Certification Problem

Input (TPDB SRS_Standard/ICFP_2010/41378)

The rewrite relation of the following TRS is considered.

0(0(1(1(0(0(2(0(0(1(1(1(3(3(1(2(2(4(5(3(2(1(4(1(0(5(0(4(5(4(4(3(4(4(1(0(5(5(2(5(3(5(2(4(3(0(0(2(2(4(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 5(1(0(0(2(5(2(1(4(5(5(2(3(3(1(1(3(2(1(4(1(3(0(3(2(5(0(4(3(2(2(3(4(2(1(5(2(4(4(5(2(2(1(0(2(1(2(2(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (1)
0(0(3(3(1(1(5(1(0(3(0(1(4(0(3(2(0(3(1(3(4(4(2(4(5(3(5(0(2(1(0(1(3(5(0(5(2(3(4(4(3(4(1(3(5(4(4(5(5(0(2(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 3(2(1(5(0(4(2(3(3(1(2(4(4(3(1(5(4(2(4(4(3(5(1(0(1(1(1(2(1(3(0(2(5(0(4(5(1(0(0(2(2(0(2(4(3(1(0(5(2(2(2(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (2)
0(3(3(4(0(0(0(1(2(4(3(0(1(3(2(3(1(0(4(4(3(4(5(0(1(3(2(1(5(3(1(5(5(2(0(5(1(0(4(5(3(3(0(5(1(5(5(0(4(2(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 3(3(5(4(1(2(5(3(3(3(4(5(3(0(1(0(4(3(4(5(4(5(5(4(1(2(1(1(2(1(4(4(0(3(5(2(3(1(1(3(3(1(3(1(4(1(4(1(5(5(3(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (3)
0(4(2(5(3(2(4(2(4(3(3(2(3(2(2(0(1(4(5(4(1(4(3(2(5(0(4(1(4(3(4(3(5(0(2(3(0(1(1(0(5(2(3(0(4(4(1(2(1(0(5(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(3(1(1(4(5(3(5(4(2(0(2(0(1(5(4(0(5(1(4(1(3(1(4(2(5(0(4(2(0(1(2(2(3(5(4(1(1(2(1(4(1(1(2(1(0(4(1(4(2(3(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (4)
1(2(5(1(0(4(5(4(2(0(3(0(3(0(0(3(3(1(2(0(1(4(3(0(1(1(0(0(4(0(0(3(0(0(4(0(3(0(0(0(0(5(0(3(5(4(2(3(0(1(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 5(1(2(4(2(2(2(2(1(1(2(4(5(0(4(3(0(0(3(2(0(4(5(0(3(1(5(3(2(1(5(5(1(5(1(2(0(5(0(0(5(5(4(4(1(1(3(3(5(0(2(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (5)
1(3(4(5(0(0(3(5(2(4(4(0(4(4(0(4(5(5(5(3(2(2(0(2(0(1(3(0(5(4(5(5(4(0(1(5(5(3(2(1(5(4(0(3(3(2(0(3(5(5(4(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 2(1(0(5(2(2(2(1(0(2(3(3(4(2(5(2(0(2(3(2(4(5(1(3(1(3(3(5(0(4(5(4(4(5(3(2(4(1(4(0(4(5(4(2(0(4(2(1(3(5(5(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (6)
1(5(0(0(4(0(2(0(5(4(3(5(0(4(2(3(3(1(1(0(5(5(4(5(0(1(1(5(5(0(5(5(2(2(1(1(1(5(1(2(3(4(3(4(1(3(3(0(0(2(5(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 4(3(1(0(3(1(5(3(2(1(1(4(3(0(1(3(0(3(2(1(2(3(0(2(2(0(0(2(0(2(2(0(2(0(3(5(5(4(0(2(1(1(5(3(2(1(3(2(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (7)
2(2(0(4(4(2(3(2(3(5(0(4(5(2(2(2(3(2(3(0(4(5(0(0(5(4(3(2(0(5(2(1(0(5(2(4(4(3(5(4(5(0(5(5(5(5(4(0(0(3(2(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(3(5(3(4(5(1(4(1(2(5(1(1(2(3(1(3(2(3(1(1(5(5(3(4(5(1(5(1(1(3(1(5(3(5(2(1(4(1(3(1(0(4(0(1(4(1(0(3(5(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (8)
