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Classically, in order to resolve an equation $u\approx v$ over a free monoid $X^{*}$, we reduce it by a suitable family $ℱ$ of substitutions to a family of equations $uf\approx vf$, $f\in ℱ$, each involving less variables than $u\approx v$, and then combine solutions of $uf\approx vf$ into solutions of $u\approx v$. The problem is to get $ℱ$ in a handy parametrized form. The method we propose consists in parametrizing the path traces in the so called graph of prime equations associated to $u\approx v$. We carry out such a parametrization in the case the prime equations in the graph...

Classically, in order to resolve an equation ≈ over a free monoid *, we reduce it by a suitable family $ℱ$ of substitutions to a family of equations ≈ , $f\in ℱ$, each involving less variables than ≈ , and then combine solutions of ≈ into solutions of ≈ . The problem is to get $ℱ$ in a handy form. The method we propose consists in parametrizing the path traces in the so called associated to ≈ . We carry out such a parametrization in the case the prime equations in the graph involve at most three...