Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/57852)

The rewrite relation of the following TRS is considered.

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

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 Rule Removal

Using the linear polynomial interpretation over the naturals
[0(x1)] = 1 · x1 + 6
[1(x1)] = 1 · x1 + 5
[2(x1)] = 1 · x1
all of the following rules can be deleted.
0(1(2(1(x1)))) 0(2(2(2(1(x1))))) (1)
0(2(1(1(2(0(2(x1))))))) 2(2(2(0(2(1(2(2(x1)))))))) (2)
2(0(0(0(0(1(0(x1))))))) 1(2(2(2(1(2(1(0(1(x1))))))))) (3)
0(0(0(1(1(0(0(1(0(1(1(0(0(x1))))))))))))) 2(2(1(2(0(2(2(1(1(1(2(2(1(0(x1)))))))))))))) (4)
0(1(1(0(0(1(1(2(1(2(0(0(2(x1))))))))))))) 1(2(2(2(1(2(1(0(2(2(0(0(1(2(2(2(2(x1))))))))))))))))) (5)
1(0(0(0(1(0(1(1(0(1(1(0(1(2(0(1(x1)))))))))))))))) 2(2(1(1(2(1(2(0(0(1(2(0(0(1(1(0(0(0(x1)))))))))))))))))) (6)
1(1(0(1(1(2(0(0(0(0(0(0(1(2(0(0(x1)))))))))))))))) 2(0(1(1(0(0(2(0(0(2(2(2(0(2(1(2(2(x1))))))))))))))))) (8)
2(0(0(2(2(2(0(1(2(1(2(0(1(1(0(0(x1)))))))))))))))) 2(2(2(2(2(2(2(1(2(0(0(2(1(0(1(0(1(2(1(2(x1)))))))))))))))))))) (9)
1(1(1(1(1(1(2(1(0(1(2(1(0(2(2(0(1(x1))))))))))))))))) 1(1(2(2(0(2(2(2(2(1(0(1(2(0(2(1(0(0(0(x1))))))))))))))))))) (10)
0(2(0(0(2(1(0(0(0(0(1(0(2(1(1(1(0(1(x1)))))))))))))))))) 0(1(2(2(1(0(0(2(2(1(1(1(1(2(1(1(2(1(0(x1))))))))))))))))))) (11)
1(1(2(1(2(1(1(1(1(1(1(2(2(1(0(1(2(1(x1)))))))))))))))))) 2(0(2(2(2(2(2(1(1(1(2(0(1(0(2(1(2(2(1(2(2(2(1(2(2(2(x1)))))))))))))))))))))))))) (12)
0(0(1(0(2(0(1(0(1(1(2(0(0(1(0(0(0(1(1(x1))))))))))))))))))) 0(2(2(2(0(2(0(1(2(1(1(0(1(2(2(0(1(0(0(2(2(2(2(x1))))))))))))))))))))))) (13)
0(2(0(2(1(0(2(2(1(0(0(2(0(0(0(2(0(0(1(x1))))))))))))))))))) 2(2(0(0(1(2(1(2(1(2(2(2(2(1(0(2(1(1(2(0(x1)))))))))))))))))))) (14)
1(0(0(2(2(0(2(0(2(0(0(2(1(1(0(0(0(1(2(x1))))))))))))))))))) 2(2(1(0(2(1(0(2(1(2(1(2(1(0(2(2(2(1(2(2(1(2(x1)))))))))))))))))))))) (15)
0(1(0(0(1(2(2(0(1(0(1(1(1(2(1(1(1(1(0(2(0(x1))))))))))))))))))))) 1(0(1(1(1(1(2(2(1(1(2(1(0(0(0(2(2(0(2(0(0(2(x1)))))))))))))))))))))) (16)
1(1(0(1(0(1(1(2(1(0(0(0(1(0(2(0(1(0(0(1(0(1(x1)))))))))))))))))))))) 0(1(1(1(1(1(0(0(2(1(0(0(2(1(2(0(2(2(1(2(2(1(1(x1))))))))))))))))))))))) (17)
0(2(0(2(2(1(0(1(2(1(0(0(1(0(2(0(0(0(0(0(2(2(0(x1))))))))))))))))))))))) 2(1(1(2(2(1(2(2(2(1(0(0(2(2(0(1(0(1(2(0(0(2(1(1(x1)))))))))))))))))))))))) (18)
1(0(0(1(2(1(2(0(0(0(2(1(0(2(0(2(0(0(0(0(0(1(1(2(2(x1))))))))))))))))))))))))) 1(1(1(1(2(0(1(2(2(2(1(2(1(0(1(2(2(0(2(2(2(0(0(1(0(2(x1)))))))))))))))))))))))))) (19)
2(1(2(2(1(2(2(2(0(0(2(1(1(1(0(1(1(2(0(1(1(2(0(2(2(x1))))))))))))))))))))))))) 2(2(2(2(0(0(1(2(1(2(0(0(2(1(2(0(2(2(1(2(0(0(2(2(0(1(x1)))))))))))))))))))))))))) (20)
