* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: and(x,false()) -> false() and(x,true()) -> x double(0()) -> 0() double(s(x)) -> s(s(double(x))) f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y)) gt(0(),v) -> false() gt(s(u),0()) -> true() gt(s(u),s(v)) -> gt(u,v) plus(n,0()) -> n plus(n,s(m)) -> s(plus(n,m)) - Signature: {and/2,double/1,f/3,gt/2,plus/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {and,double,f,gt,plus} 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: and(x,false()) -> false() and(x,true()) -> x double(0()) -> 0() double(s(x)) -> s(s(double(x))) f(true(),x,y) -> f(and(gt(x,y),gt(y,s(s(0())))),plus(s(0()),x),double(y)) gt(0(),v) -> false() gt(s(u),0()) -> true() gt(s(u),s(v)) -> gt(u,v) plus(n,0()) -> n plus(n,s(m)) -> s(plus(n,m)) - Signature: {and/2,double/1,f/3,gt/2,plus/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {and,double,f,gt,plus} 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),?)