Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/259405)

The rewrite relation of the following TRS is considered.

0(0(1(0(1(1(0(0(0(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(0(1(0(0(1(1(1(1(1(1(0(0(0(1(0(0(1(0(0(1(1(0(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(1(1(0(0(1(1(0(0(0(1(0(0(0(1(0(0(1(0(1(1(1(1(0(1(0(0(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (1)
0(0(1(0(1(1(0(0(0(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(0(1(0(0(1(1(1(1(1(1(0(0(0(1(0(0(1(0(0(1(1(0(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(0(0(0(0(0(1(1(1(1(1(0(1(0(0(1(1(0(1(0(0(0(1(0(0(1(1(1(0(0(0(1(0(1(0(1(1(0(0(1(0(0(0(1(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (2)
0(0(1(1(0(0(1(0(0(1(1(1(1(0(1(0(1(1(1(0(1(0(1(0(1(0(1(0(0(1(1(0(0(1(0(0(0(0(0(0(0(1(1(0(1(0(1(1(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(1(1(0(1(0(1(1(1(1(1(0(1(0(1(0(0(0(0(0(0(0(1(0(1(0(0(1(0(1(1(0(1(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (3)
0(0(1(1(0(0(1(0(0(1(1(1(1(0(1(0(1(1(1(0(1(0(1(0(1(0(1(0(0(1(1(0(0(1(0(0(0(0(0(0(0(1(1(0(1(0(1(1(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(1(1(1(1(0(0(1(0(0(0(1(0(1(1(1(0(1(0(1(1(1(0(0(0(1(0(1(1(0(1(1(0(1(0(0(1(1(0(1(0(1(0(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (4)
0(0(1(1(0(0(1(0(0(1(1(1(1(0(1(0(1(1(1(0(1(0(1(0(1(0(1(0(0(1(1(0(0(1(0(0(0(0(0(0(0(1(1(0(1(0(1(1(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(1(1(0(0(0(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(0(1(0(0(1(1(1(1(1(1(0(0(0(1(0(0(1(0(0(1(1(0(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (5)
0(1(0(0(1(1(0(0(0(0(1(1(1(0(1(1(0(0(0(1(1(0(1(1(0(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(1(1(1(0(1(1(0(1(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(1(1(1(1(0(0(1(0(0(0(1(0(1(1(1(0(1(0(1(1(1(0(0(0(1(0(1(1(0(1(1(0(1(0(0(1(1(0(1(0(1(0(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (6)
0(1(0(0(1(1(0(0(0(0(1(1(1(0(1(1(0(0(0(1(1(0(1(1(0(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(1(1(1(0(1(1(0(1(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(0(0(0(0(0(1(1(1(1(1(0(1(0(0(1(1(0(1(0(0(0(1(0(0(1(1(1(0(0(0(1(0(1(0(1(1(0(0(1(0(0(0(1(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (7)
0(1(0(0(1(1(0(0(0(0(1(1(1(0(1(1(0(0(0(1(1(0(1(1(0(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(1(1(1(0(1(1(0(1(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(1(1(0(0(0(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(0(1(0(0(1(1(1(1(1(1(0(0(0(1(0(0(1(0(0(1(1(0(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (8)
