Certification Problem

Input (COPS 951)

We consider the TRS containing the following rules:

0(1(2(3(4(x))))) → 0(2(1(3(4(x))))) (1)
0(5(1(2(4(3(x)))))) → 0(5(2(1(4(3(x)))))) (2)
0(5(2(4(1(3(x)))))) → 0(1(5(2(4(3(x)))))) (3)
0(5(3(1(2(4(x)))))) → 0(1(5(3(2(4(x)))))) (4)
0(5(4(1(3(2(x)))))) → 0(5(4(3(1(2(x)))))) (5)

The underlying signature is as follows:

{0/1, 1/1, 2/1, 3/1, 4/1, 5/1}

Property / Task

Prove or disprove confluence.

Answer / Result

Yes.

Proof (by ACP @ CoCo 2023)

1 Development Closed

Confluence is proven since the TRS is development closed. The joins can be performed using 1 development step(s).