WORST_CASE(Omega(n^1),O(n^1)) * Step 1: Sum. WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: f(g(x)) -> g(g(f(x))) f(g(x)) -> g(g(g(x))) - Signature: {f/1} / {g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(g(x)) -> g(g(f(x))) f(g(x)) -> g(g(g(x))) - Signature: {f/1} / {g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:2: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(g(x)) -> g(g(f(x))) f(g(x)) -> g(g(g(x))) - Signature: {f/1} / {g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x){x -> g(x)} = f(g(x)) ->^+ g(g(f(x))) = C[f(x) = f(x){}] ** Step 1.b:1: Ara. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(g(x)) -> g(g(f(x))) f(g(x)) -> g(g(g(x))) - Signature: {f/1} / {g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {g} + Applied Processor: Ara {minDegree = 1, maxDegree = 1, araTimeout = 8, araRuleShifting = Just 1, isBestCase = False, mkCompletelyDefined = False, verboseOutput = False} + Details: Signatures used: ---------------- F (TrsFun "f") :: ["A"(1)] -(0)-> "A"(0) F (TrsFun "g") :: ["A"(1)] -(1)-> "A"(1) F (TrsFun "g") :: ["A"(0)] -(0)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- Following Still Strict Rules were Typed as: ------------------------------------------- 1. Strict: f(g(x)) -> g(g(f(x))) f(g(x)) -> g(g(g(x))) 2. Weak: WORST_CASE(Omega(n^1),O(n^1))