2(3(1(0(3(4(1(5(1(5(0(1(4(5(5(3(3(4(3(2(5(2(0(2(0(1(5(2(2(3(5(0(1(5(0(0(2(4(1(0(2(5(0(3(4(2(3(5(4(3(3(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(2(3(4(4(0(3(5(3(2(4(3(2(2(5(1(0(2(2(1(3(2(2(4(2(1(0(5(5(1(1(4(4(2(5(5(1(1(3(2(1(4(2(3(0(5(0(1(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (9)
3(1(1(1(5(2(0(3(5(3(3(5(3(2(4(2(2(0(0(2(2(3(1(5(0(2(3(4(5(2(3(3(2(5(4(1(5(5(4(2(0(4(1(3(4(0(4(5(4(4(3(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(3(4(5(2(1(2(0(3(1(1(5(3(4(0(1(3(1(3(2(4(0(2(5(0(3(5(0(4(4(4(1(1(2(4(5(1(3(0(3(1(4(0(1(3(0(3(2(2(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (10)
3(1(5(1(5(2(0(3(0(0(3(1(0(4(5(0(0(3(2(5(2(2(1(4(0(5(1(0(4(0(1(4(0(2(0(4(2(5(3(3(2(0(3(4(5(1(1(2(0(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 4(3(4(5(5(4(2(2(1(2(1(5(1(1(5(2(3(0(4(1(5(5(2(1(2(1(3(5(1(0(3(2(5(1(3(0(2(3(2(1(0(5(5(4(0(1(3(2(1(5(3(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (11)
3(4(4(2(1(3(2(3(3(1(2(3(2(3(4(1(4(5(5(5(0(4(5(4(2(1(0(5(1(0(1(5(5(5(3(3(5(4(0(4(3(4(4(5(2(4(0(5(5(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(5(0(0(4(2(3(1(1(0(0(4(1(5(2(0(2(1(1(2(3(1(2(3(1(0(3(3(5(4(1(3(5(4(0(3(4(1(2(4(5(3(3(2(2(2(5(4(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (12)
4(5(2(4(5(2(5(3(0(4(2(5(0(2(2(2(0(0(3(4(2(5(3(0(3(2(5(3(3(5(1(3(3(5(4(2(3(2(4(3(5(1(0(1(4(5(3(4(1(5(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 4(2(1(0(4(1(4(1(1(2(2(5(3(1(5(1(4(3(2(4(5(3(0(1(1(3(4(3(3(1(1(4(2(4(0(1(4(2(3(3(5(4(5(0(0(4(0(5(0(0(5(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (13)
5(0(3(5(3(2(3(4(3(0(3(0(3(5(1(0(5(0(2(2(5(4(2(3(3(1(5(5(4(2(5(5(3(2(2(2(2(1(0(5(5(0(3(3(4(0(5(0(1(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 4(1(1(1(2(2(2(3(5(1(2(1(0(0(5(2(3(1(0(1(2(2(1(2(2(2(4(2(2(2(3(3(3(4(2(5(4(3(5(4(5(3(2(0(0(2(2(2(3(3(2(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (14)
5(3(4(4(2(1(4(2(4(2(3(4(4(2(3(5(5(1(5(3(4(0(1(5(4(0(5(4(4(1(0(4(3(2(4(5(2(3(1(4(3(4(0(2(3(2(0(5(5(2(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(1(1(1(3(4(2(1(3(3(3(3(3(4(0(5(4(1(3(4(5(5(0(1(5(3(5(0(5(4(2(4(2(1(1(3(4(2(1(5(1(4(0(3(1(4(5(3(1(5(3(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (15)
5(5(0(4(5(5(5(2(4(2(5(3(0(1(5(2(3(4(5(5(0(0(0(3(2(3(4(4(3(2(2(0(3(3(0(5(1(4(2(5(0(2(4(1(4(2(0(4(2(0(2(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 2(3(1(5(5(5(1(5(1(5(4(4(4(3(1(1(1(3(3(5(5(1(1(1(4(1(1(1(4(4(4(1(2(4(4(2(0(5(2(4(2(2(0(3(3(5(5(1(4(2(3(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (16)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by ttt2 @ termCOMP 2023)

