* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: double(0()) -> 0() double(s(x)) -> s(s(double(x))) exp(0()) -> s(0()) exp(s(x)) -> double(exp(x)) f(a(),0(),y) -> y f(a(),s(x),y) -> f(b(),y,s(x)) f(b(),y,x) -> f(a(),half(x),exp(y)) half(0()) -> double(0()) half(s(0())) -> half(0()) half(s(s(x))) -> s(half(x)) tower(x) -> f(a(),x,s(0())) - Signature: {double/1,exp/1,f/3,half/1,tower/1} / {0/0,a/0,b/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {double,exp,f,half,tower} and constructors {0,a,b,s} + 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))) exp(0()) -> s(0()) exp(s(x)) -> double(exp(x)) f(a(),0(),y) -> y f(a(),s(x),y) -> f(b(),y,s(x)) f(b(),y,x) -> f(a(),half(x),exp(y)) half(0()) -> double(0()) half(s(0())) -> half(0()) half(s(s(x))) -> s(half(x)) tower(x) -> f(a(),x,s(0())) - Signature: {double/1,exp/1,f/3,half/1,tower/1} / {0/0,a/0,b/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {double,exp,f,half,tower} and constructors {0,a,b,s} + 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),?)