L_R is not decidable. Deciding if x##y is in L requires simulating y until it produces |x| digits of output. x being anything and y = “while(true) {}” is a counterexample. Another way to look at it is that for any fixed x, "y produces x as its first |x| digits of output" is a nontrivial semantic property of y, so Rice's theorem shows that the property is undecidable.