Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/150188)

The rewrite relation of the following TRS is considered.

0(x1) 1(1(x1)) (1)
2(x1) 1(1(x1)) (2)
0(0(x1)) 1(1(2(x1))) (3)
0(1(2(1(2(x1))))) 1(1(2(2(1(1(x1)))))) (4)
2(1(0(2(2(x1))))) 1(1(2(1(2(0(2(1(1(x1))))))))) (5)
2(2(0(1(0(0(2(0(0(2(x1)))))))))) 0(2(1(1(0(0(2(1(2(2(2(x1))))))))))) (6)
1(1(0(0(2(0(2(2(0(2(0(2(0(x1))))))))))))) 1(1(1(2(0(0(2(1(2(1(1(2(1(1(0(0(2(2(x1)))))))))))))))))) (7)
2(1(2(0(0(2(2(0(1(2(0(0(0(x1))))))))))))) 2(0(2(1(1(2(1(1(0(1(1(0(1(2(2(0(2(0(x1)))))))))))))))))) (8)
0(2(2(0(2(1(0(1(1(0(1(0(2(2(0(1(x1)))))))))))))))) 0(1(1(2(1(1(0(1(2(2(2(1(1(0(1(2(1(x1))))))))))))))))) (9)
2(2(1(0(1(1(1(1(2(1(0(0(0(1(0(2(x1)))))))))))))))) 0(2(1(0(1(1(2(2(2(0(1(1(1(1(2(2(1(1(0(x1))))))))))))))))))) (10)
0(0(2(2(0(0(0(0(1(1(1(2(1(2(2(0(1(x1))))))))))))))))) 2(1(1(1(1(1(1(2(2(2(2(1(2(2(0(0(0(2(1(x1))))))))))))))))))) (11)
0(0(2(1(1(2(0(0(0(2(0(1(2(0(1(2(1(0(x1)))))))))))))))))) 2(1(0(2(2(1(1(1(1(1(1(1(2(1(1(0(1(2(0(1(0(x1))))))))))))))))))))) (12)
1(2(2(1(0(1(0(1(2(1(0(0(2(0(2(1(2(1(2(1(x1)))))))))))))))))))) 1(1(1(2(2(2(1(2(1(0(0(0(0(0(1(1(1(1(0(0(1(1(1(x1))))))))))))))))))))))) (13)
2(1(2(0(0(1(2(2(1(2(0(0(0(1(2(2(1(0(0(1(x1)))))))))))))))))))) 2(2(1(1(0(1(2(0(0(1(2(0(2(0(2(2(1(0(0(1(x1)))))))))))))))))))) (14)
2(2(0(1(0(0(1(2(0(1(2(0(2(0(1(2(0(2(2(0(x1)))))))))))))))))))) 1(1(1(2(1(1(0(1(2(0(2(2(2(0(1(2(1(1(1(0(2(1(0(x1))))))))))))))))))))))) (15)
0(1(2(0(1(1(2(2(2(0(2(0(1(0(2(0(2(2(1(2(0(x1))))))))))))))))))))) 1(1(1(1(2(0(2(0(1(0(0(0(2(0(1(2(1(1(0(1(2(1(2(1(1(2(1(x1))))))))))))))))))))))))))) (16)
1(2(2(1(0(0(1(2(1(0(1(2(1(0(0(1(2(2(2(0(1(x1))))))))))))))))))))) 1(1(1(2(1(2(1(1(2(2(1(1(1(1(1(1(0(0(1(0(1(1(1(1(1(0(2(0(1(x1))))))))))))))))))))))))))))) (17)
2(1(2(2(1(2(2(1(2(1(2(1(0(0(1(0(0(0(1(0(0(x1))))))))))))))))))))) 2(1(1(1(1(1(2(2(1(1(0(1(2(0(1(2(0(1(0(0(0(0(1(1(1(x1))))))))))))))))))))))))) (18)
2(2(0(0(0(0(2(1(2(2(1(2(2(0(0(0(0(1(1(2(2(x1))))))))))))))))))))) 2(0(0(1(1(1(1(1(2(2(0(2(1(2(2(2(2(0(2(1(1(0(x1)))))))))))))))))))))) (19)
