Unambiguous 1-uniform morphisms

If, for a morphism σ : ∆∗ → Σ∗ (where ∆ and Σ are arbitrary alphabets) and a word α ∈ ∆∗, there exists another morphism τ mapping α to σ(α), then σ is called ambiguous with respect to α ; if such a τ does not exist, then σ is unambiguous. For example, the morphism σ0 : {A,B,C}∗ → {a,b}∗ – given by σ0(A) := a, σ0(B) := a, σ0(C) := b – is ambiguous with respect to the word α0 := ABCACB, since the morphism τ0 – defined by τ0(A) := ε (i. e., τ0 maps A to the empty word), τ0(B) := a, τ0(C) := ab – satisfies τ0(α0) = σ0(α0) and, for a symbol X occuring in α , τ0(X) 6= σ0(X):