On constructing an unsolvable Thue system on two letters

This paper presents in detail the construction of an unsolvable Thue system on two letters. The approach employed consists of first constructing a Thue system ${\Gamma}$ on n letters whose decision problem is recursively unsolvable. Then along the lines suggested by Davis [1], a combinatorial system ${\Gamma}^*$ whose alphabet-consists of two letters is constructed whose decision problem is recursively solvable if and only if that for ${\Gamma}$ is.