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