1 String Reversal

Since only unary symbols occur, one can reverse all terms and obtains the TRS
3(1(5(5(3(2(0(3(4(0(4(5(0(0(5(1(2(1(2(0(3(4(2(4(5(3(4(2(1(0(0(5(3(5(1(4(2(2(0(0(3(4(2(5(3(5(2(5(5(0(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 0(4(1(0(1(4(1(5(1(0(3(1(2(3(3(4(5(5(5(0(1(3(4(3(5(2(5(4(5(3(0(0(2(0(5(1(5(1(5(2(0(2(1(2(2(0(3(4(4(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (17)
0(3(4(3(5(4(2(3(0(1(3(4(1(1(0(5(0(4(0(3(3(5(1(5(4(3(1(0(0(3(1(4(5(0(2(0(5(5(4(4(5(3(1(4(3(4(4(3(2(5(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 5(4(5(0(2(3(4(1(3(2(2(4(2(1(5(1(3(2(2(4(0(0(4(1(2(5(1(2(2(1(4(0(1(2(2(2(2(4(2(2(0(5(3(4(2(0(3(5(2(2(2(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (18)
5(0(4(0(4(3(4(0(2(2(3(5(0(3(0(3(0(5(4(3(4(2(1(2(3(5(1(0(2(3(3(2(2(3(1(2(4(0(5(5(1(5(0(3(3(5(4(0(1(5(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(5(2(5(2(4(1(2(4(3(1(1(0(2(0(0(2(2(1(1(2(2(4(1(2(1(3(4(3(2(2(1(5(0(4(1(0(3(4(2(4(2(5(5(0(3(5(1(4(3(5(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (19)
3(0(1(4(0(1(1(0(4(3(5(5(4(4(3(2(4(2(3(4(4(5(3(4(2(5(3(3(4(2(4(5(0(5(5(0(1(2(1(4(4(0(3(2(5(0(1(1(0(3(2(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 5(5(5(5(3(0(3(2(5(4(1(4(0(4(3(0(3(0(5(3(4(4(4(5(2(3(4(2(1(2(3(4(4(3(1(2(2(1(2(0(4(2(2(3(0(1(2(4(5(3(2(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (20)
1(1(0(0(2(0(3(0(3(3(3(0(2(5(4(4(0(1(0(1(5(1(1(5(4(5(5(4(5(5(2(3(4(1(0(1(0(3(2(4(5(3(0(5(0(0(0(0(3(0(4(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 4(1(0(1(3(1(5(5(2(5(5(0(1(0(3(1(4(3(5(3(3(1(4(2(4(1(2(3(0(5(2(4(4(1(0(3(1(0(2(0(4(2(4(4(3(4(5(2(4(2(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (21)
1(1(0(0(1(3(0(1(1(4(1(5(5(4(5(4(4(5(3(1(2(0(0(2(1(3(5(1(4(0(5(5(3(5(4(5(5(3(0(2(3(3(0(4(5(1(2(3(5(5(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 5(0(0(3(2(1(5(1(2(2(1(1(2(4(1(2(1(0(2(1(3(2(2(1(1(3(1(2(5(2(5(4(5(0(3(2(3(0(4(2(1(4(3(0(3(5(1(1(0(5(5(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (22)
0(4(3(1(1(4(4(0(0(2(2(5(3(2(0(4(3(5(2(2(4(3(5(1(3(5(4(2(3(5(0(0(0(4(5(2(0(0(3(3(1(4(3(4(3(2(1(5(1(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 4(2(0(5(3(2(2(4(3(0(2(1(2(3(5(5(2(1(2(1(1(2(2(0(5(4(2(3(0(0(5(2(0(4(2(4(5(0(5(1(2(4(3(3(1(5(3(5(0(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (23)
5(5(3(5(2(5(5(3(3(5(4(2(5(0(0(5(3(5(0(1(1(3(4(5(3(4(5(3(2(0(3(0(3(5(2(3(0(0(4(5(5(5(5(0(5(4(5(3(4(4(2(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 4(4(3(2(5(5(4(2(1(1(0(4(1(5(4(2(3(3(5(2(1(5(2(0(3(3(3(1(1(1(2(0(4(0(1(2(5(3(2(5(5(3(1(2(3(1(1(4(3(5(3(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (24)
