#### Techniques

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

**Be aware:** the lists are still preliminary.

#### Derivational Complexity

Method | 2013 | 2012 | 2011 | 2010 | 2009 |
---|---|---|---|---|---|

Arctic Interpretation | CaT | CaT | CaT | CaT, TcT | CaT, TcT |

Match Bounds | CaT, TcT | CaT, TcT | CaT, TcT | CaT, TcT | CaT, TcT |

Matrix Interpretation Triangular | --- | --- | TcT (N) | TcT (N) | CaT (N), Matchbox (N), TcT (N) |

Matrix Interpretation Non-Triangular | 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 | CaT | CaT |

Rewriting Right Hand Sides | --- | --- | --- | --- | TcT |

Root Labeling | CaT | CaT | CaT | CaT | CaT, TcT |

Weight Gap Principle | CaT, TcT | CaT, TcT | CaT, TcT | CaT, TcT | CaT |

#### Runtime Complexity

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 | --- | --- |