Higher Order Termination

ion, 13Abstraction-simple, 182Accessibility Relation, 100AFS, 55AFSM, 12, 16Algebraic Functional System, 55Algebraic Functional System with Meta-variables, 12, 16Alpha-conversion, 11Application, 11, 13Application-free, 45Applicative Syntax, 18Approximation, 226Argument Filtering, 202Argument Function, 135, 202Argument Preserving Function, 135Arity, 10, 11, 13Arrow Decreasingness, 100Arrow Preservation, 100 Base Type, 11Beta Rule, 12Beta-first, 17Beta-normal Form, 12Beta-redex, 12Beta-reduced Sub-meta-term, 155Beta-saturating, 153Binding, 11Bit, 274BRSMT, 155 C , 232Cand, 155Candidate Term, 145, 155Chain-free, 148, 164Clause, 269Closed, 11CNF, 269Collapsing Dependency Pair, 157Collapsing Rule, 152Collapsing Set, 165Combinatory Reduction System, 41, 71Combinatory Reduction Systems with Ex-tensions, 64Compatible, 30Complete Processor, 207, 215Computability Path Ordering, 100Computable, 113Conjunctive Normal Form, 269Constructor Symbol, 153Contains Beta, 30Context, 10, 11, 14Contraction Scheme, 41, 68CPO, 100CRS, 71CRSX, 64CS, 68cur, 19Currying, 19Cycle, 225 Dangling Variable, 152Default Requirements, 197Defined Symbol, 145, 153Dependency Chain, 146, 158Dependency Graph, 209, 225Dependency Graph Approximation, 226Dependency Graph Processor, 210, 227Dependency Pair, 146 Dependency Pair Problem, 207, 214Dependency Pair Processor, 207, 215Domain, 10DP, 146, 156DP Problem, 214Dynamic Dependency Pair, 157 Empty Set Processor, 208, 216Essentially First-order Dependency Pair,237Essentially First-order Meta-term, 237Essentially First-order Rule, 237Eta-expansion, 12, 17Eta-long Beta-normal Form, 12Eta-long Form, 12exp, 60expL, 62Expression Reduction System, 41Extended Monotonic Algebra, 85Extended Meta-application Processor,220 Finite Dependency Pair Problem, 214Finitely Branching, 231First-order Dependency Chain, 146First-order Dependency Pair, 146First-order Dependency Pair Problem,207First-order Rewrite Rule, 10First-order Term Rewriting System, 10flat, 27FMV, 13Formative Chain-free, 177Formative Dependency Chain, 176Formative Rules, 173Formative Rules Processor, 217Formative Symbols, 173FR, 173Free Of Abstractions, 180Free Variable, 11Function Symbol, 10Functional Meta-term, 13Functional Type, 11FV, 11, 13Graph Approximation, 226 Head, 13Head Variable, 57Headmost Step, 15Headmost Variable, 56Higher-order Dependency Pair Problem,214Higher-order Iterative Path Ordering, 104Higher-order Recursive Path Ordering,98Higher-order Rewrite Systems, 48HOIPO, 104HORPO, 98HRS, 48HRS-term, 48 IDTS, 45ILPO, 96Inductive Data Type System, 45Infinite Dependency Pair Problem, 214Innermost, 16Input Type, 11Introducing Minimality Processor, 217Inverse Compatible, 36Irreflexive Relation, 29Iterative Lexicographic Path Ordering,96 Lambda-abstraction, 11Lambda-calculus, 11Leading Variable, 56Left-linear, 16Lexicographic Extension, 93Lexicographic Path Ordering, 95Limited Functional, 57LPO, 95 Markable Term, 109Meta-application, 13Meta-context, 15, 106Meta-rewriting, 106Meta-stable, 30Meta-substitution, 106 Meta-term, 13Meta-variable, 13Meta-variable Application, 13Meta-variable Conditions, 155Minimal Dependency Chain, 158Minimal Non-terminating, 159MNT, 159Monotonic, 30Monotonic Algebra Approach, 75Multiset Extension, 92 Non-collapsing Set, 165Non-overlapping, 74Norm, 287 oa, 57Order, 11, 16Orthogonal, 74Outermost, 16Output Arity, 57Output Type, 11Overlay, 243 Parameter, 273Pattern, 15Pattern Higher-order Rewrite System, 48Pattern HRS, 48PHO, 242Plain Function Passing, 244Pol, 87Polynomial Interpretation, 75Potentially Higher-order Symbol, 242Pre-term, 48Precedence, 93Processor, 215Projection Function, 229PRS, 48 Quasi-ordering, 29Quasi-simplification Ordering, 141 Recursive Path Ordering, 94Reduction Ordering, 30, 31Reduction Pair, 32Reduction Pair Processor, 208, 216Reduction Pair Processor with UsableRules, 209Reduction Strategy, 16Reduction Triple, 164Reflexive Relation, 29Respect, 225Respect Arity, 33Restricted η-expansion, 12, 17Rewrite Relation, 10, 15Rewrite Rule, 10, 15Right Arrow Subterm, 100RPO, 94Rule, 10, 15Rule Removal, 31Rule Removal Processor, 208, 217Rule Scheme, 96 SAT-solver, 269SCC, 225Shape, 172Signature, 10, 13Simple Meta-applications, 26Simple Types, 11Sound Processor, 207, 215SPFP, 250Stable, 30Standard Reduction Pair For (. . . ), 195StarHorpo, 116stat, 94Static Candidate Term, 245Static Dependency Chain, 246Static Dependency Pair, 245Status, 94Strict Ordering, 29Strong Reduction Pair, 30Strong Reduction Pair for TRSs, 30Strongly Connected Component, 210,225Strongly Monotonic, 84Strongly Plain Function Passing, 250Sub-metaterm, 15Substitute, 11Substitution, 10, 11, 14Subterm, 15 Subterm Criterion, 211, 229Subterm Criterion Processor, 211, 229Symb, 172Syntactic Variable, 65 tag, 182Tagged Dependency Chain, 187Tagged Reduction Pair For (. . . ), 195Term, 10, 11, 13Terminating, 10, 16Termination Problem Database, 8TFO, 242Todo List, 282Topmost Step, 15TPDB, 270Transitive Relation, 29TRS, 10Truly First-order (Meta-)term, 242Truly First-order Rule, 243Truly First-order Symbol, 242Type, 11Type Declaration, 11Type Ordering, 100Type-changing Function, 28Typed Symbol, 173typeof, 60 uncur, 20Uncurrying, 19UR, 231Usable Rules, 150, 231Usable Rules Processor, 209Usable Symbol, 233