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