* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(x,a(b(c(y)))) -> f(b(c(a(b(x)))),y) f(a(x),y) -> f(x,a(y)) f(b(x),y) -> f(x,b(y)) f(c(x),y) -> f(x,c(y)) - Signature: {f/2} / {a/1,b/1,c/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {a,b,c} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(x,a(b(c(y)))) -> f(b(c(a(b(x)))),y) f(a(x),y) -> f(x,a(y)) f(b(x),y) -> f(x,b(y)) f(c(x),y) -> f(x,c(y)) - Signature: {f/2} / {a/1,b/1,c/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {a,b,c} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x,y){y -> a(b(c(y)))} = f(x,a(b(c(y)))) ->^+ f(b(c(a(b(x)))),y) = C[f(b(c(a(b(x)))),y) = f(x,y){x -> b(c(a(b(x))))}] WORST_CASE(Omega(n^1),?)