Certification Problem

Input (COPS 44)

We consider the TRS containing the following rules:

H(H(x)) K(x) (1)

The underlying signature is as follows:

{H/1, K/1}

Property / Task

Prove or disprove confluence.

Answer / Result

No.

Proof (by csi @ CoCo 2020)

1 Non-Joinable Fork

The system is not confluent due to the following forking derivations.

t0 = H(H(H(x3)))
H(K(x3))
= t1

t0 = H(H(H(x3)))
K(H(x3))
= t1

The two resulting terms cannot be joined for the following reason: