* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: double(0()) -> 0() double(s(x)) -> s(s(double(x))) greater(x,0()) -> first() greater(0(),s(y)) -> second() greater(s(x),s(y)) -> greater(x,y) if(false(),x,y,z) -> true() if(first(),x,y,z) -> if(le(s(x),y,s(z)),s(x),y,s(z)) if(second(),x,y,z) -> if(le(s(x),s(y),z),s(x),s(y),z) le(0(),y,z) -> greater(y,z) le(s(x),0(),z) -> false() le(s(x),s(y),0()) -> false() le(s(x),s(y),s(z)) -> le(x,y,z) triple(x) -> if(le(x,x,double(x)),x,0(),0()) - Signature: {double/1,greater/2,if/4,le/3,triple/1} / {0/0,false/0,first/0,s/1,second/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {double,greater,if,le,triple} and constructors {0,false ,first,s,second,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: double(0()) -> 0() double(s(x)) -> s(s(double(x))) greater(x,0()) -> first() greater(0(),s(y)) -> second() greater(s(x),s(y)) -> greater(x,y) if(false(),x,y,z) -> true() if(first(),x,y,z) -> if(le(s(x),y,s(z)),s(x),y,s(z)) if(second(),x,y,z) -> if(le(s(x),s(y),z),s(x),s(y),z) le(0(),y,z) -> greater(y,z) le(s(x),0(),z) -> false() le(s(x),s(y),0()) -> false() le(s(x),s(y),s(z)) -> le(x,y,z) triple(x) -> if(le(x,x,double(x)),x,0(),0()) - Signature: {double/1,greater/2,if/4,le/3,triple/1} / {0/0,false/0,first/0,s/1,second/0,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {double,greater,if,le,triple} and constructors {0,false ,first,s,second,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),?)