0(2(1(1(1(2(2(1(1(2(2(0(2(1(0(0(2(1(0(1(2(0(x1)))))))))))))))))))))) 2(1(2(0(1(0(0(0(1(1(1(1(2(2(0(2(2(0(2(1(1(2(x1)))))))))))))))))))))) (20)
1(0(1(0(2(2(1(0(0(1(2(0(0(2(2(2(0(1(2(2(1(0(x1)))))))))))))))))))))) 1(1(0(0(0(1(2(2(1(0(2(2(1(2(1(1(1(2(2(1(1(0(0(1(1(2(2(2(0(x1))))))))))))))))))))))))))))) (21)
0(2(0(1(2(2(0(2(1(1(2(0(1(2(2(2(0(0(1(0(0(2(0(2(x1)))))))))))))))))))))))) 0(2(2(2(1(1(0(2(1(2(1(1(0(1(1(1(2(0(0(0(0(1(2(0(2(x1))))))))))))))))))))))))) (22)
2(2(0(1(0(0(2(0(0(0(1(1(1(2(2(1(0(2(1(0(0(2(1(2(x1)))))))))))))))))))))))) 2(2(0(1(0(0(1(2(0(2(1(2(2(1(1(1(0(0(1(0(1(1(1(1(2(x1))))))))))))))))))))))))) (23)
1(2(0(0(0(0(2(2(0(0(2(0(0(2(2(1(1(0(0(0(2(1(2(0(2(1(x1)))))))))))))))))))))))))) 1(2(1(0(1(1(2(1(0(2(2(0(2(1(0(1(1(2(0(1(1(2(0(0(2(0(1(0(1(x1))))))))))))))))))))))))))))) (24)
1(0(2(0(0(1(0(1(1(0(2(1(2(2(2(2(0(0(1(0(2(1(1(0(2(2(0(0(x1)))))))))))))))))))))))))))) 1(2(1(1(1(1(2(1(0(2(1(2(0(1(1(0(1(0(1(0(2(2(2(0(0(1(1(1(2(1(x1)))))))))))))))))))))))))))))) (25)
2(0(1(0(2(1(0(2(0(0(0(2(0(1(0(0(0(2(2(0(0(1(1(1(1(0(0(1(x1)))))))))))))))))))))))))))) 2(1(2(2(1(1(1(1(0(1(1(2(2(2(1(1(2(2(2(0(1(1(1(2(1(0(0(1(2(1(0(2(1(x1))))))))))))))))))))))))))))))))) (26)
0(0(2(0(0(0(1(1(0(0(1(0(0(0(2(1(2(2(0(2(2(0(2(2(0(2(1(0(2(x1))))))))))))))))))))))))))))) 2(2(1(2(1(1(1(0(2(2(0(0(1(0(1(1(2(2(2(1(2(1(2(2(1(0(2(1(1(2(0(2(2(0(x1)))))))))))))))))))))))))))))))))) (27)
2(0(1(2(1(1(0(1(0(2(2(2(1(0(0(0(0(0(0(1(2(1(0(2(2(0(1(0(0(x1))))))))))))))))))))))))))))) 2(2(1(2(1(0(0(1(0(0(0(2(1(2(1(0(0(0(1(1(0(0(0(2(2(0(1(2(0(x1))))))))))))))))))))))))))))) (28)
0(2(2(0(0(0(0(1(1(0(0(0(0(1(0(2(1(0(0(2(0(1(1(2(2(0(0(2(0(2(x1)))))))))))))))))))))))))))))) 1(1(2(1(0(0(2(1(0(2(2(1(1(2(1(1(1(2(1(1(0(0(1(1(2(2(1(1(0(2(2(0(2(x1))))))))))))))))))))))))))))))))) (29)
1(2(0(1(0(2(2(1(0(0(1(1(0(1(2(0(1(1(2(1(0(0(1(1(1(1(1(2(0(0(x1)))))))))))))))))))))))))))))) 1(1(1(1(0(1(1(0(0(2(0(0(2(0(1(0(1(1(2(2(0(1(0(1(0(1(1(2(1(2(x1)))))))))))))))))))))))))))))) (30)
