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