0(1(0(0(1(1(0(0(0(0(1(1(1(0(1(1(0(0(0(1(1(0(1(1(0(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(1(1(1(0(1(1(0(1(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(1(1(0(0(1(1(0(0(0(0(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(1(1(0(1(0(1(0(0(0(0(0(0(0(1(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (9)
0(1(0(0(1(1(0(0(0(0(1(1(1(0(1(1(0(0(0(1(1(0(1(1(0(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(1(1(1(0(1(1(0(1(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(0(0(0(0(0(1(1(0(1(0(0(1(0(0(0(0(1(1(0(0(1(0(0(1(1(0(0(1(1(1(0(1(0(1(1(1(0(1(0(0(1(0(1(0(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (10)
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0(1(0(0(1(1(0(0(1(1(0(0(0(1(0(0(0(1(0(0(1(0(1(1(1(1(0(1(0(0(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(1(1(0(0(1(1(0(0(0(0(0(0(1(0(0(1(1(1(1(1(0(1(0(0(0(0(0(1(1(1(0(1(0(1(0(0(0(0(0(0(0(1(0(1(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (12)
0(1(0(0(1(1(0(0(1(1(0(0(0(1(0(0(0(1(0(0(1(0(1(1(1(1(0(1(0(0(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(1(1(1(1(0(0(1(0(0(0(1(0(1(1(1(0(1(0(1(1(1(0(0(0(1(0(1(1(0(1(1(0(1(0(0(1(1(0(1(0(1(0(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (13)
0(1(0(0(1(1(0(0(1(1(0(0(0(1(0(0(0(1(0(0(1(0(1(1(1(1(0(1(0(0(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(1(1(0(0(1(1(0(0(0(1(0(0(0(1(0(0(1(0(1(1(1(1(0(1(0(0(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (14)
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0(1(0(0(1(1(0(0(1(1(0(0(0(1(0(0(0(1(0(0(1(0(1(1(1(1(0(1(0(0(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(1(1(0(0(0(0(1(0(1(1(0(1(0(0(0(1(1(1(1(0(1(0(1(0(0(1(1(1(1(1(1(0(0(0(1(0(0(1(0(0(1(1(0(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (16)
0(1(0(0(1(1(0(0(1(1(0(0(0(1(0(0(0(1(0(0(1(0(1(1(1(1(0(1(0(0(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(1(1(0(0(1(1(0(0(0(1(0(0(0(1(0(0(1(0(1(1(1(1(0(1(0(0(1(1(0(0(0(1(0(0(1(1(1(0(0(0(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (17)
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0(1(0(0(1(1(0(1(0(1(1(1(1(1(0(1(0(1(0(0(0(0(0(0(0(1(0(1(0(0(1(0(1(1(0(1(0(1(1(0(0(1(1(0(1(0(0(0(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(1(1(1(1(0(0(1(0(0(0(1(0(1(1(1(0(1(0(1(1(1(0(0(0(1(0(1(1(0(1(1(0(1(0(0(1(1(0(1(0(1(0(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (25)
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0(1(0(0(1(1(0(1(0(1(1(1(1(1(0(1(0(1(0(0(0(0(0(0(0(1(0(1(0(0(1(0(1(1(0(1(0(1(1(0(0(1(1(0(1(0(0(1(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(1(1(1(1(0(0(1(0(0(0(1(0(1(1(1(0(1(0(1(1(1(0(0(0(1(0(1(1(0(1(1(0(1(0(0(1(1(0(1(0(1(0(0(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (32)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by AProVE @ termCOMP 2023)

