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name: termination-analyzer description: Prove termination of algorithms and programs using ranking functions and well-founded orderings allowed-tools:

• Bash
• Read
• Write
• Edit
• Glob
• Grep metadata: specialization: computer-science domain: science category: algorithm-analysis phase: 6 graph: domains: [domain:computer-science] specializations: [specialization:theoretical-computer-science] skillAreas: [skill-area:compiler-implementation, skill-area:mathematical-reasoning, skill-area:language-design] workflows: [workflow:research-grant-lifecycle] roles: [role:computational-scientist, role:research-scientist]

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Termination Analyzer

Purpose

Provides expert guidance on proving termination of algorithms through ranking functions, well-founded orderings, and automated analysis.

Capabilities

• Identify ranking/variant functions automatically
• Prove well-founded orderings
• Handle mutual recursion
• Detect potential non-termination
• Generate termination certificates
• Analyze complex control flow

Usage Guidelines

1. Structure Analysis: Identify recursive calls and loop structures
2. Ranking Function: Find or construct appropriate ranking function
3. Ordering Proof: Prove well-foundedness of the ordering
4. Certificate Generation: Generate formal termination proof
5. Non-termination Detection: Flag potential infinite loops

Tools/Libraries

• AProVE
• T2
• Ultimate Automizer
• SMT solvers