*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: a(b(x)) -> b(b(a(x))) Weak DP Rules: Weak TRS Rules: Signature: {a/1} / {b/1} Obligation: Innermost basic terms: {a}/{b} Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} Proof: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. a_0(2) -> 1 a_1(2) -> 4 b_0(2) -> 2 b_1(3) -> 1 b_1(3) -> 4 b_1(4) -> 3 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: a(b(x)) -> b(b(a(x))) Signature: {a/1} / {b/1} Obligation: Innermost basic terms: {a}/{b} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).