1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
0(1(1(1(0(1(1(0(0(1(0(0(0(1(1(1(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(0(0(0(0(1(1(0(0(1(0(0(1(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(0(1(0(1(0(0(1(1(0(0(1(1(0(0(0(0(1(1(0(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (33)
1(1(1(1(0(1(1(0(0(1(0(0(0(1(1(1(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(0(0(0(0(1(1(0(0(1(0(0(1(0(0(0(1(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(1(0(1(0(0(0(0(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(0(0(1(0(1(1(0(0(1(1(0(0(1(0(0(0(1(0(0(1(1(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (34)
1(1(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(0(0(0(1(1(1(1(0(1(0(1(0(0(1(1(0(1(0(1(1(0(0(0(0(0(0(0(1(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(0(0(0(0(1(1(1(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (35)
1(1(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(0(0(0(1(1(1(1(0(1(0(1(0(0(1(1(0(1(0(1(1(0(0(0(0(0(0(0(1(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (36)
1(1(1(1(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(0(0(0(1(1(1(1(0(1(0(1(0(0(1(1(0(1(0(1(1(0(0(0(0(0(0(0(1(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(0(0(0(1(1(0(0(0(1(0(0(0(1(1(1(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(0(0(0(0(1(1(0(0(1(0(0(1(0(0(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (37)
1(1(0(1(0(0(1(1(0(1(0(0(1(1(0(0(1(0(1(1(0(1(0(1(1(0(0(1(1(0(0(0(0(1(0(1(1(0(1(1(1(0(1(1(0(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(1(0(0(1(0(1(0(0(0(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (38)
0(1(1(1(1(0(1(1(0(1(0(0(1(1(0(0(1(0(1(1(0(1(0(1(1(0(0(1(1(0(0(0(0(1(0(1(1(0(1(1(1(0(1(1(0(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(0(1(1(0(1(0(1(0(0(0(0(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(0(0(1(0(1(1(0(0(1(1(0(0(1(0(0(0(1(0(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (39)
0(0(1(0(1(1(1(1(0(1(0(0(1(1(0(0(1(0(1(1(0(1(0(1(1(0(0(1(1(0(0(0(0(1(0(1(1(0(1(1(1(0(1(1(0(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(1(0(0(0(1(1(0(0(0(1(0(0(0(1(1(1(1(1(1(0(0(1(1(0(1(0(1(1(1(0(0(0(0(0(0(1(1(0(0(1(0(0(1(0(0(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (40)
1(0(0(1(0(0(1(1(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(1(0(0(0(0(1(0(1(1(0(1(1(1(0(1(1(0(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(1(1(1(1(1(1(0(0(0(1(0(1(0(0(1(0(0(1(0(0(1(0(0(1(1(0(1(0(0(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(1(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (41)
1(0(0(1(0(0(1(1(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(1(0(0(0(0(1(0(1(1(0(1(1(1(0(1(1(0(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(0(0(0(0(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(1(0(1(1(0(0(1(0(1(1(0(0(1(0(1(0(0(1(0(1(1(1(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (42)
1(1(0(1(0(0(1(1(1(0(1(1(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(1(0(0(0(0(1(0(1(1(0(1(1(1(0(1(1(0(0(0(1(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(1(1(1(1(1(1(0(0(0(1(0(1(0(0(1(0(0(1(0(0(1(0(0(1(1(0(1(0(0(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(1(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (43)
0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(0(0(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(1(1(1(1(1(1(0(0(0(1(0(1(0(0(1(0(0(1(0(0(1(0(0(1(1(0(1(0(0(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(1(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (44)
0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(0(0(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(1(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (45)
0(1(1(0(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(0(0(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(1(0(1(1(0(0(1(1(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(0(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (46)
0(0(0(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(0(0(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(1(0(1(1(0(0(1(0(1(1(0(0(1(0(1(0(0(1(0(1(1(1(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (47)
1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(0(0(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(1(1(1(0(0(1(1(1(1(0(0(1(1(0(0(0(1(1(0(0(1(1(0(1(0(1(1(1(0(0(0(0(0(0(1(1(0(0(1(0(0(1(0(0(0(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (48)
1(0(0(1(1(0(0(0(1(1(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(0(0(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(0(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (49)
1(1(1(0(0(0(1(1(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(0(0(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(0(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (50)
1(0(1(1(0(0(1(1(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(0(0(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(0(0(0(0(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(1(0(1(1(0(0(1(0(1(1(0(0(1(0(1(0(0(1(0(1(1(1(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (51)
0(1(1(1(0(0(1(1(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(0(0(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(0(0(1(0(0(1(1(1(1(0(1(1(0(0(0(0(0(1(0(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(1(0(0(0(0(1(1(1(0(0(1(0(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (52)
0(1(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(1(1(1(0(1(1(0(1(0(0(0(1(1(0(1(1(0(0(0(1(1(1(0(0(1(0(0(0(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(1(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (53)
0(1(1(1(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(1(1(1(0(1(1(0(1(0(0(0(1(1(0(1(1(0(0(0(1(1(1(0(0(1(0(0(0(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(0(0(1(1(0(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (54)
0(0(1(1(0(0(0(1(0(0(0(1(1(0(1(1(0(0(0(0(1(1(1(0(1(1(0(1(0(0(0(1(1(0(1(1(0(0(0(1(1(1(0(0(1(0(0(0(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(0(1(1(0(1(0(1(0(0(0(0(0(1(1(0(0(0(0(1(0(0(1(1(0(0(1(0(0(1(0(1(1(0(0(1(1(0(0(1(0(0(0(1(0(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (55)
1(1(0(0(0(1(1(1(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(0(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (56)
0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(0(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (57)
0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (58)
1(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(0(0(0(0(1(1(1(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (59)
1(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(0(0(0(0(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(1(0(1(1(0(0(1(0(1(1(0(0(1(0(1(0(0(1(0(1(1(1(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (60)
1(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(0(0(1(1(0(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (61)
0(1(0(1(0(1(0(0(0(1(0(0(0(1(1(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(1(1(1(1(1(1(0(0(0(1(0(1(0(0(1(0(0(1(0(0(1(0(0(1(1(0(1(0(0(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(1(0(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (62)
0(0(0(0(1(1(0(1(1(1(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(1(0(1(0(0(1(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(0(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (63)
0(0(0(0(1(1(0(1(1(1(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(1(0(1(0(0(1(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(0(1(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(1(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (64)

