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