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