The complexity of normal form rewrite sequences for Associativity
<|reference_start|>The complexity of normal form rewrite sequences for Associativity: 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.<|reference_end|>
@article{niv1994the,
    title={The complexity of normal form rewrite sequences for Associativity},
    author={Michael Niv (Technion)},
    journal={arXiv preprint arXiv:cmp-lg/9406030},
    year={1994},
    number={Computer Science Department, LCL 94-6},
    archivePrefix={arXiv},
    eprint={cmp-lg/9406030},
    primaryClass={cmp-lg cs.CL}
}