Develop effective methods to decide whether a system decreases with respect to some exponential interpretation.

The source page states the original problem together with its recorded qualifications and progress updates as follows.

Polynomial and exponential interpretations have been used to prove termination. For the former there are some reasonable methods [Lescanne, 1991] that can help determine if a particular interpretation decreases with each application of a rule. Are there other implementable methods suitable for exponential interpretations?

Recorded progress.

Some work on this problem has been reported in [Lescanne, 1991].