This book constitutes the refereed proceedings of the Joint 25th International Conference on Rewriting Techniques and Applications, RTA 2014, and 12th International Conference on Typed Lambda-Calculi and Applications, TLCA 2014, held as part of the Vienna Summer of Logic, VSL 2014, in Vienna, Austria, in July 2014. The 28 revised full papers and 3 short papers presented were carefully reviewed and selected from 87 submissions. The papers provide research results on all aspects of rewriting and typed lambda calculi, ranging from theoretical and methodological issues to applications in various contexts. They address a wide variety of topics such as algorithmic aspects, implementation, logic, types, semantics, and programming.

Process Types as a Descriptive Tool for Interaction: Control and the Pi-Calculus.- Concurrent Programming Languages and Methods for Semantic Analyses (Extended Abstract of Invited Talk).- Unnesting of Copatterns.- Proving Confluence of Term Rewriting Systems via Persistency and Decreasing Diagrams.- Predicate Abstraction of Rewrite Theories.- Unification and Logarithmic Space.- Ramsey Theorem as an Intuitionistic Property of Well Founded Relations.- A Model of Countable Nondeterminism in Guarded Type Theory.- Cut Admissibility by Saturation.- Automatic Evaluation of Context-Free Grammars (System Description).- Tree Automata with Height Constraints between Brothers.- A Coinductive Confluence Proof for Infinitary Lambda-Calculus.- An Implicit Characterization of the Polynomial-Time Decidable Sets by Cons-Free Rewriting.- Preciseness of Subtyping on Intersection and Union Types.- Abstract Datatypes for Real Numbers in Type Theory.- Self Types for Dependently Typed Lambda Encodings.- First-Order Formative Rules.- Automated Complexity Analysis Based on Context-Sensitive Rewriting.- Amortised Resource Analysis and Typed Polynomial Interpretations.- Confluence by Critical Pair Analysis.- Proof Terms for Infinitary Rewriting.- Construction of Retractile Proof Structures.- Local States in String Diagrams.- Reduction System for Extensional Lambda-mu Calculus.- The Structural Theory of Pure Type Systems.- Applicative May- and Should-Simulation in the Call-by-Value Lambda Calculus with AMB.- Implicational Relevance Logic is 2-ExpTime-Complete.- Near Semi-rings and Lambda Calculus.- All-Path Reachability Logic.- Formalizing Monotone Algebras for Certification of Termination and Complexity Proofs.- Conditional Confluence (System Description).- Nagoya Termination Tool.- Termination of Cycle Rewriting.