Section MPCP_PCP.
Local Definition card := card nat.
Local Definition string := string nat.
Local Notation "x / y" := (x, y).
Variable R : list (card).
Variable x0 y0 : string.
Definition Sigma := sym (x0/y0 :: R).
Definition R_Sigma : sym R <<= Sigma.

Lemma PCP_MPCP x y B :
B <<= P -> x <<= Sigma -> y <<= Sigma ->
(#_L x) ++ tau1 B = # :: (#_R y) ++ tau2 B ->
exists A, A <<= x0/y0::R /\ x ++ tau1 A = y ++ tau2 A.