2(0(2(1(0(2(1(0(0(1(2(2(0(0(0(2(1(0(2(1(2(2(1(0(0(1(2(1(2(0(x1)))))))))))))))))))))))))))))) 0(1(2(1(0(0(1(2(1(0(0(0(0(2(2(2(0(1(0(1(1(2(0(1(1(2(1(2(1(1(0(0(0(1(1(1(0(x1))))))))))))))))))))))))))))))))))))) (31)
2(2(2(0(2(0(2(0(2(0(2(2(2(1(0(0(0(1(2(1(1(1(2(0(0(1(2(1(2(2(x1)))))))))))))))))))))))))))))) 2(0(2(2(1(1(2(0(0(2(1(0(1(0(0(0(2(2(2(0(2(1(2(0(1(1(2(2(1(1(0(1(x1)))))))))))))))))))))))))))))))) (32)
0(1(2(2(0(2(2(1(0(0(1(0(0(1(0(0(1(2(0(1(2(1(2(0(0(0(1(1(0(2(0(2(x1)))))))))))))))))))))))))))))))) 0(0(0(0(1(1(1(1(0(0(1(1(1(1(0(2(1(2(1(1(1(2(2(1(1(0(2(2(0(1(0(1(0(0(1(1(1(0(0(0(1(2(2(x1))))))))))))))))))))))))))))))))))))))))))) (33)
2(2(0(2(0(0(2(0(2(0(0(1(2(1(1(0(2(1(0(2(2(0(2(1(0(1(0(2(0(1(2(2(x1)))))))))))))))))))))))))))))))) 1(2(1(2(1(2(2(1(1(0(0(2(1(1(2(1(0(1(1(1(2(0(2(0(0(0(0(2(2(1(0(2(0(2(0(1(1(x1))))))))))))))))))))))))))))))))))))) (34)
2(2(0(2(2(2(2(2(2(2(0(0(0(1(1(1(0(0(0(1(0(0(0(1(0(2(0(1(1(2(2(2(x1)))))))))))))))))))))))))))))))) 2(1(1(0(0(0(2(2(1(0(2(1(0(0(2(1(2(1(2(1(1(2(2(0(2(0(1(1(1(1(2(1(1(1(x1)))))))))))))))))))))))))))))))))) (35)
0(0(2(2(2(0(0(0(1(2(0(1(1(1(0(0(2(1(0(2(2(1(2(0(0(2(2(2(0(1(0(0(2(x1))))))))))))))))))))))))))))))))) 0(2(0(2(2(2(2(2(0(1(0(1(1(2(0(2(2(1(1(0(0(1(1(1(2(0(2(2(0(2(2(1(1(1(0(2(1(0(x1)))))))))))))))))))))))))))))))))))))) (36)
0(1(2(0(0(0(1(0(1(2(0(0(0(0(2(2(2(0(1(2(0(0(1(0(2(2(1(0(0(2(0(0(0(x1))))))))))))))))))))))))))))))))) 1(1(2(2(1(1(1(1(1(2(1(0(2(1(1(1(2(1(0(2(0(2(2(2(2(2(1(1(1(1(0(0(1(1(0(0(0(1(2(1(0(2(1(1(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))) (37)
2(1(0(1(2(1(2(2(1(0(0(0(2(1(2(0(2(2(2(2(0(1(2(0(1(2(1(2(2(1(0(1(2(0(x1)))))))))))))))))))))))))))))))))) 1(1(1(2(2(1(1(0(0(2(2(2(1(0(1(0(1(0(2(1(2(1(2(1(1(2(0(2(0(0(2(0(1(1(2(1(1(2(1(0(1(x1))))))))))))))))))))))))))))))))))))))))) (38)
0(2(2(0(0(1(0(0(2(0(0(2(2(0(2(1(0(0(0(0(1(0(0(2(0(2(2(1(2(1(2(2(0(2(2(x1))))))))))))))))))))))))))))))))))) 0(1(1(1(1(2(2(0(2(0(2(0(2(2(1(1(2(2(1(2(0(2(0(1(1(1(1(0(1(1(1(2(0(0(1(2(2(x1))))))))))))))))))))))))))))))))))))) (39)
