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