Consider the following parse tree for the expression a#b$c$d#e#f, involving…

Key insight: $ has higher precedence than #; $ is left-associative; # is right-associative.

1. Look at the root of the parse tree: the top operator is # with left child a and right child another #. This structure groups the # operators to the right (i.e., an expression of the form x # y # z is parsed as x # (y # z)), so # is right-associative.

2. Examine the left part of the right subtree: there are two nested $ nodes combining b, c and then d, giving ((b $ c) $ d). This shows $ groups left-to-right, so $ is left-associative.

3. Because the $ nodes occur deeper in the tree (they are evaluated before the # nodes that appear higher), $ has higher precedence than #.

Final parenthesized grouping implied by the tree: a # ( ((b $ c) $ d) # (e # f) ).