3(1(1(5(1(2(4(0(1(3(0(1(5(4(4(1(2(0(3(0(0(1(5(3(0(4(0(4(1(0(4(0(5(3(3(3(4(5(3(2(4(3(0(5(2(0(1(4(2(0(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 5(5(3(1(3(4(0(5(2(2(1(1(4(2(0(4(1(1(0(3(4(4(2(3(5(1(4(1(4(1(4(3(2(4(4(2(3(3(5(3(5(3(4(0(3(0(4(4(4(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (25)
3(0(0(3(4(2(2(5(2(0(1(0(4(3(5(4(4(4(2(4(3(2(4(4(5(3(0(5(3(1(1(5(4(4(3(4(4(5(4(0(4(3(1(4(0(2(4(5(5(1(4(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(3(0(2(1(2(2(3(0(4(3(4(5(4(1(2(2(0(1(1(5(1(2(1(1(4(3(1(4(2(4(0(0(1(2(3(4(3(3(5(0(0(5(1(3(2(0(4(0(1(2(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (26)
0(0(0(2(1(0(2(1(5(3(3(3(0(4(4(4(0(4(0(1(0(3(4(3(4(4(5(4(1(1(2(5(1(0(1(0(0(2(1(1(5(4(3(0(2(3(3(5(2(4(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 4(3(2(4(5(3(3(2(1(1(0(0(4(2(4(2(1(0(5(2(4(3(5(4(1(4(4(3(5(1(3(1(3(5(0(2(1(1(3(2(2(3(1(2(0(0(2(5(5(3(5(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (27)
1(0(2(4(4(0(1(0(4(0(5(0(4(1(2(5(5(0(0(5(4(0(4(5(2(5(1(5(0(5(0(5(0(3(1(1(5(5(0(4(2(5(4(4(3(4(0(4(5(3(3(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 5(4(1(4(3(3(1(2(3(2(3(5(0(0(3(2(0(2(3(2(1(2(4(5(5(1(0(1(3(4(1(0(5(5(0(4(2(5(4(3(2(4(5(1(2(2(3(0(4(1(1(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (28)
0(3(1(1(5(1(0(3(3(3(1(5(4(3(2(4(0(4(5(2(1(5(0(4(1(2(1(5(4(5(5(5(5(5(0(5(1(4(3(5(4(1(0(1(5(3(4(2(3(2(4(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 1(4(0(1(1(2(5(1(2(4(0(3(2(2(3(4(1(2(3(2(3(0(1(1(2(3(4(4(3(3(1(5(2(1(5(2(4(5(1(2(0(0(2(4(2(1(0(4(1(5(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (29)
3(5(3(4(5(3(1(5(0(4(3(5(2(1(5(4(4(2(3(4(3(3(5(2(4(1(5(0(2(3(1(0(2(1(0(0(1(0(5(0(4(3(3(0(5(5(0(1(2(2(2(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 2(0(0(1(4(0(0(5(1(2(2(5(0(3(4(5(4(5(1(0(2(4(2(3(1(2(1(0(5(3(2(3(0(1(1(4(0(0(4(5(5(0(2(1(2(2(2(5(4(2(3(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (30)
1(3(2(0(2(3(3(1(4(4(1(0(5(1(0(5(0(0(4(5(4(3(5(5(5(4(3(2(3(2(5(5(4(4(0(2(5(5(0(2(3(2(0(4(3(4(1(3(2(5(4(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 4(5(0(2(1(2(4(1(0(1(0(1(0(5(2(3(1(3(5(4(1(3(4(3(3(4(2(4(5(1(1(2(1(3(1(4(4(1(1(2(1(1(1(2(3(0(2(1(1(3(5(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (31)
3(0(2(5(0(3(5(5(0(3(2(1(0(5(5(2(5(5(5(0(0(5(4(3(1(2(1(3(0(3(3(5(0(4(2(0(2(4(0(2(4(1(4(2(0(5(2(4(1(5(0(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) 4(1(4(3(5(0(1(5(3(1(1(2(1(2(0(1(2(1(3(2(1(3(2(2(3(4(0(0(2(3(1(2(5(0(1(2(0(0(3(3(2(3(3(4(1(5(5(2(1(3(2(...display limit reached...))))))))))))))))))))))))))))))))))))))))))))))))))) (32)

1.1 Bounds

The given TRS is match-(raise)-bounded by 1. This is shown by the following automaton. The automaton is closed under rewriting as it is compatible.