1.1 Closure Under Flat Contexts

Using the flat contexts

{0(), 1()}

We obtain the transformed TRS
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0(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (75)
1(0(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(0(1(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (76)
0(1(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(0(0(0(1(1(0(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (77)
1(1(0(1(1(1(1(1(1(1(0(0(0(1(0(1(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(0(0(0(1(1(0(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (78)
0(0(1(0(1(0(1(0(0(0(1(0(0(0(1(1(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(1(1(1(1(1(1(1(0(0(0(1(0(1(0(0(1(0(0(1(0(0(1(0(0(1(1(0(1(0(0(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (79)
1(0(1(0(1(0(1(0(0(0(1(0(0(0(1(1(1(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(0(0(0(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(1(1(1(1(1(1(1(0(0(0(1(0(1(0(0(1(0(0(1(0(0(1(0(0(1(1(0(1(0(0(0(1(1(1(0(1(0(0(0(0(0(0(0(1(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (80)
0(0(0(0(0(1(1(0(1(1(1(1(0(1(0(1(1(1(1(1(0(1(0(1(1(1(1(0(1(0(0(1(0(0(1(0(0(1(0(1(1(0(0(1(1(0(1(0(1(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(0(0(0(0(0(0(0(0(1(0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(0(1(0(1(1(0(0(1(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (81)
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1.1.1 Semantic Labeling

Root-labeling is applied.

