Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/262998)

The rewrite relation of the following TRS is considered.

0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (1)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (2)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (3)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (4)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (5)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (6)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (7)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (8)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (9)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (10)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (11)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (12)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (13)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (14)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (15)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (16)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (17)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (18)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(1(0(1(1(0(0(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (19)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (20)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(1(0(1(1(0(0(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (21)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (22)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (23)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (24)
1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(0(0(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (25)
1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (26)
1(0(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(0(1(1(0(0(0(0(0(0(1(1(1(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (27)
1(0(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(0(1(1(0(0(0(0(0(0(1(1(1(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (28)
1(0(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(0(1(1(0(0(0(0(0(0(1(1(1(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (29)
1(0(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(0(1(1(0(0(0(0(0(0(1(1(1(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(1(0(1(1(0(0(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (30)
1(0(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(0(1(1(0(0(0(0(0(0(1(1(1(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (31)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Rule Removal

Using the matrix interpretations of dimension 1 with strict dimension 1 over the rationals with delta = 1
[1(x1)] = x1 +
1
[0(x1)] = x1 +
0
all of the following rules can be deleted.
0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (1)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (3)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (4)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (5)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (6)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (7)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (8)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (9)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (10)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (11)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (12)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (13)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (14)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (15)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (16)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (17)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (18)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(1(0(1(1(0(0(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (19)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (20)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(1(0(1(1(0(0(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (21)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (22)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (23)
0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (24)
1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(0(1(0(1(1(1(0(1(0(0(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (25)
1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(0(1(0(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(0(1(1(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (26)
1(0(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(0(1(1(0(0(0(0(0(0(1(1(1(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(0(0(0(1(1(1(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (27)
1(0(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(0(1(1(0(0(0(0(0(0(1(1(1(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (28)
1(0(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(0(1(1(0(0(0(0(0(0(1(1(1(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(1(0(1(1(0(0(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(0(1(1(0(0(1(1(1(1(0(1(1(1(0(1(0(0(1(1(1(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (29)
1(0(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(0(1(1(0(0(0(0(0(0(1(1(1(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(1(0(1(1(0(0(1(0(1(1(1(1(0(0(0(0(0(1(1(0(0(1(0(0(1(1(0(0(0(1(0(0(0(0(1(0(0(1(0(1(1(0(1(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (30)
1(0(0(1(1(1(1(0(1(0(1(0(1(0(1(0(1(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(0(1(1(0(0(0(0(0(0(1(1(1(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 1(0(0(0(1(0(1(0(0(1(0(1(0(0(0(1(0(0(1(1(1(0(0(1(1(0(0(1(0(0(0(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (31)

1.1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
0(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (32)

1.1.1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.
0#(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0#(1(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (33)
0#(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0#(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (34)
0#(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0#(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (35)
0#(1(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) → 0#(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(0(1(1(1(0(0(0(0(0(0(1(0(1(1(1(1(1(0(0(0(1(0(0(1(0(1(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (36)

1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.