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