1(0(2(0(2(2(0(2(0(1(2(2(0(1(2(0(0(1(0(2(1(0(2(0(0(0(1(1(2(0(0(2(0(0(2(x1))))))))))))))))))))))))))))))))))) 1(2(2(2(0(2(2(2(1(1(0(2(1(2(2(0(0(2(1(2(1(0(2(1(1(1(2(2(2(1(0(2(1(0(1(1(2(1(1(2(2(x1))))))))))))))))))))))))))))))))))))))))) (40)
1(2(2(2(0(0(2(0(2(0(0(2(1(2(2(2(2(1(1(2(0(2(2(1(0(0(1(2(0(0(2(1(0(0(2(x1))))))))))))))))))))))))))))))))))) 1(2(1(2(2(2(0(2(2(2(0(0(2(2(2(2(2(0(1(2(1(2(0(1(2(0(0(0(1(1(2(0(0(0(0(x1))))))))))))))))))))))))))))))))))) (41)
1(2(2(2(2(2(2(1(1(0(0(0(2(0(0(1(2(0(1(0(0(1(2(0(2(0(0(2(0(1(1(0(2(0(2(x1))))))))))))))))))))))))))))))))))) 1(0(1(1(1(2(1(0(2(1(1(1(0(0(2(0(0(1(1(1(1(1(0(2(0(1(2(1(0(0(0(0(1(2(2(2(2(2(0(1(2(x1))))))))))))))))))))))))))))))))))))))))) (42)
2(0(1(0(0(0(0(1(0(2(2(2(1(1(2(2(2(0(2(2(1(2(0(2(1(0(1(0(0(0(2(0(2(1(1(x1))))))))))))))))))))))))))))))))))) 1(1(1(2(1(1(1(1(2(0(0(0(1(1(1(1(0(1(0(0(1(2(0(1(2(0(2(1(1(2(0(1(0(0(1(1(2(0(2(1(0(2(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))) (43)
2(1(0(0(0(0(1(2(0(1(2(0(1(0(0(2(0(1(1(1(0(0(0(0(0(2(0(1(2(2(2(0(1(2(2(x1))))))))))))))))))))))))))))))))))) 2(1(0(1(0(2(2(2(0(2(1(1(2(2(2(2(0(2(0(2(0(1(0(1(1(2(1(1(2(0(2(2(1(0(2(2(1(x1))))))))))))))))))))))))))))))))))))) (44)
2(2(1(2(2(0(0(1(1(1(2(2(1(0(2(1(1(2(2(2(2(2(0(2(1(0(0(2(0(0(2(1(1(0(2(x1))))))))))))))))))))))))))))))))))) 1(0(1(2(2(2(1(2(1(0(0(2(1(2(2(2(1(1(0(1(1(0(1(1(1(1(1(0(2(2(0(0(0(0(0(0(0(x1))))))))))))))))))))))))))))))))))))) (45)
2(2(1(2(2(2(0(1(0(2(1(1(0(2(1(2(2(0(0(1(0(1(0(2(0(2(1(1(2(0(2(2(1(0(0(x1))))))))))))))))))))))))))))))))))) 1(0(2(2(1(1(1(1(0(0(2(2(2(1(1(2(2(1(1(2(1(2(2(2(1(1(1(0(0(0(2(1(2(1(2(1(0(1(2(2(x1)))))))))))))))))))))))))))))))))))))))) (46)
2(2(2(1(0(0(0(0(2(2(0(2(2(1(2(2(2(0(0(0(0(1(0(2(1(1(2(0(1(2(1(1(2(0(0(x1))))))))))))))))))))))))))))))))))) 1(1(1(1(0(2(2(1(2(2(1(0(0(0(1(0(0(0(0(2(0(0(1(1(2(1(1(0(1(0(1(0(1(1(2(0(1(0(2(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))) (47)
0(1(2(0(1(1(0(1(0(1(1(2(1(2(2(1(1(1(0(2(0(0(0(0(0(2(1(0(1(2(0(0(2(1(0(0(x1)))))))))))))))))))))))))))))))))))) 0(0(0(2(2(1(0(1(2(1(2(1(1(2(0(0(2(1(0(1(1(1(1(2(0(0(0(1(0(0(0(2(2(1(1(1(1(x1))))))))))))))))))))))))))))))))))))) (48)
