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