* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: 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 runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: 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 runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x,z){z -> cons(y,z)} = f(x,cons(y,z)) ->^+ f(cons(y,x),z) = C[f(cons(y,x),z) = f(x,z){x -> cons(y,x)}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: 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 runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. cons_0(1,1) -> 1 cons_0(1,1) -> 4 cons_0(1,2) -> 1 cons_0(1,2) -> 4 cons_0(2,1) -> 1 cons_0(2,1) -> 4 cons_0(2,2) -> 1 cons_0(2,2) -> 4 cons_1(1,1) -> 4 cons_1(1,1) -> 5 cons_1(1,2) -> 4 cons_1(1,2) -> 5 cons_1(1,5) -> 4 cons_1(1,5) -> 5 cons_1(1,6) -> 3 cons_1(1,6) -> 6 cons_1(1,7) -> 3 cons_1(1,7) -> 6 cons_1(2,1) -> 4 cons_1(2,1) -> 5 cons_1(2,2) -> 4 cons_1(2,2) -> 5 cons_1(2,5) -> 4 cons_1(2,5) -> 5 cons_1(2,6) -> 3 cons_1(2,6) -> 6 cons_1(2,7) -> 3 cons_1(2,7) -> 6 cons_2(1,6) -> 3 cons_2(1,6) -> 7 cons_2(1,7) -> 3 cons_2(1,7) -> 7 cons_2(2,6) -> 3 cons_2(2,6) -> 7 cons_2(2,7) -> 3 cons_2(2,7) -> 7 empty_0() -> 2 empty_0() -> 4 empty_1() -> 3 empty_1() -> 6 f_0(1,1) -> 3 f_0(1,2) -> 3 f_0(2,1) -> 3 f_0(2,2) -> 3 f_1(5,1) -> 3 f_1(5,2) -> 3 g_0(1,1) -> 4 g_0(1,2) -> 4 g_0(2,1) -> 4 g_0(2,2) -> 4 g_1(1,5) -> 4 g_1(1,6) -> 3 g_1(2,5) -> 4 g_1(2,6) -> 3 g_1(5,6) -> 3 g_2(1,7) -> 3 g_2(2,7) -> 3 g_2(5,7) -> 3 1 -> 4 2 -> 4 5 -> 4 6 -> 3 7 -> 3 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: 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 runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))