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

Be aware: the lists are still preliminary.

Derivational Complexity

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Method	2014	2013	2012	2011	2010
Arctic Interpretation	CaT	CaT	CaT	CaT	CaT, TcT
Match Bounds	CaT, TcT	CaT, TcT	CaT, TcT	CaT, TcT	CaT, TcT
Matrix Interpretation Triangular	---	---	---	TcT (N)	TcT (N)
Matrix Interpretation Non-Triangular	CaT (N,R,Q), TcT (N)	CaT (N,R,Q), TcT (N)	CaT (N,R,Q), TcT (N)	CaT (N,R,Q), Matchbox (N)	CaT (N,R,Q), Matchbox (N)
Modular (Relative) Complexity Analysis	CaT, TcT	CaT, TcT	CaT, TcT	CaT	CaT
Rewriting Right Hand Sides	---	---	---	---	---
Root Labeling	CaT	CaT	CaT	CaT	CaT
Weight Gap Principle	CaT, TcT	CaT, TcT	CaT, TcT	CaT, TcT	CaT, TcT

Runtime Complexity

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Method	2012	2011	2010	2009	2008
Arctic Interpretation	CaT	CaT	CaT	CaT, TcT	---
Match Bounds	AProVE, CaT, TcT	CaT, TcT	CaT, TcT	CaT, TcT	TcT
Matrix Interpretation Triangular	AProVE (N)	AProVE (N), TcT (N)	AProVE (N), TcT (N)	CaT (N), TcT (N)	TcT (N)
Matrix Interpretation Non-Triangular	CaT (N,R,Q), TcT (N)	CaT (N,R,Q)	CaT (N,R,Q)	---	---
Modular (Relative) Complexity Analysis	AProVE, CaT, TcT	AProVE, CaT	AProVE, CaT	CaT	---
Polynomial Interpretations	AProVE (N), TcT (N)	AProVE (N)	AProVE (N)	---	---
Polynomial Path Orders	TcT (sPOP*)	TcT	TcT	TcT	TcT
Rewriting Right Hand Sides	AProVE	AProVE	AProVE	---	---
Root Labeling	---	---	---	CaT, TcT	---
Weak Dependency Pairs	TcT	TcT	TcT	TcT	TcT
Dependency Tuples	AProVE, TcT	AProVE, TcT	AProVE	---	---
Path Analysis	TcT	TcT	TcT	TcT	TcT
Weight Gap Principle	CaT, TcT	CaT, TcT	CaT, TcT	TcT	TcT
DG Decomposition	TcT	---	---	---	---