We obtain the labeled TRS
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00(01(10(01(11(11(11(10(01(10(00(01(11(10(00(01(10(01(11(10(01(10(01(11(10(00(01(11(10(00(00(00(01(10(01(11(10(01(11(11(10(01(11(10(00(00(01(10(01(10(00(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 00(01(11(10(00(00(01(11(10(00(00(01(10(00(00(01(11(11(11(11(11(10(00(01(11(10(01(10(01(11(11(10(00(00(00(00(00(01(11(10(00(01(10(00(01(10(00(00(01(11(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (96)
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00(00(00(01(11(10(00(00(01(11(11(10(01(10(01(11(11(11(10(01(10(01(10(01(11(11(11(10(01(10(01(10(01(11(10(01(10(00(00(00(01(11(11(10(00(01(10(00(00(01(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(11(10(00(00(00(01(11(11(11(11(11(11(10(00(00(00(00(00(01(11(10(00(00(01(11(10(01(11(10(00(01(10(01(11(10(00(01(10(01(10(00(01(10(01(11(11(10(01(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (137)
00(00(00(01(11(10(00(00(01(11(11(10(01(10(01(11(11(11(10(01(10(01(10(01(11(11(11(10(01(10(01(10(01(11(10(01(10(00(00(00(01(11(11(10(00(01(10(00(00(01(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(11(10(00(00(00(01(11(11(11(11(11(11(10(00(00(00(00(00(01(11(10(00(00(01(11(10(01(11(10(00(01(10(01(11(10(00(01(10(01(10(00(01(10(01(11(11(10(01(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (138)
10(00(00(01(11(10(00(00(01(11(11(10(01(10(01(11(11(11(10(01(10(01(10(01(11(11(11(10(01(10(01(10(01(11(10(01(10(00(00(00(01(11(11(10(00(01(10(00(00(01(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 11(11(10(00(00(00(01(11(11(11(11(11(11(10(00(00(00(00(00(01(11(10(00(00(01(11(10(01(11(10(00(01(10(01(11(10(00(01(10(01(10(00(01(10(01(11(11(10(01(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (139)
10(00(00(01(11(10(00(00(01(11(11(10(01(10(01(11(11(11(10(01(10(01(10(01(11(11(11(10(01(10(01(10(01(11(10(01(10(00(00(00(01(11(11(10(00(01(10(00(00(01(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 11(11(10(00(00(00(01(11(11(11(11(11(11(10(00(00(00(00(00(01(11(10(00(00(01(11(10(01(11(10(00(01(10(01(11(10(00(01(10(01(10(00(01(10(01(11(11(10(01(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (140)
00(01(11(11(10(00(01(11(11(11(10(01(11(10(00(00(00(00(01(10(00(01(10(00(01(10(01(11(10(01(11(10(01(11(10(01(10(00(00(00(01(11(11(10(00(01(10(00(00(01(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(10(00(00(01(10(00(01(11(11(11(10(01(11(10(00(00(00(00(01(10(00(01(10(00(01(10(01(11(10(01(11(10(01(11(10(01(10(00(00(00(01(11(11(10(00(01(10(00(00(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (141)
00(01(11(11(10(00(01(11(11(11(10(01(11(10(00(00(00(00(01(10(00(01(10(00(01(10(01(11(10(01(11(10(01(11(10(01(10(00(00(00(01(11(11(10(00(01(10(00(00(01(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(10(00(00(01(10(00(01(11(11(11(10(01(11(10(00(00(00(00(01(10(00(01(10(00(01(10(01(11(10(01(11(10(01(11(10(01(10(00(00(00(01(11(11(10(00(01(10(00(00(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (142)
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00(00(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(10(00(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (145)
00(00(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(10(00(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (146)
10(00(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 11(10(00(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (147)
10(00(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 11(10(00(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (148)
00(00(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(10(01(10(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (149)
00(00(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(10(01(10(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (150)
10(00(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 11(10(01(10(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (151)
10(00(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 11(10(01(10(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (152)
01(10(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 00(00(00(00(01(11(10(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (153)
01(10(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 00(00(00(00(01(11(10(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (154)
11(10(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 10(00(00(00(01(11(10(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (155)
11(10(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 10(00(00(00(01(11(10(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (156)
00(01(10(01(10(01(10(00(00(01(10(00(00(01(11(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(11(11(11(11(11(11(11(10(00(00(01(10(01(10(00(01(10(00(01(10(00(01(10(00(01(11(10(01(10(00(00(01(11(11(10(01(10(00(00(00(00(00(00(01(10(01(10(01(11(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (157)
00(01(10(01(10(01(10(00(00(01(10(00(00(01(11(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(11(11(11(11(11(11(11(10(00(00(01(10(01(10(00(01(10(00(01(10(00(01(10(00(01(11(10(01(10(00(00(01(11(11(10(01(10(00(00(00(00(00(00(01(10(01(10(01(11(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (158)
10(01(10(01(10(01(10(00(00(01(10(00(00(01(11(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 11(11(11(11(11(11(11(11(10(00(00(01(10(01(10(00(01(10(00(01(10(00(01(10(00(01(11(10(01(10(00(00(01(11(11(10(01(10(00(00(00(00(00(00(01(10(01(10(01(11(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (159)
10(01(10(01(10(01(10(00(00(01(10(00(00(01(11(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 11(11(11(11(11(11(11(11(10(00(00(01(10(01(10(00(01(10(00(01(10(00(01(10(00(01(11(10(01(10(00(00(01(11(11(10(01(10(00(00(00(00(00(00(01(10(01(10(01(11(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (160)
00(00(00(00(01(11(10(01(11(11(11(10(01(10(01(11(11(11(11(10(01(10(01(11(11(11(10(01(10(00(01(10(00(01(10(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(10(00(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (161)
00(00(00(00(01(11(10(01(11(11(11(10(01(10(01(11(11(11(11(10(01(10(01(11(11(11(10(01(10(00(01(10(00(01(10(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(10(00(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (162)
10(00(00(00(01(11(10(01(11(11(11(10(01(10(01(11(11(11(11(10(01(10(01(11(11(11(10(01(10(00(01(10(00(01(10(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 11(10(00(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (163)
10(00(00(00(01(11(10(01(11(11(11(10(01(10(01(11(11(11(11(10(01(10(01(11(11(11(10(01(10(00(01(10(00(01(10(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 11(10(00(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (164)

