Complexity of terms, superpositions, and generalized hypersubstitutions
In this paper, we consider the four useful measurements of the complexity of a term, called the maximum depth, the minimum depth, the variable count, and the operation count. We construct a formula for the complexity of the superposition Sm(s,t1,,tm) S m ( s , t 1 ,  , t m ) in terms of complexity of the inputs s,t1,,tm s , t 1 ,  , t m for each of these measurements. We also obtain formulas for the complexity of ?  [ t ] in terms of the complexity where t t is a compound term and ? ? is a generalized hypersubstitution. We apply these formulas to the theory of M M -strongly solid varieties, examining the k k -normalization chains of a variety with respect to these complexity measurements.
superposition generalized hypersubstitution the maximum depth the minimum depth the variable count the operation count m m -strongly solid variety m m m m m k k -normalization chains k k k k k