* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: *(x,0()) -> 0() *(0(),x) -> 0() *(s(x),s(y)) -> s(+(*(x,y),+(x,y))) +(x,0()) -> x +(0(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) prod(cons(x,l)) -> *(x,prod(l)) prod(nil()) -> s(0()) sum(cons(x,l)) -> +(x,sum(l)) sum(nil()) -> 0() - Signature: {*/2,+/2,prod/1,sum/1} / {0/0,cons/2,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {*,+,prod,sum} and constructors {0,cons,nil,s} + 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() *(s(x),s(y)) -> s(+(*(x,y),+(x,y))) +(x,0()) -> x +(0(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) prod(cons(x,l)) -> *(x,prod(l)) prod(nil()) -> s(0()) sum(cons(x,l)) -> +(x,sum(l)) sum(nil()) -> 0() - Signature: {*/2,+/2,prod/1,sum/1} / {0/0,cons/2,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {*,+,prod,sum} and constructors {0,cons,nil,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)) ->^+ s(+(*(x,y),+(x,y))) = C[*(x,y) = *(x,y){}] WORST_CASE(Omega(n^1),?)