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Let two nonperiodic binary morphisms ... be given. A word w is called a solution of g and h if g(w) = h(w). We say that a solution w is simple if whenever ... are prefixes of wu such that ... for some word z, then |u| = |u'| = k|w|, for some k ∈ N. In this paper we will study simple solutions and show that if a word w is a simple solution containing at least nine occurrences of the letter a and at least nine occurrences of the letter b, then either w = (ab)ia, or w = ajbk with gcd (j, k) = 1, up to the exchange of letters a and b. [ABSTRACT FROM AUTHOR]