* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: +(+(x,y),z) -> +(x,+(y,z)) +(f(x),+(f(y),z)) -> +(f(+(x,y)),z) +(f(x),f(y)) -> f(+(x,y)) - Signature: {+/2} / {f/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {f} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: +(+(x,y),z) -> +(x,+(y,z)) +(f(x),+(f(y),z)) -> +(f(+(x,y)),z) +(f(x),f(y)) -> f(+(x,y)) - Signature: {+/2} / {f/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {f} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: +(x,y){x -> f(x),y -> f(y)} = +(f(x),f(y)) ->^+ f(+(x,y)) = C[+(x,y) = +(x,y){}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: +(+(x,y),z) -> +(x,+(y,z)) +(f(x),+(f(y),z)) -> +(f(+(x,y)),z) +(f(x),f(y)) -> f(+(x,y)) - Signature: {+/2} / {f/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {f} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. +_0(2,2) -> 1 +_1(2,2) -> 3 f_0(2) -> 2 f_1(3) -> 1 f_1(3) -> 3 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: +(+(x,y),z) -> +(x,+(y,z)) +(f(x),+(f(y),z)) -> +(f(+(x,y)),z) +(f(x),f(y)) -> f(+(x,y)) - Signature: {+/2} / {f/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {f} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))