*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: dbl(0(),y) -> y dbl(S(0()),S(0())) -> S(S(S(S(0())))) save(0()) -> 0() save(S(x)) -> dbl(0(),save(x)) Weak DP Rules: Weak TRS Rules: Signature: {dbl/2,save/1} / {0/0,S/1} Obligation: Innermost basic terms: {dbl,save}/{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() -> 1 0_0() -> 2 0_1() -> 1 0_1() -> 6 0_1() -> 7 S_0(2) -> 1 S_0(2) -> 2 S_1(3) -> 1 S_1(4) -> 3 S_1(5) -> 4 S_1(6) -> 5 dbl_0(2,2) -> 1 dbl_1(6,7) -> 1 dbl_1(7,7) -> 1 dbl_1(7,7) -> 7 save_0(2) -> 1 save_1(2) -> 1 save_1(2) -> 7 2 -> 1 7 -> 1 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: dbl(0(),y) -> y dbl(S(0()),S(0())) -> S(S(S(S(0())))) save(0()) -> 0() save(S(x)) -> dbl(0(),save(x)) Signature: {dbl/2,save/1} / {0/0,S/1} Obligation: Innermost basic terms: {dbl,save}/{0,S} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).