* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: -(x,0()) -> x -(s(x),s(y)) -> -(x,y) f(x,s(y)) -> f(p(-(x,s(y))),p(-(s(y),x))) f(s(x),y) -> f(p(-(s(x),y)),p(-(y,s(x)))) p(s(x)) -> x - Signature: {-/2,f/2,p/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {-,f,p} 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 -(s(x),s(y)) -> -(x,y) f(x,s(y)) -> f(p(-(x,s(y))),p(-(s(y),x))) f(s(x),y) -> f(p(-(s(x),y)),p(-(y,s(x)))) p(s(x)) -> x - Signature: {-/2,f/2,p/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {-,f,p} 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),?)