Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/25731)

The rewrite relation of the following TRS is considered.

0(1(2(1(x1)))) 1(2(1(1(0(1(2(0(1(2(x1)))))))))) (1)
0(1(2(1(x1)))) 1(2(1(1(0(1(2(0(1(2(0(1(2(x1))))))))))))) (2)

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
1(2(1(0(x1)))) 2(1(0(2(1(0(1(1(2(1(x1)))))))))) (3)
1(2(1(0(x1)))) 2(1(0(2(1(0(2(1(0(1(1(2(1(x1))))))))))))) (4)

1.1 Bounds

The given TRS is match-(raise)-bounded by 3. This is shown by the following automaton.