1(0(0(2(1(1(1(1(1(2(2(1(1(1(0(2(1(0(1(2(1(2(0(0(1(2(x1)))))))))))))))))))))))))) 2(1(2(2(1(2(1(0(2(2(2(1(0(2(2(1(0(1(0(2(2(2(2(1(2(1(2(1(1(0(2(x1))))))))))))))))))))))))))))))) (21)
0(1(2(1(2(2(0(0(0(1(2(1(0(2(0(0(0(1(2(2(2(0(0(0(1(2(1(x1))))))))))))))))))))))))))) 2(2(1(2(2(2(1(2(2(2(2(1(2(2(0(2(1(1(1(0(1(0(2(2(1(1(0(1(x1)))))))))))))))))))))))))))) (22)
1(2(2(0(2(0(1(2(1(2(2(0(2(1(1(1(1(2(0(1(0(0(1(2(0(1(2(x1))))))))))))))))))))))))))) 1(2(0(0(2(2(0(2(2(0(0(2(0(0(1(2(0(0(2(2(2(0(1(2(1(0(1(2(x1)))))))))))))))))))))))))))) (23)
0(2(0(2(0(1(0(0(1(0(2(0(0(0(0(1(0(0(2(2(2(1(1(2(0(2(1(2(2(2(x1)))))))))))))))))))))))))))))) 2(2(1(2(0(1(1(1(2(2(1(2(2(2(0(1(2(2(2(1(2(1(1(1(0(0(1(2(2(0(0(x1))))))))))))))))))))))))))))))) (24)
1(0(2(0(2(0(2(0(0(1(1(1(2(0(1(0(0(0(1(2(0(1(1(2(0(0(2(1(0(0(x1)))))))))))))))))))))))))))))) 1(0(1(2(2(1(2(1(2(0(1(1(0(0(2(2(2(2(1(2(0(1(1(1(1(1(2(2(2(2(1(1(x1)))))))))))))))))))))))))))))))) (25)
1(0(2(2(0(2(1(1(0(2(0(1(2(0(2(1(0(1(0(2(1(0(0(1(0(0(2(0(2(2(x1)))))))))))))))))))))))))))))) 1(1(0(1(2(2(1(1(1(2(1(2(2(0(0(2(2(1(1(2(0(1(2(1(2(0(2(0(2(0(0(2(x1)))))))))))))))))))))))))))))))) (26)
1(2(0(2(0(0(1(2(2(1(1(0(1(2(0(1(0(1(0(0(2(0(1(0(1(0(1(0(2(0(x1)))))))))))))))))))))))))))))) 2(1(0(2(2(2(0(2(1(2(0(0(2(1(2(2(2(0(1(2(2(2(1(1(0(1(1(0(1(1(0(2(x1)))))))))))))))))))))))))))))))) (27)
2(2(2(1(2(0(0(1(1(1(2(0(0(2(0(1(1(0(2(1(0(2(0(2(1(1(0(0(0(2(x1)))))))))))))))))))))))))))))) 2(2(2(1(2(1(2(2(2(1(0(0(2(2(1(0(2(2(0(0(2(0(0(0(2(1(1(2(1(1(1(2(2(2(x1)))))))))))))))))))))))))))))))))) (28)
0(1(1(0(0(2(2(1(0(1(1(1(2(2(1(2(0(0(1(1(0(0(2(0(2(2(0(1(1(1(1(x1))))))))))))))))))))))))))))))) 0(2(2(0(1(0(1(1(2(1(2(0(0(0(0(0(1(0(1(0(1(2(2(2(2(0(0(0(1(2(1(2(x1)))))))))))))))))))))))))))))))) (29)
0(1(1(1(2(1(1(0(1(2(2(2(0(1(2(1(0(0(1(2(2(1(1(2(0(1(1(1(2(1(1(x1))))))))))))))))))))))))))))))) 2(2(1(1(2(1(2(1(2(2(1(0(0(2(1(2(2(2(0(0(0(2(2(0(2(1(1(1(0(2(2(2(x1)))))))))))))))))))))))))))))))) (30)
1(2(1(1(1(1(2(1(0(1(0(2(2(0(0(1(0(1(0(1(2(1(1(1(1(0(2(2(2(2(1(x1))))))))))))))))))))))))))))))) 2(0(1(2(2(2(1(2(0(0(2(2(1(1(2(2(2(0(1(2(1(2(1(2(2(1(2(1(1(2(0(1(0(x1))))))))))))))))))))))))))))))))) (31)
2(0(1(0(1(2(1(2(2(2(0(1(0(0(0(1(2(0(1(1(1(1(2(2(0(0(0(1(0(0(0(x1))))))))))))))))))))))))))))))) 2(2(0(2(2(0(2(1(1(2(1(2(2(1(0(0(1(0(2(0(2(2(2(1(0(2(2(0(1(0(2(2(1(2(x1)))))))))))))))))))))))))))))))))) (32)
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1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

There are 140 ruless (increase limit for explicit display).

1.1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.