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

Runtime Complexity

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Method	2014	2013	2012	2011	2010
Arctic Interpretation	CaT	CaT	CaT	CaT	CaT
Match Bounds	AProVE, CaT, TcT	AProVE, CaT, TcT	AProVE, CaT, TcT	CaT, TcT	CaT, TcT
Matrix Interpretation Triangular	AProVE (N)	AProVE (N)	AProVE (N)	AProVE (N), TcT (N)	AProVE (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)	CaT (N,R,Q)
Modular (Relative) Complexity Analysis	AProVE, CaT, TcT	AProVE, CaT, TcT	AProVE, CaT, TcT	AProVE, CaT	AProVE, CaT
Polynomial Interpretations	AProVE (N), TcT (N)	AProVE (N), TcT (N)	AProVE (N), TcT (N)	AProVE (N)	AProVE (N)
Polynomial Path Orders	TcT (sPOP*)	TcT (sPOP*)	TcT (sPOP*)	TcT	TcT
Rewriting Right Hand Sides	AProVE	AProVE	AProVE	AProVE	AProVE
Root Labeling	---	---	---	---	---
Weak Dependency Pairs	TcT	TcT	TcT	TcT	TcT
Dependency Tuples	AProVE, TcT	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	CaT, TcT
DG Decomposition	TcT	TcT	TcT	---	---