1(0(1(1(2(0(2(0(1(0(0(1(2(2(0(2(1(0(0(0(2(1(1(0(0(2(x1))))))))))))))))))))))))))))))))))))) 0(2(1(1(1(1(2(0(2(1(1(2(2(2(1(1(2(1(1(0(1(0(2(0(2(1(0(1(2(1(1(0(1(1(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))) (46)
2(0(2(1(0(0(1(1(0(0(0(1(1(0(0(0(0(0(2(2(1(2(2(0(2(0(2(2(2(0(1(1(2(0(0(1(0(x1))))))))))))))))))))))))))))))))))))) 2(1(2(0(1(2(0(0(2(1(1(0(0(1(2(0(1(1(1(2(0(0(0(0(0(1(2(1(1(1(0(1(2(2(2(2(1(0(x1)))))))))))))))))))))))))))))))))))))) (47)
0(0(1(1(2(0(2(0(1(2(1(1(0(0(0(2(2(0(2(2(0(0(1(2(2(2(1(1(0(0(1(0(0(1(2(0(2(1(0(x1))))))))))))))))))))))))))))))))))))))) 2(1(2(1(2(0(1(0(1(1(1(2(2(1(1(0(2(1(1(1(0(1(0(0(1(1(0(1(2(1(2(0(0(1(2(1(0(1(1(1(x1)))))))))))))))))))))))))))))))))))))))) (48)
0(0(2(2(0(0(2(1(0(1(0(0(1(0(1(2(2(2(1(1(2(2(0(0(2(1(0(0(2(2(0(2(2(1(0(1(2(2(2(x1))))))))))))))))))))))))))))))))))))))) 1(1(1(2(1(0(0(0(0(0(1(0(2(0(1(2(2(1(2(0(2(0(0(1(2(2(2(2(0(2(1(0(1(2(2(0(1(0(0(0(x1)))))))))))))))))))))))))))))))))))))))) (49)
0(1(0(0(2(2(2(2(1(1(1(0(2(0(1(0(0(2(1(2(2(1(0(0(1(2(2(2(2(1(2(2(0(2(2(0(2(2(2(x1))))))))))))))))))))))))))))))))))))))) 1(0(2(0(1(2(1(0(1(2(0(1(1(1(1(0(1(1(1(2(0(0(2(1(1(2(1(0(2(0(1(0(0(0(2(1(1(2(2(1(x1)))))))))))))))))))))))))))))))))))))))) (50)
0(1(1(2(1(2(1(2(2(2(2(2(0(0(2(1(0(2(1(0(2(0(0(0(0(0(2(1(0(2(0(0(2(2(1(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))) 0(0(1(0(1(2(1(2(1(2(2(2(1(2(2(1(1(2(1(2(1(1(0(2(0(1(2(1(1(2(2(0(0(2(1(1(0(1(1(1(0(x1))))))))))))))))))))))))))))))))))))))))) (51)
0(2(0(2(1(0(1(1(0(0(0(1(2(2(2(0(0(0(0(0(2(1(0(1(2(2(2(0(2(0(1(0(0(2(1(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))) 2(0(2(2(1(2(2(2(1(1(1(2(2(1(2(1(2(1(2(0(0(0(1(1(1(2(0(0(1(1(2(1(1(2(1(1(2(1(0(0(0(2(x1)))))))))))))))))))))))))))))))))))))))))) (52)
0(0(2(2(2(2(2(0(2(1(1(2(2(0(0(2(2(0(0(2(2(1(1(2(2(2(1(2(2(1(0(1(1(2(2(2(0(0(0(2(x1)))))))))))))))))))))))))))))))))))))))) 1(2(2(0(1(2(2(2(0(2(1(2(1(2(1(2(1(1(2(1(2(2(2(0(0(1(2(1(1(1(0(1(1(0(1(2(0(1(1(1(0(0(0(0(2(x1))))))))))))))))))))))))))))))))))))))))))))) (53)
0(1(0(1(1(0(1(1(2(0(1(2(0(0(0(0(2(2(0(0(2(1(2(0(1(2(0(0(1(2(0(0(0(1(0(1(1(2(0(0(x1)))))))))))))))))))))))))))))))))))))))) 1(2(2(1(2(1(2(0(2(2(0(2(1(2(1(2(1(0(1(0(2(0(1(0(1(2(0(1(0(1(2(1(1(0(2(2(0(1(0(2(1(1(x1)))))))))))))))))))))))))))))))))))))))))) (54)
