* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(x,c(x),c(y)) -> f(y,y,f(y,x,y)) f(c(x),x,y) -> c(y) f(s(x),y,z) -> f(x,s(c(y)),c(z)) g(x,y) -> x g(x,y) -> y - Signature: {f/3,g/2} / {c/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(x,c(x),c(y)) -> f(y,y,f(y,x,y)) f(c(x),x,y) -> c(y) f(s(x),y,z) -> f(x,s(c(y)),c(z)) g(x,y) -> x g(x,y) -> y - Signature: {f/3,g/2} / {c/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x,y,z){x -> s(x)} = f(s(x),y,z) ->^+ f(x,s(c(y)),c(z)) = C[f(x,s(c(y)),c(z)) = f(x,y,z){y -> s(c(y)),z -> c(z)}] WORST_CASE(Omega(n^1),?)