* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: b(r(x)) -> r(b(x)) b(w(x)) -> w(b(x)) w(r(x)) -> r(w(x)) - Signature: {b/1,w/1} / {r/1} - Obligation: innermost runtime complexity wrt. defined symbols {b,w} and constructors {r} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: b(r(x)) -> r(b(x)) b(w(x)) -> w(b(x)) w(r(x)) -> r(w(x)) - Signature: {b/1,w/1} / {r/1} - Obligation: innermost runtime complexity wrt. defined symbols {b,w} and constructors {r} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: b(x){x -> r(x)} = b(r(x)) ->^+ r(b(x)) = C[b(x) = b(x){}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: b(r(x)) -> r(b(x)) b(w(x)) -> w(b(x)) w(r(x)) -> r(w(x)) - Signature: {b/1,w/1} / {r/1} - Obligation: innermost runtime complexity wrt. defined symbols {b,w} and constructors {r} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. b_0(2) -> 1 b_1(2) -> 3 r_0(2) -> 2 r_1(3) -> 1 r_1(3) -> 3 w_0(2) -> 1 w_1(2) -> 3 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: b(r(x)) -> r(b(x)) b(w(x)) -> w(b(x)) w(r(x)) -> r(w(x)) - Signature: {b/1,w/1} / {r/1} - Obligation: innermost runtime complexity wrt. defined symbols {b,w} and constructors {r} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))