* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__a() -> a() a__a() -> b() a__f(X,X) -> a__h(a__a()) a__f(X1,X2) -> f(X1,X2) a__g(X1,X2) -> g(X1,X2) a__g(a(),X) -> a__f(b(),X) a__h(X) -> a__g(mark(X),X) a__h(X) -> h(X) mark(a()) -> a__a() mark(b()) -> b() mark(f(X1,X2)) -> a__f(mark(X1),X2) mark(g(X1,X2)) -> a__g(mark(X1),X2) mark(h(X)) -> a__h(mark(X)) - Signature: {a__a/0,a__f/2,a__g/2,a__h/1,mark/1} / {a/0,b/0,f/2,g/2,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__a,a__f,a__g,a__h,mark} and constructors {a,b,f,g,h} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__a() -> a() a__a() -> b() a__f(X,X) -> a__h(a__a()) a__f(X1,X2) -> f(X1,X2) a__g(X1,X2) -> g(X1,X2) a__g(a(),X) -> a__f(b(),X) a__h(X) -> a__g(mark(X),X) a__h(X) -> h(X) mark(a()) -> a__a() mark(b()) -> b() mark(f(X1,X2)) -> a__f(mark(X1),X2) mark(g(X1,X2)) -> a__g(mark(X1),X2) mark(h(X)) -> a__h(mark(X)) - Signature: {a__a/0,a__f/2,a__g/2,a__h/1,mark/1} / {a/0,b/0,f/2,g/2,h/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__a,a__f,a__g,a__h,mark} and constructors {a,b,f,g,h} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: mark(x){x -> f(x,y)} = mark(f(x,y)) ->^+ a__f(mark(x),y) = C[mark(x) = mark(x){}] WORST_CASE(Omega(n^1),?)