*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: activate(X) -> X and(tt(),X) -> activate(X) plus(N,0()) -> N plus(N,s(M)) -> s(plus(N,M)) Weak DP Rules: Weak TRS Rules: Signature: {activate/1,and/2,plus/2} / {0/0,s/1,tt/0} Obligation: Innermost basic terms: {activate,and,plus}/{0,s,tt} 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() -> 1 0_0() -> 2 0_0() -> 3 activate_0(2) -> 1 activate_1(2) -> 1 and_0(2,2) -> 1 plus_0(2,2) -> 1 plus_1(2,2) -> 3 s_0(2) -> 1 s_0(2) -> 2 s_0(2) -> 3 s_1(3) -> 1 s_1(3) -> 3 tt_0() -> 1 tt_0() -> 2 tt_0() -> 3 2 -> 1 2 -> 3 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: activate(X) -> X and(tt(),X) -> activate(X) plus(N,0()) -> N plus(N,s(M)) -> s(plus(N,M)) Signature: {activate/1,and/2,plus/2} / {0/0,s/1,tt/0} Obligation: Innermost basic terms: {activate,and,plus}/{0,s,tt} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).