* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: f(c(X,s(Y))) -> f(c(s(X),Y)) g(c(s(X),Y)) -> f(c(X,s(Y))) - Signature: {f/1,g/1} / {c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(c(X,s(Y))) -> f(c(s(X),Y)) g(c(s(X),Y)) -> f(c(X,s(Y))) - Signature: {f/1,g/1} / {c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(c(x,y)){y -> s(y)} = f(c(x,s(y))) ->^+ f(c(s(x),y)) = C[f(c(s(x),y)) = f(c(x,y)){x -> s(x)}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(c(X,s(Y))) -> f(c(s(X),Y)) g(c(s(X),Y)) -> f(c(X,s(Y))) - Signature: {f/1,g/1} / {c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. c_0(1,1) -> 1 c_0(1,4) -> 1 c_0(4,1) -> 1 c_0(4,4) -> 1 c_1(1,6) -> 7 c_1(4,6) -> 7 c_1(6,1) -> 5 c_1(6,4) -> 5 c_1(10,1) -> 7 c_1(10,4) -> 7 c_2(9,1) -> 8 c_2(9,4) -> 8 c_2(9,6) -> 8 f_0(1) -> 2 f_0(4) -> 2 f_1(5) -> 2 f_1(7) -> 3 f_2(8) -> 3 g_0(1) -> 3 g_0(4) -> 3 s_0(1) -> 4 s_0(4) -> 4 s_1(1) -> 6 s_1(4) -> 6 s_1(6) -> 6 s_1(9) -> 10 s_1(10) -> 10 s_2(1) -> 9 s_2(4) -> 9 s_2(9) -> 9 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(c(X,s(Y))) -> f(c(s(X),Y)) g(c(s(X),Y)) -> f(c(X,s(Y))) - Signature: {f/1,g/1} / {c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))