* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: minus(f(x,y)) -> f(minus(y),minus(x)) minus(h(x)) -> h(minus(x)) minus(minus(x)) -> x - Signature: {minus/1} / {f/2,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {minus} and constructors {f,h} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: minus(f(x,y)) -> f(minus(y),minus(x)) minus(h(x)) -> h(minus(x)) minus(minus(x)) -> x - Signature: {minus/1} / {f/2,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {minus} and constructors {f,h} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: minus(y){y -> f(x,y)} = minus(f(x,y)) ->^+ f(minus(y),minus(x)) = C[minus(y) = minus(y){}] ** Step 1.b:1: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: minus(f(x,y)) -> f(minus(y),minus(x)) minus(h(x)) -> h(minus(x)) minus(minus(x)) -> x - Signature: {minus/1} / {f/2,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {minus} and constructors {f,h} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. f_0(2,2) -> 2 f_1(3,4) -> 1 f_1(4,4) -> 3 f_1(4,4) -> 4 h_0(2) -> 2 h_1(4) -> 1 h_1(4) -> 3 h_1(4) -> 4 minus_0(2) -> 1 minus_1(2) -> 3 minus_1(2) -> 4 ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: minus(f(x,y)) -> f(minus(y),minus(x)) minus(h(x)) -> h(minus(x)) minus(minus(x)) -> x - Signature: {minus/1} / {f/2,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {minus} and constructors {f,h} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))