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### The complexity of normal form rewrite sequences for Associativity

**1994-06-20**

9406030 | cmp-lg

The complexity of a particular term-rewrite system is considered: the rule of
associativity (x*y)*z --> x*(y*z). Algorithms and exact calculations are given
for the longest and shortest sequences of applications of --> that result in
normal form (NF). The shortest NF sequence for a term x is always n-drm(x),
where n is the number of occurrences of * in x and drm(x) is the depth of the
rightmost leaf of x. The longest NF sequence for any term is of length
n(n-1)/2.

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