1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[01(x1)] = 1 · x1
[11(x1)] = 1 · x1 + 1
[10(x1)] = 1 · x1 + 2
[00(x1)] = 1 · x1
all of the following rules can be deleted.
11(11(11(10(01(11(10(00(01(10(00(00(01(11(11(11(11(11(10(00(01(11(10(01(10(01(11(11(10(00(00(00(00(00(01(11(10(00(01(10(00(01(10(00(00(01(11(11(11(11(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 10(01(11(10(01(10(00(00(00(00(01(11(10(00(00(00(01(10(00(01(11(10(00(01(10(00(01(10(01(11(10(00(01(11(10(00(01(10(00(00(01(10(00(01(11(10(01(10(01(10(00(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (85)
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10(00(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 11(10(01(10(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (152)
01(10(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 00(00(00(00(01(11(10(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (153)
01(10(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 00(00(00(00(01(11(10(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (154)
11(10(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 10(00(00(00(01(11(10(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (155)
11(10(01(11(11(11(11(11(11(10(00(00(01(10(01(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 10(00(00(00(01(11(10(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (156)
00(01(10(01(10(01(10(00(00(01(10(00(00(01(11(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(11(11(11(11(11(11(11(10(00(00(01(10(01(10(00(01(10(00(01(10(00(01(10(00(01(11(10(01(10(00(00(01(11(11(10(01(10(00(00(00(00(00(00(01(10(01(10(01(11(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (157)
00(01(10(01(10(01(10(00(00(01(10(00(00(01(11(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(11(11(11(11(11(11(11(10(00(00(01(10(01(10(00(01(10(00(01(10(00(01(10(00(01(11(10(01(10(00(00(01(11(11(10(01(10(00(00(00(00(00(00(01(10(01(10(01(11(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (158)
10(01(10(01(10(01(10(00(00(01(10(00(00(01(11(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 11(11(11(11(11(11(11(11(10(00(00(01(10(01(10(00(01(10(00(01(10(00(01(10(00(01(11(10(01(10(00(00(01(11(11(10(01(10(00(00(00(00(00(00(01(10(01(10(01(11(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (159)
10(01(10(01(10(01(10(00(00(01(10(00(00(01(11(11(11(10(00(01(11(11(10(01(10(00(01(10(01(11(10(00(00(00(00(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 11(11(11(11(11(11(11(11(10(00(00(01(10(01(10(00(01(10(00(01(10(00(01(10(00(01(11(10(01(10(00(00(01(11(11(10(01(10(00(00(00(00(00(00(01(10(01(10(01(11(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (160)
00(00(00(00(01(11(10(01(11(11(11(10(01(10(01(11(11(11(11(10(01(10(01(11(11(11(10(01(10(00(01(10(00(01(10(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(10(00(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (161)
00(00(00(00(01(11(10(01(11(11(11(10(01(10(01(11(11(11(11(10(01(10(01(11(11(11(10(01(10(00(01(10(00(01(10(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(10(00(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (162)
10(00(00(00(01(11(10(01(11(11(11(10(01(10(01(11(11(11(11(10(01(10(01(11(11(11(10(01(10(00(01(10(00(01(10(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 11(10(00(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (163)
10(00(00(00(01(11(10(01(11(11(11(10(01(10(01(11(11(11(11(10(01(10(01(11(11(11(10(01(10(00(01(10(00(01(10(00(01(10(01(11(10(00(01(11(10(01(10(01(11(10(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 11(10(00(00(00(00(00(00(00(00(00(01(10(01(11(10(01(11(11(11(10(00(00(00(00(00(01(10(01(10(00(00(00(01(11(10(00(00(01(10(01(10(01(11(10(00(01(10(01(11(10(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (164)

