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