shift-reduce

I'm trying to learn about shift-reduce parsing. Suppose we have the following grammar, using recursive rules that enforce order of operations, inspired by the ANSI C Yacc grammar : S: A; P : NUMBER | '(' S ')' ; M : P | M '*' P | M '/' P ; A : M | A '+' M | A '-' M ; And we want to parse 1+2 using shift-reduce parsing. First, the 1 is shifted as a NUMBER. My question is, is it then reduced to P, then M, then A, then finally S? How does it know where to stop? Suppose it does reduce all the way to S, then shifts '+'. We'd now have a stack containing: S '+' If we shift '2', the reductions might