0(2(0(1(0(0(0(0(2(2(0(0(0(0(2(0(0(2(1(2(0(0(1(2(0(0(1(1(1(2(2(0(1(1(0(2(x1)))))))))))))))))))))))))))))))))))) 2(0(0(0(2(2(0(0(1(1(0(2(2(2(1(0(1(1(1(0(1(0(2(2(1(2(1(0(1(1(2(0(0(0(0(1(1(2(2(0(2(x1))))))))))))))))))))))))))))))))))))))))) (49)
0(2(0(2(2(1(2(1(2(1(2(0(2(1(1(2(0(1(2(0(1(0(1(0(0(2(2(1(0(2(0(0(0(0(1(0(x1)))))))))))))))))))))))))))))))))))) 0(2(0(0(0(1(2(2(1(0(0(1(2(0(1(0(1(2(2(2(0(1(2(2(1(2(1(1(2(2(1(0(0(1(1(1(0(x1))))))))))))))))))))))))))))))))))))) (50)
0(0(2(0(1(0(2(1(1(1(0(1(2(2(2(2(1(1(0(2(2(0(2(2(2(2(1(2(2(2(0(1(0(2(0(2(1(x1))))))))))))))))))))))))))))))))))))) 0(2(1(1(1(0(2(2(2(2(1(1(1(1(2(2(1(0(0(1(2(0(1(2(2(0(1(1(2(0(0(0(0(2(2(1(2(0(2(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))) (51)
1(0(1(1(2(1(2(2(0(2(0(1(2(2(0(1(2(2(2(1(0(0(2(1(2(1(0(2(0(1(2(0(0(2(2(1(0(x1))))))))))))))))))))))))))))))))))))) 1(1(2(1(0(0(0(0(1(0(2(1(1(2(0(2(2(1(1(1(1(2(2(1(0(0(2(2(2(1(1(1(1(0(1(2(0(1(1(0(2(x1))))))))))))))))))))))))))))))))))))))))) (52)
2(2(0(1(2(0(0(0(0(0(2(1(2(0(0(2(1(0(2(2(2(1(0(2(2(2(2(1(0(2(0(2(0(0(2(2(0(2(x1)))))))))))))))))))))))))))))))))))))) 1(1(1(1(2(2(0(1(1(2(1(0(2(0(2(1(1(2(0(0(0(2(1(2(0(2(2(2(2(1(0(1(2(0(2(1(1(1(2(2(2(0(1(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))) (53)
2(2(1(0(0(2(1(0(1(2(2(0(0(2(2(2(0(0(1(0(2(1(2(2(2(2(1(2(0(2(0(2(0(2(1(1(1(2(x1)))))))))))))))))))))))))))))))))))))) 2(2(1(2(1(2(1(1(1(1(1(1(2(1(1(2(1(0(1(2(2(1(0(2(2(0(1(0(2(2(1(0(0(1(0(0(2(2(2(1(2(2(1(1(x1)))))))))))))))))))))))))))))))))))))))))))) (54)
0(0(1(2(2(0(0(0(2(2(2(0(0(0(0(1(1(0(0(1(0(2(2(0(0(0(0(1(1(0(2(2(0(2(0(2(0(2(2(x1))))))))))))))))))))))))))))))))))))))) 1(1(2(2(2(2(1(0(2(2(0(2(0(1(0(2(1(0(2(1(1(2(2(0(1(0(0(1(2(0(0(1(1(2(0(0(0(2(1(1(x1)))))))))))))))))))))))))))))))))))))))) (55)
0(1(0(0(2(2(0(0(2(0(0(2(0(2(0(0(2(2(2(1(2(2(0(1(1(2(2(2(2(2(2(1(2(0(0(2(2(0(1(x1))))))))))))))))))))))))))))))))))))))) 1(0(2(2(0(1(2(1(2(1(2(2(0(2(1(1(0(0(0(1(2(2(0(1(0(1(1(1(0(2(2(2(0(0(2(1(1(2(0(0(0(2(0(2(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) (56)
