* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: -(x,0()) -> x -(s(x),s(y)) -> -(x,y) gcd(x,0(),0()) -> x gcd(x,s(y),s(z)) -> gcd(x,-(max(y,z),min(y,z)),s(min(y,z))) gcd(0(),y,0()) -> y gcd(0(),0(),z) -> z gcd(s(x),y,s(z)) -> gcd(-(max(x,z),min(x,z)),y,s(min(x,z))) gcd(s(x),s(y),z) -> gcd(-(max(x,y),min(x,y)),s(min(x,y)),z) 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)) - Signature: {-/2,gcd/3,max/2,min/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {-,gcd,max,min} and constructors {0,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: -(x,0()) -> x -(s(x),s(y)) -> -(x,y) gcd(x,0(),0()) -> x gcd(x,s(y),s(z)) -> gcd(x,-(max(y,z),min(y,z)),s(min(y,z))) gcd(0(),y,0()) -> y gcd(0(),0(),z) -> z gcd(s(x),y,s(z)) -> gcd(-(max(x,z),min(x,z)),y,s(min(x,z))) gcd(s(x),s(y),z) -> gcd(-(max(x,y),min(x,y)),s(min(x,y)),z) 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)) - Signature: {-/2,gcd/3,max/2,min/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {-,gcd,max,min} and constructors {0,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: -(x,y){x -> s(x),y -> s(y)} = -(s(x),s(y)) ->^+ -(x,y) = C[-(x,y) = -(x,y){}] WORST_CASE(Omega(n^1),?)