 One can endorse RTT+COMP without endorsing CCTM. By positing a system of compositionally structured mental representations, one does not commit oneself to saying that operations over the representations are computational. Historical LOT theorists could not even formulate CCTM, for the simple reason that the Turing formalism had not been discovered. In the modern era, Harman (1973) and Sellars (1975) endorse something like RTT+COMP but not CCTM. Horgan and Tienson (1996) endorse RTT+COMP+CTM but not CCTM, i.e., classical CTM. They favor a version of CTM grounded in   connectionism, an alternative  computational framework that differs quite significantly from Turing’s approach. Thus, proponents of RTT+COMP need not accept that mental activity instantiates Turing-style computation.