Existence of finite-prime context-free non-FSRP examples

Construct a context-free fixed-observation pair $(L,h)$ that is $h$-substitutable and unit-separated, has finite relative prime spectrum, and fails the finite-state relative presentation property (FSRP), or determine whether FSRP necessarily holds under these hypotheses.

Background

The paper proves that, under context-freeness, h-substitutability, and finite relative prime spectrum, every correct-return language is context-free. However, valid-return languages are obtained by factor-minimalization through a language difference, and context-free languages are not closed under difference.

All explicit finite-prime examples in the paper satisfy FSRP, including the wrapped nonregular context-free example. Thus the authors leave unresolved whether a canonical valid right-hand-side language can be nonregular under the stated hypotheses.