2(0(2(2(1(1(0(0(2(2(0(0(1(1(2(2(0(2(1(2(2(0(1(0(0(2(1(2(2(2(1(2(0(1(2(2(1(0(2(x1))))))))))))))))))))))))))))))))))))))) 1(2(2(1(1(1(2(1(2(2(0(0(2(1(0(1(2(1(1(1(1(1(1(1(2(2(2(2(2(1(1(1(1(2(0(0(2(0(1(2(1(1(2(1(2(x1))))))))))))))))))))))))))))))))))))))))))))) (57)
2(0(0(2(2(0(2(0(1(2(0(0(0(1(0(2(2(1(0(0(0(2(0(0(2(0(1(0(2(0(2(0(2(2(1(0(2(0(0(0(2(x1))))))))))))))))))))))))))))))))))))))))) 2(1(0(0(0(2(2(0(0(1(0(0(0(0(0(2(0(2(0(2(0(2(2(1(0(1(1(1(2(0(0(1(1(0(0(2(2(0(0(0(2(2(1(1(x1)))))))))))))))))))))))))))))))))))))))))))) (58)
0(0(1(2(0(2(1(0(0(1(2(0(1(1(2(1(1(2(0(0(1(2(0(1(0(2(0(1(2(2(1(2(2(2(1(0(0(0(0(0(2(2(x1)))))))))))))))))))))))))))))))))))))))))) 0(1(1(1(0(0(2(1(1(0(1(0(1(0(2(0(2(2(1(2(1(2(1(1(1(1(1(2(2(1(2(2(1(0(0(0(1(1(0(2(2(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))) (59)
0(0(1(2(2(0(2(0(0(1(2(1(2(1(2(2(1(0(2(1(0(2(0(0(0(2(2(0(2(1(0(2(2(0(1(2(2(2(2(2(0(2(x1)))))))))))))))))))))))))))))))))))))))))) 1(2(2(1(0(0(2(0(1(0(1(1(0(2(0(2(1(2(2(0(2(2(2(1(1(2(0(1(0(2(2(2(2(1(0(0(1(2(0(1(1(1(1(1(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))) (60)
0(0(2(2(2(2(2(0(1(0(2(0(1(2(0(0(0(0(1(1(1(0(1(0(1(0(0(1(0(0(2(1(0(1(0(2(0(0(0(2(1(0(x1)))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(1(0(1(2(2(1(1(1(1(2(1(0(1(1(0(1(1(2(0(1(0(2(0(1(2(2(0(1(2(0(0(1(0(0(2(0(2(2(0(1(2(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))) (61)
0(1(2(0(1(0(1(2(2(2(0(0(0(2(0(0(0(0(0(0(2(2(1(0(0(2(2(0(0(1(2(2(1(2(2(1(2(2(2(2(0(2(x1)))))))))))))))))))))))))))))))))))))))))) 2(0(2(1(1(2(1(0(1(0(1(2(0(0(1(1(1(1(1(0(1(0(1(2(1(1(0(2(0(1(1(1(0(2(0(2(0(1(1(1(1(1(1(0(1(1(0(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) (62)
0(1(2(2(0(2(0(1(2(0(2(1(0(1(0(0(1(2(1(0(0(1(0(0(0(0(2(2(0(0(0(1(1(0(0(2(0(2(2(1(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))) 1(0(0(0(0(0(0(0(0(1(1(0(0(2(2(2(1(2(2(1(2(0(1(0(1(1(2(0(1(1(1(1(1(0(1(0(1(1(0(1(0(2(2(1(2(2(0(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))) (63)