2(1(1(2(2(2(2(2(0(2(1(2(2(2(2(0(1(2(0(2(0(0(2(2(1(1(1(2(1(1(1(0(2(0(0(2(0(2(2(1(x1)))))))))))))))))))))))))))))))))))))))) 2(2(1(2(1(2(1(2(2(0(1(2(0(2(0(2(2(2(0(2(1(0(2(2(2(2(1(0(1(1(1(2(2(0(0(2(1(2(0(1(x1)))))))))))))))))))))))))))))))))))))))) (55)
0(1(0(2(1(0(0(2(0(0(1(2(2(1(0(2(2(2(2(2(1(1(1(0(0(0(0(1(0(1(1(2(2(0(0(0(1(1(1(1(1(x1))))))))))))))))))))))))))))))))))))))))) 0(0(1(2(1(1(0(0(2(1(1(0(2(1(2(2(0(2(2(2(0(0(0(0(2(0(1(0(0(0(0(1(2(1(1(0(0(1(2(1(2(1(x1)))))))))))))))))))))))))))))))))))))))))) (56)
0(2(0(0(0(0(0(2(0(1(1(1(0(0(2(2(2(2(2(0(2(1(2(0(2(0(0(1(1(0(2(2(0(1(1(2(2(0(1(1(0(x1))))))))))))))))))))))))))))))))))))))))) 1(0(2(1(1(1(1(1(2(2(1(2(0(1(1(2(1(0(0(1(0(1(0(2(0(0(1(1(1(2(0(0(2(1(0(2(1(0(2(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))) (57)
1(0(2(0(2(2(1(1(0(1(2(0(1(0(1(1(1(1(2(2(2(2(2(0(1(2(2(0(0(0(0(2(0(2(0(1(2(2(2(2(0(x1))))))))))))))))))))))))))))))))))))))))) 1(1(0(0(2(2(1(1(2(1(0(1(2(1(2(0(1(2(2(2(0(0(1(0(0(1(2(0(1(1(1(0(0(0(0(1(0(1(2(2(0(1(x1)))))))))))))))))))))))))))))))))))))))))) (58)
2(1(0(2(1(0(1(2(2(0(1(2(1(1(1(0(1(2(0(0(0(1(1(0(0(0(2(2(1(1(2(0(2(0(1(0(1(1(0(1(2(2(x1)))))))))))))))))))))))))))))))))))))))))) 0(1(1(0(1(2(2(2(0(0(0(1(2(1(0(1(0(1(1(2(1(1(1(2(0(1(0(2(1(2(1(0(1(2(0(0(1(2(1(2(1(2(0(x1))))))))))))))))))))))))))))))))))))))))))) (59)
0(2(1(1(2(2(0(1(1(0(0(1(2(2(2(0(2(2(2(2(2(0(2(0(2(0(2(2(1(0(2(2(1(0(0(0(1(0(2(2(2(1(2(x1))))))))))))))))))))))))))))))))))))))))))) 2(2(0(0(1(0(2(1(1(2(1(0(1(2(1(0(1(1(0(0(2(2(2(2(0(0(2(0(1(2(0(1(0(1(0(0(2(2(1(2(1(1(2(1(1(x1))))))))))))))))))))))))))))))))))))))))))))) (60)
1(2(0(2(0(0(1(2(2(1(1(2(2(1(0(2(0(2(2(1(1(1(0(0(0(2(2(0(1(1(0(2(2(2(1(0(0(1(1(2(0(2(2(x1))))))))))))))))))))))))))))))))))))))))))) 1(1(0(2(2(2(2(2(1(2(2(1(1(2(0(0(2(0(2(1(0(1(1(1(2(0(0(1(1(2(0(0(0(2(2(1(2(1(1(1(0(1(2(0(x1)))))))))))))))))))))))))))))))))))))))))))) (61)
0(2(2(0(2(1(1(2(1(1(2(1(1(1(0(2(0(0(1(1(1(2(0(1(1(1(0(0(2(0(0(2(1(1(0(1(1(2(2(0(0(2(0(1(x1)))))))))))))))))))))))))))))))))))))))))))) 1(1(2(2(0(0(1(1(2(1(2(1(0(1(1(2(0(0(1(2(2(1(1(0(0(2(1(0(1(2(1(1(0(2(0(2(1(1(2(2(0(0(0(0(1(x1))))))))))))))))))))))))))))))))))))))))))))) (62)
