* 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(-(max(*(s(x),s(x)),+(s(x),s(s(s(0()))))),max(s(*(s(x),s(x))),+(s(x),s(s(s(s(0())))))))) max(x,0()) -> x max(0(),y) -> y max(s(x),s(y)) -> s(max(x,y)) min(x,0()) -> 0() min(0(),y) -> 0() min(s(x),s(y)) -> s(min(x,y)) - Signature: {*/2,+/2,-/2,f/1,max/2,min/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {*,+,-,f,max,min} 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(-(max(*(s(x),s(x)),+(s(x),s(s(s(0()))))),max(s(*(s(x),s(x))),+(s(x),s(s(s(s(0())))))))) max(x,0()) -> x max(0(),y) -> y max(s(x),s(y)) -> s(max(x,y)) min(x,0()) -> 0() min(0(),y) -> 0() min(s(x),s(y)) -> s(min(x,y)) - Signature: {*/2,+/2,-/2,f/1,max/2,min/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {*,+,-,f,max,min} 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),?)