*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: f(a,cons(x,k)) -> f(cons(x,a),k) f(a,empty()) -> g(a,empty()) g(cons(x,k),d) -> g(k,cons(x,d)) g(empty(),d) -> d Weak DP Rules: Weak TRS Rules: Signature: {f/2,g/2} / {cons/2,empty/0} Obligation: Full basic terms: {f,g}/{cons,empty} Applied Processor: ToInnermost Proof: switch to innermost, as the system is overlay and right linear and does not contain weak rules *** 1.1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: f(a,cons(x,k)) -> f(cons(x,a),k) f(a,empty()) -> g(a,empty()) g(cons(x,k),d) -> g(k,cons(x,d)) g(empty(),d) -> d Weak DP Rules: Weak TRS Rules: Signature: {f/2,g/2} / {cons/2,empty/0} Obligation: Innermost basic terms: {f,g}/{cons,empty} Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} Proof: The problem is match-bounded by 3. The enriched problem is compatible with follwoing automaton. cons_0(2,2) -> 1 cons_0(2,2) -> 2 cons_1(2,2) -> 1 cons_1(2,2) -> 3 cons_1(2,3) -> 1 cons_1(2,3) -> 3 cons_1(2,4) -> 1 cons_1(2,4) -> 3 cons_1(2,5) -> 1 cons_1(2,5) -> 3 cons_2(2,4) -> 1 cons_2(2,4) -> 5 cons_2(2,5) -> 1 cons_2(2,5) -> 5 cons_3(2,5) -> 1 cons_3(2,5) -> 6 cons_3(2,6) -> 1 cons_3(2,6) -> 6 empty_0() -> 1 empty_0() -> 2 empty_1() -> 1 empty_1() -> 4 f_0(2,2) -> 1 f_1(3,2) -> 1 g_0(2,2) -> 1 g_1(2,3) -> 1 g_1(2,4) -> 1 g_1(3,4) -> 1 g_2(2,5) -> 1 g_2(3,5) -> 1 g_2(4,5) -> 1 g_2(5,5) -> 1 g_3(4,6) -> 1 g_3(5,6) -> 1 2 -> 1 3 -> 1 4 -> 1 5 -> 1 6 -> 1 *** 1.1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: f(a,cons(x,k)) -> f(cons(x,a),k) f(a,empty()) -> g(a,empty()) g(cons(x,k),d) -> g(k,cons(x,d)) g(empty(),d) -> d Signature: {f/2,g/2} / {cons/2,empty/0} Obligation: Innermost basic terms: {f,g}/{cons,empty} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).