2(2(2(0(2(0(2(2(0(2(1(1(1(2(1(0(0(1(0(2(0(2(0(1(0(2(1(0(1(0(0(1(2(2(1(0(2(2(0(2(0(2(2(0(x1)))))))))))))))))))))))))))))))))))))))))))) 0(2(2(2(1(2(2(0(2(1(2(2(2(0(1(0(1(1(2(1(2(1(0(0(0(2(1(1(2(0(0(0(2(0(0(2(1(2(2(0(0(1(2(0(0(x1))))))))))))))))))))))))))))))))))))))))))))) (63)
0(1(2(2(1(1(2(1(1(1(2(0(2(2(0(0(0(0(2(2(0(1(0(0(0(0(0(0(2(1(2(0(0(1(1(2(1(1(0(0(1(0(1(1(2(x1))))))))))))))))))))))))))))))))))))))))))))) 1(1(1(0(0(1(2(1(1(1(2(1(0(2(2(1(2(2(1(2(0(1(1(2(1(2(1(2(1(2(1(0(0(1(0(2(0(1(2(2(2(2(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) (64)
1(1(0(1(0(2(1(0(0(2(1(2(1(2(0(2(2(0(1(0(1(0(1(2(1(1(2(2(1(0(2(2(2(2(2(1(0(0(1(0(1(2(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))) 1(1(2(0(0(0(1(0(1(1(2(1(2(1(0(2(2(2(1(2(1(2(0(2(0(0(2(0(1(0(0(1(2(2(0(1(0(0(2(1(1(2(1(2(1(x1))))))))))))))))))))))))))))))))))))))))))))) (65)
1(2(2(1(1(2(0(1(0(0(1(2(1(2(1(1(1(1(2(0(1(1(2(2(1(2(0(0(0(2(2(1(1(0(0(0(0(2(0(0(2(2(0(0(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))) 1(0(2(2(1(2(1(1(2(1(2(0(0(1(0(1(0(2(1(1(0(0(1(1(1(2(1(2(1(2(0(1(1(0(2(0(0(2(2(2(2(0(2(1(2(2(0(x1))))))))))))))))))))))))))))))))))))))))))))))) (66)
0(0(1(2(2(2(2(1(1(0(2(2(1(0(2(0(1(2(2(2(1(1(0(2(0(2(0(1(2(0(1(0(2(2(0(2(1(2(1(0(0(0(2(0(2(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) 1(2(1(0(2(2(0(0(0(2(0(2(1(2(1(0(2(1(0(1(0(2(0(2(2(0(1(2(1(0(2(0(1(0(2(2(0(2(1(1(1(2(2(2(1(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) (67)
2(0(2(0(1(0(1(1(2(0(1(1(1(2(2(1(0(0(0(1(0(0(2(2(0(1(0(0(1(1(1(1(1(2(0(0(1(1(1(1(0(0(0(0(2(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(2(1(1(2(2(0(0(0(2(1(1(1(0(1(1(1(0(0(1(0(2(0(1(2(2(1(1(2(0(0(2(2(0(1(1(0(0(2(0(0(1(2(1(2(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))) (68)
0(0(1(0(0(0(2(2(1(0(1(2(0(1(2(0(2(1(1(0(1(1(0(0(1(0(0(2(0(2(0(2(0(2(0(1(1(1(1(2(1(0(0(1(1(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) 0(1(2(1(1(1(1(0(2(2(1(1(2(0(1(2(1(0(1(2(0(1(0(1(2(2(0(1(2(1(0(1(2(2(0(1(1(1(0(1(1(2(1(0(1(0(2(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) (69)
0(0(2(1(2(2(0(0(2(0(1(1(1(0(1(0(0(0(1(0(2(2(2(1(1(0(2(2(1(2(1(0(2(1(0(0(0(2(2(0(2(0(1(1(2(2(1(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))) 0(2(0(1(2(1(1(0(0(2(0(2(1(2(0(2(2(1(2(0(0(1(2(0(0(1(2(2(0(0(1(2(2(2(1(2(2(0(1(2(1(2(1(0(2(0(0(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))) (70)
