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