3.4 (1969)

(Well-known problems).
a) Is there an algorithm that decides, for any set of group words $f_1, \dots, f_m$ (in a fixed set of variables $x_1, x_2, \dots$) and a separate word $f$, whether $f = 1$ is a consequence of $f_1 = 1, \dots, f_m = 1$?
b) Given words $f_1, \dots, f_m$, is there an algorithm that decides, for any word $f$, whether $f = 1$ is a consequence of $f_1 = 1, \dots, f_m = 1$?