0(0(2(2(2(2(2(2(2(0(2(1(2(0(1(2(2(1(2(2(0(2(2(0(1(0(1(2(0(0(0(1(0(1(0(0(2(2(0(0(1(0(1(1(0(0(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) 2(0(0(1(2(2(1(2(2(2(1(1(2(2(2(2(2(0(2(0(1(1(1(0(1(2(1(0(0(2(2(1(0(0(2(0(0(0(1(1(0(2(1(2(2(2(1(1(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))) (71)
0(2(2(1(1(2(1(0(0(1(2(2(0(0(2(0(1(2(0(2(2(0(1(0(0(2(2(0(2(1(1(0(2(0(1(0(1(0(0(0(2(1(0(0(1(2(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) 0(2(0(2(2(1(2(0(2(0(1(0(1(1(1(0(1(0(0(0(1(2(1(1(1(0(1(2(1(0(2(1(1(0(2(2(2(1(2(2(1(0(2(1(2(2(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))) (72)
0(2(2(1(2(0(1(2(1(0(1(1(2(0(2(2(2(1(0(2(2(2(1(0(2(2(0(1(0(0(0(0(2(2(0(1(2(2(2(0(2(1(2(0(2(2(1(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(2(1(2(0(2(0(0(1(2(1(1(1(0(2(0(0(2(2(0(1(1(1(0(0(1(1(2(1(0(0(2(2(0(2(1(0(0(1(0(1(2(1(2(2(1(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))) (73)
2(0(1(2(2(0(2(2(1(0(1(2(2(2(0(2(2(2(1(0(1(2(0(2(1(0(1(0(1(0(0(2(2(2(2(0(2(1(1(0(2(2(0(0(0(2(2(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(2(2(2(2(2(1(1(0(1(2(2(2(0(0(1(2(0(0(1(2(2(0(2(0(1(2(1(0(0(2(2(2(2(0(1(0(0(2(2(2(2(0(0(2(1(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) (74)
2(2(1(0(1(1(0(0(2(1(0(2(1(2(2(2(1(1(0(2(0(2(1(2(2(2(1(0(1(1(1(0(1(1(0(0(2(2(0(2(0(0(0(1(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(0(1(0(1(1(2(1(1(1(1(0(0(1(1(1(1(0(1(1(2(2(0(1(2(0(2(1(1(0(0(0(1(2(1(0(1(1(1(1(2(1(0(0(1(1(0(0(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 +
896141/542
[23(x1)] = x1 +
4327908/4607
[26(x1)] = x1 +
895599/542
[21(x1)] = x1 +
0
[24(x1)] = x1 +
10
[27(x1)] = x1 +
8861477/9214
[22(x1)] = x1 +
900477/542
[25(x1)] = x1 +
7692953/9214
[28(x1)] = x1 +
6876207/4607
[10(x1)] = x1 +
901019/542
[13(x1)] = x1 +
0
[16(x1)] = x1 +
5548398/4607
[11(x1)] = x1 +
770502/4607
[14(x1)] = x1 +
4270967/4607
[17(x1)] = x1 +
449290/271
[12(x1)] = x1 +
6155389/9214
[15(x1)] = x1 +
802041/9214
[18(x1)] = x1 +
5396728/4607
[00(x1)] = x1 +
900477/542
[03(x1)] = x1 +
895599/542
[06(x1)] = x1 +
900477/542
[01(x1)] = x1 +
10
[04(x1)] = x1 +
14267891/9214
[07(x1)] = x1 +
6862821/4607
[02(x1)] = x1 +
11421991/9214
[05(x1)] = x1 +
0
[08(x1)] = x1 +
900477/542
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.