Seems curious to ban functions. If you ban function-pointers then you can statically ensure there's no recursion (including mutual recursion). At that point, all function calls are in principle able to be inlined, so any backtracking is merely a compiler-level implementation detail.

iirc, OpenCL C does something similar, banning function pointers and recursion (including mutual recursion), although it does so for different reasons than this pattern.