1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[01(x1)] = 1 · x1 + 1
[11(x1)] = 1 · x1 + 1
[10(x1)] = 1 · x1
[00(x1)] = 1 · x1 + 1
all of the following rules can be deleted.
01(11(11(10(01(11(10(00(01(10(00(00(01(11(11(11(11(11(10(00(01(11(10(01(10(01(11(11(10(00(00(00(00(00(01(11(10(00(01(10(00(01(10(00(00(01(11(11(11(11(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 00(01(10(00(01(10(01(10(00(01(11(10(00(01(11(10(00(00(00(01(11(10(00(01(10(00(01(10(01(11(10(01(11(10(01(11(10(01(10(00(00(00(01(11(11(10(00(01(10(00(00(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (83)
01(11(11(10(01(11(10(00(01(10(00(00(01(11(11(11(11(11(10(00(01(11(10(01(10(01(11(11(10(00(00(00(00(00(01(11(10(00(01(10(00(01(10(00(00(01(11(11(11(11(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 00(01(10(00(01(10(01(10(00(01(11(10(00(01(11(10(00(00(00(01(11(10(00(01(10(00(01(10(01(11(10(01(11(10(01(11(10(01(10(00(00(00(01(11(11(10(00(01(10(00(00(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (84)

1.1.1.1.1.1 Rule Removal

Using the linear polynomial interpretation over the naturals
[00(x1)] = 1 · x1 + 1
[01(x1)] = 1 · x1
[11(x1)] = 1 · x1 + 1
[10(x1)] = 1 · x1
all of the following rules can be deleted.
00(01(11(11(10(00(01(11(11(11(10(01(11(10(00(00(00(00(01(10(00(01(10(00(01(10(01(11(10(01(11(10(01(11(10(01(10(00(00(00(01(11(11(10(00(01(10(00(00(01(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(10(00(00(01(10(00(01(11(11(11(10(01(11(10(00(00(00(00(01(10(00(01(10(00(01(10(01(11(10(01(11(10(01(11(10(01(10(00(00(00(01(11(11(10(00(01(10(00(00(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (141)
00(01(11(11(10(00(01(11(11(11(10(01(11(10(00(00(00(00(01(10(00(01(10(00(01(10(01(11(10(01(11(10(01(11(10(01(10(00(00(00(01(11(11(10(00(01(10(00(00(01(11(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 01(10(00(00(01(10(00(01(11(11(11(10(01(11(10(00(00(00(00(01(10(00(01(10(00(01(10(01(11(10(01(11(10(01(11(10(01(10(00(00(00(01(11(11(10(00(01(10(00(00(01(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (142)

1.1.1.1.1.1.1 R is empty

There are no rules in the TRS. Hence, it is terminating.