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