* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: check(free(x)) -> free(check(x)) check(new(x)) -> new(check(x)) check(old(x)) -> old(x) check(old(x)) -> old(check(x)) new(free(x)) -> free(new(x)) new(serve()) -> free(serve()) old(free(x)) -> free(old(x)) old(serve()) -> free(serve()) top1(free(x),y) -> top2(x,check(new(y))) top1(free(x),y) -> top2(check(x),new(y)) top1(free(x),y) -> top2(check(new(x)),y) top1(free(x),y) -> top2(new(x),check(y)) top2(x,free(y)) -> top1(x,check(new(y))) top2(x,free(y)) -> top1(check(x),new(y)) top2(x,free(y)) -> top1(check(new(x)),y) top2(x,free(y)) -> top1(new(x),check(y)) - Signature: {check/1,new/1,old/1,top1/2,top2/2} / {free/1,serve/0} - Obligation: innermost runtime complexity wrt. defined symbols {check,new,old,top1,top2} and constructors {free,serve} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: check(free(x)) -> free(check(x)) check(new(x)) -> new(check(x)) check(old(x)) -> old(x) check(old(x)) -> old(check(x)) new(free(x)) -> free(new(x)) new(serve()) -> free(serve()) old(free(x)) -> free(old(x)) old(serve()) -> free(serve()) top1(free(x),y) -> top2(x,check(new(y))) top1(free(x),y) -> top2(check(x),new(y)) top1(free(x),y) -> top2(check(new(x)),y) top1(free(x),y) -> top2(new(x),check(y)) top2(x,free(y)) -> top1(x,check(new(y))) top2(x,free(y)) -> top1(check(x),new(y)) top2(x,free(y)) -> top1(check(new(x)),y) top2(x,free(y)) -> top1(new(x),check(y)) - Signature: {check/1,new/1,old/1,top1/2,top2/2} / {free/1,serve/0} - Obligation: innermost runtime complexity wrt. defined symbols {check,new,old,top1,top2} and constructors {free,serve} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: check(x){x -> free(x)} = check(free(x)) ->^+ free(check(x)) = C[check(x) = check(x){}] WORST_CASE(Omega(n^1),?)