0(2(0(2(2(1(0(1(2(0(2(0(2(1(0(2(1(2(1(1(1(1(2(2(2(0(0(1(1(2(1(1(0(0(2(0(1(1(2(0(1(2(0(x1))))))))))))))))))))))))))))))))))))))))))) 1(1(0(1(1(2(0(1(2(1(0(1(1(2(0(0(0(2(2(2(2(0(0(2(0(0(0(2(2(0(2(1(1(1(1(1(0(0(1(2(2(2(1(2(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))) (64)
1(2(2(0(1(0(1(0(1(2(0(0(0(1(2(2(1(2(1(0(0(0(0(0(2(2(1(1(0(1(0(2(0(0(0(1(2(1(1(0(2(2(0(1(x1)))))))))))))))))))))))))))))))))))))))))))) 1(1(2(2(0(1(0(0(2(0(1(0(0(1(0(0(1(2(0(0(1(2(0(1(1(2(0(2(0(2(2(2(2(1(1(2(0(1(1(2(1(0(0(1(0(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))) (65)
0(2(0(2(2(0(0(0(0(2(0(2(1(0(1(1(0(2(0(1(1(0(2(2(0(0(2(1(0(2(1(2(1(2(1(2(2(1(0(0(1(0(1(1(0(x1))))))))))))))))))))))))))))))))))))))))))))) 2(2(1(2(2(0(0(1(1(2(1(2(0(0(0(0(1(1(1(2(2(2(1(2(1(1(1(1(1(0(2(0(0(2(0(1(0(0(1(1(1(1(0(2(0(2(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) (66)
2(2(1(0(2(1(2(1(0(0(0(2(1(0(2(2(0(2(2(0(2(0(1(2(0(0(2(1(2(2(1(0(0(1(2(0(2(1(0(2(1(2(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))))) 2(2(0(0(2(1(2(2(0(2(0(2(2(2(2(2(1(0(1(2(0(2(1(0(0(0(2(1(0(2(0(0(2(1(2(1(0(1(0(2(1(1(0(1(0(x1))))))))))))))))))))))))))))))))))))))))))))) (67)
0(2(2(2(1(1(2(1(0(2(2(1(0(1(0(0(2(0(2(2(2(1(2(1(0(2(0(2(1(2(2(0(0(1(0(0(1(0(0(1(1(2(1(1(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))) 1(1(1(0(2(2(0(0(1(0(1(1(1(1(1(0(2(0(1(1(0(1(0(0(2(2(1(1(1(1(0(2(2(1(2(2(2(0(0(0(1(0(0(2(0(1(2(0(0(x1))))))))))))))))))))))))))))))))))))))))))))))))) (68)
2(2(1(2(2(1(2(1(1(2(0(1(2(1(0(1(2(1(0(2(2(2(0(2(1(0(0(2(0(1(0(2(2(0(2(2(2(1(1(2(2(0(2(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))) 2(0(1(1(1(0(0(0(2(0(0(0(0(1(2(2(0(2(0(1(1(1(2(1(2(0(2(1(2(2(1(1(0(1(1(0(1(2(2(1(2(1(1(2(2(1(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) (69)
0(1(0(2(0(0(0(1(1(0(1(0(2(1(2(0(2(2(1(1(0(2(0(1(0(2(2(1(0(0(2(1(0(2(1(2(1(1(0(1(2(0(0(0(0(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))) 2(1(1(0(2(2(0(1(1(0(0(2(2(1(1(2(2(1(1(1(1(2(0(1(0(0(0(2(0(2(0(2(2(2(0(1(2(1(0(2(0(1(1(1(0(0(0(2(0(x1))))))))))))))))))))))))))))))))))))))))))))))))) (70)
