| Abstract | .... 2 | |
| Keywords | .... 2 | |
| 1 | Introduction | .... 3 |
| 2 | Basic Unfold/Fold Transformation with Counters | .... 3 |
| 2.1 | Transformation Process | .... 3 |
| 2.2 | Basic Transformation Rules | .... 4 |
| 2.3 | Equivalence Preservation Theorem | .... 5 |
| 3 | Presevation of equivalence | .... 5 |
| 3.1 | Proof,Rank and Rank-Ordering of Ground Atom | .... 6 |
| 3.2 | Rank-Consistent Proof | .... 7 |
| 3.3 | Proof of the Equivalence Preservation Theorem | .... 7 |
| 4 | Servel Refinements of the Basic Unfold/Fold Transformation | .... 9 |
| 4.1 | Introduction of A Static Ordering on Predicate Symbols | .... 9 |
| 4.2 | Introduction of Folding by Programs and A Dynamic Ordering on Predicate Symbols | .... 11 |
| 4.3 | Introduction of Folding by Previous Programs and Negative Counters | .... 12 |
| 5 | Goal Replacement in the Refined Unfold/Fold Transformation | .... 13 |
| 6 | Source of Optimization in UnFold/Fold Transformation | .... 16 |
| 7 | Discussion | .... 17 |
| 8 | Conclusion | .... 18 |
| Acknowledgements | .... 18 | |
| References | .... 18 |
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