*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: eq0(0(),0()) -> S(0()) eq0(0(),S(x)) -> 0() eq0(S(x),0()) -> 0() eq0(S(x'),S(x)) -> eq0(x',x) Weak DP Rules: Weak TRS Rules: Signature: {eq0/2} / {0/0,S/1} Obligation: Innermost basic terms: {eq0}/{0,S} Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} Proof: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. 0_0() -> 2 0_1() -> 1 0_1() -> 3 S_0(2) -> 2 S_1(3) -> 1 eq0_0(2,2) -> 1 eq0_1(2,2) -> 1 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: eq0(0(),0()) -> S(0()) eq0(0(),S(x)) -> 0() eq0(S(x),0()) -> 0() eq0(S(x'),S(x)) -> eq0(x',x) Signature: {eq0/2} / {0/0,S/1} Obligation: Innermost basic terms: {eq0}/{0,S} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).