This page is for listing all techniques applied by the participants of the complexity competitions.

Be aware: the lists are still preliminary.

Derivational Complexity

next year or prev year

Method	2011	2010	2009	2008
Arctic Interpretation	CaT	CaT, TcT	CaT, TcT	CaT, TcT
Match Bounds	CaT, TcT	CaT, TcT	CaT, TcT	CaT, TcT
Matrix Interpretation Triangular	TcT (N)	TcT (N)	CaT (N), Matchbox (N), TcT (N)	TcT (N)
Matrix Interpretation Non-Triangular	CaT (N,R,Q), Matchbox (N)	CaT (N,R,Q), Matchbox (N)	---	---
Modular (Relative) Complexity Analysis	CaT	CaT	CaT	---
Rewriting Right Hand Sides	---	---	TcT	CaT
Root Labeling	CaT	CaT	CaT, TcT	CaT
Weight Gap Principle	CaT, TcT	CaT, TcT	CaT	---

Runtime Complexity

next year or prev year

Method	2013	2012	2011	2010	2009
Arctic Interpretation	CaT	CaT	CaT	CaT	CaT, TcT
Match Bounds	AProVE, CaT, TcT	AProVE, CaT, TcT	CaT, TcT	CaT, TcT	CaT, TcT
Matrix Interpretation Triangular	AProVE (N)	AProVE (N)	AProVE (N), TcT (N)	AProVE (N), TcT (N)	CaT (N), TcT (N)
Matrix Interpretation Non-Triangular	CaT (N,R,Q), TcT (N)	CaT (N,R,Q), TcT (N)	CaT (N,R,Q)	CaT (N,R,Q)	---
Modular (Relative) Complexity Analysis	AProVE, CaT, TcT	AProVE, CaT, TcT	AProVE, CaT	AProVE, CaT	CaT
Polynomial Interpretations	AProVE (N), TcT (N)	AProVE (N), TcT (N)	AProVE (N)	AProVE (N)	---
Polynomial Path Orders	TcT (sPOP*)	TcT (sPOP*)	TcT	TcT	TcT
Rewriting Right Hand Sides	AProVE	AProVE	AProVE	AProVE	---
Root Labeling	---	---	---	---	CaT, TcT
Weak Dependency Pairs	TcT	TcT	TcT	TcT	TcT
Dependency Tuples	AProVE, TcT	AProVE, TcT	AProVE, TcT	AProVE	---
Path Analysis	TcT	TcT	TcT	TcT	TcT
Weight Gap Principle	CaT, TcT	CaT, TcT	CaT, TcT	CaT, TcT	TcT
DG Decomposition	TcT	TcT	---	---	---