Term rewriting has been used as a formal model to reason about the

complexity of logic, functional, and imperative programs. In contrast

to term rewriting, term graph rewriting permits sharing of

common sub-expressions, and consequently is able to capture more

closely reasonable implementations of rule based languages. However,

the automated complexity analysis of term graph rewriting has received

little to no attention.

With this work, we provide first steps towards overcoming this

situation. We present adaptions of two prominent complexity techniques

from term rewriting, viz, the interpretation method and

dependency tuples. Our adaptions are non-trivial, in the sense

that they can observe not only term but also graph structures, i.e.

take sharing into account. In turn, the developed methods allow us to

more precisely estimate the runtime complexity of programs where

sharing of sub-expressions is essential.