Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/254704)

The rewrite relation of the following TRS is considered.

0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(0(0(1(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(1(1(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (1)
0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(0(0(1(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(1(1(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (2)
0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(0(0(1(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(1(1(0(1(1(1(1(0(1(1(0(1(0(0(1(0(1(1(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (3)
0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(0(0(1(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(0(0(0(1(1(1(0(1(1(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(1(1(0(1(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (4)
0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(0(0(1(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (5)
0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(0(0(1(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(1(0(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (6)
0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(0(0(1(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(1(0(1(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(1(1(1(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (7)
0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(0(0(1(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(1(0(1(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(1(1(1(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (8)
0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(0(0(1(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(1(0(1(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(1(1(1(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (9)
0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(0(0(1(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(1(1(0(1(1(1(1(0(1(1(0(1(0(0(1(0(1(1(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (10)
0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(0(0(1(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(1(0(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (11)
0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(1(1(1(0(0(1(1(1(1(0(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(1(0(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (12)
0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(1(1(1(0(0(1(1(1(1(0(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(1(1(0(1(1(1(1(0(1(1(0(1(0(0(1(0(1(1(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (13)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(1(0(1(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(1(1(1(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (14)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(1(0(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (15)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(1(0(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (16)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(1(0(1(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(1(1(1(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (17)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (18)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(1(0(1(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(1(1(1(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (19)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(1(0(1(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(1(1(1(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (20)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(1(0(1(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(1(1(1(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (21)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(1(0(1(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(1(1(1(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (22)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(1(1(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (23)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(1(0(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (24)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(1(0(1(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(1(1(1(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (25)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(1(1(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (26)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(1(1(0(1(1(1(1(0(1(1(0(1(0(0(1(0(1(1(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (27)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(1(0(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (28)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(1(0(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (29)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(1(0(1(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(1(1(1(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (30)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(1(1(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (31)
0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(1(1(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (32)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by matchbox @ termCOMP 2023)

1 Closure Under Flat Contexts

Using the flat contexts

{1(), 0()}

We obtain the transformed TRS
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0(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(1(1(0(1(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(1(1(1(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (84)
0(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(1(1(0(1(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(1(1(1(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (85)
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0(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(1(1(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (87)
0(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (88)
0(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(1(1(0(1(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(1(1(1(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (89)
0(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(0(0(0(1(0(1(0(0(0(1(1(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (90)
0(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(0(1(0(0(1(0(0(0(0(1(0(1(0(0(0(1(1(1(0(1(1(0(1(1(1(1(0(0(0(1(1(0(1(1(1(1(0(1(1(0(1(0(0(1(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (91)
0(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (92)
0(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(1(0(0(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (93)
0(0(0(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(1(0(0(1(1(0(1(1(0(1(1(0(0(0(0(0(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(1(1(0(1(1(0(0(1(0(1(1(1(0(0(1(0(1(0(0(1(0(1(0(1(0(1(1(1(1(1(1(0(1(0(0(0(0(0(0(0(0(1(1(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (94)
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1.1 Closure Under Flat Contexts

Using the flat contexts

{1(), 0()}

We obtain the transformed TRS

There are 128 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,...,3}. Symbols are labeled by the interpretation of their arguments using the interpretations (modulo 4):

[1(x1)] = 2x1 + 0
[0(x1)] = 2x1 + 1

We obtain the labeled TRS

There are 512 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
[10(x1)] = x1 +
20/3
[12(x1)] = x1 +
17/3
[11(x1)] = x1 +
1
[13(x1)] = x1 +
0
[00(x1)] = x1 +
0
[02(x1)] = x1 +
1
[01(x1)] = x1 +
0
[03(x1)] = x1 +
17/3
all of the following rules can be deleted.

There are 512 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.