0(0(2(2(2(2(2(1(2(1(0(1(2(0(0(2(0(1(0(2(1(0(2(1(2(0(2(1(2(2(0(0(2(0(1(2(0(1(2(0(2(2(1(0(2(0(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))) 0(2(2(1(2(2(2(0(2(0(1(2(2(1(2(2(1(1(1(2(1(2(2(2(1(1(2(1(0(1(2(2(0(1(0(0(2(0(2(0(0(0(0(2(2(1(1(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) (71)
1(2(0(2(1(2(2(0(2(2(1(2(1(0(1(0(1(2(2(1(1(0(2(1(2(2(2(1(1(0(0(0(0(1(1(0(1(2(0(2(1(0(0(2(0(2(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(2(0(0(1(0(2(1(0(0(2(2(1(2(1(1(0(0(2(1(1(2(2(0(2(2(2(2(1(2(0(0(0(1(1(1(1(0(1(2(1(2(2(0(2(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) (72)
2(0(0(2(0(0(1(2(2(1(2(1(1(0(0(2(1(0(2(1(0(0(1(2(0(1(1(1(2(0(2(1(2(1(2(0(0(0(0(0(0(2(0(1(0(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))) 0(0(0(0(0(0(0(2(2(1(0(2(1(0(0(2(1(1(0(1(1(0(1(0(2(1(1(2(2(0(2(2(1(0(2(2(0(0(0(0(1(2(2(1(1(2(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))) (73)
2(1(2(2(1(2(2(2(0(1(0(0(2(2(2(2(1(1(1(2(1(0(1(1(2(2(2(1(2(0(2(2(0(2(1(0(2(0(2(2(2(2(0(2(0(0(0(2(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(1(0(2(1(2(2(1(0(2(2(0(0(2(0(2(2(1(1(1(1(1(0(2(0(0(1(0(2(1(2(1(2(0(2(0(2(0(1(2(1(1(1(0(0(1(0(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))) (74)
0(0(1(1(0(0(2(2(1(2(2(1(2(2(1(0(2(0(0(1(1(2(2(1(1(1(2(2(2(0(1(2(0(0(1(2(1(2(2(1(1(0(2(2(0(2(1(0(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(2(1(0(2(2(1(1(2(2(1(1(0(1(1(2(0(1(1(1(2(2(1(2(1(2(2(2(2(2(2(0(0(1(0(0(2(1(0(2(0(2(2(0(1(1(0(2(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 +
21296/9
[23(x1)] = x1 +
20927/9
[26(x1)] = x1 +
7766/3
[21(x1)] = x1 +
8519/9
[24(x1)] = x1 +
0
[27(x1)] = x1 +
7775/3
[22(x1)] = x1 +
7766/3
[25(x1)] = x1 +
12853/9
[28(x1)] = x1 +
7766/3
[10(x1)] = x1 +
6341/9
[13(x1)] = x1 +
3
[16(x1)] = x1 +
16940/9
[11(x1)] = x1 +
0
[14(x1)] = x1 +
0
[17(x1)] = x1 +
1
[12(x1)] = x1 +
7766/3
[15(x1)] = x1 +
1
[18(x1)] = x1 +
11071/9
[00(x1)] = x1 +
7766/3
[03(x1)] = x1 +
7766/3
[06(x1)] = x1 +
7775/3
[01(x1)] = x1 +
7775/3
[04(x1)] = x1 +
1
[07(x1)] = x1 +
7766/3
[02(x1)] = x1 +
7775/3
[05(x1)] = x1 +
7766/3
[08(x1)] = x1 +
7775/3
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.