* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(true(),x,y,z) -> g(gt(x,y),x,y,z) g(true(),x,y,z) -> f(gt(x,z),x,y,s(z)) g(true(),x,y,z) -> f(gt(x,z),x,s(y),z) gt(0(),v) -> false() gt(s(u),0()) -> true() gt(s(u),s(v)) -> gt(u,v) - Signature: {f/4,g/4,gt/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {f,g,gt} 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: f(true(),x,y,z) -> g(gt(x,y),x,y,z) g(true(),x,y,z) -> f(gt(x,z),x,y,s(z)) g(true(),x,y,z) -> f(gt(x,z),x,s(y),z) gt(0(),v) -> false() gt(s(u),0()) -> true() gt(s(u),s(v)) -> gt(u,v) - Signature: {f/4,g/4,gt/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {f,g,gt} and constructors {0,false,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: gt(x,y){x -> s(x),y -> s(y)} = gt(s(x),s(y)) ->^+ gt(x,y) = C[gt(x,y) = gt(x,y){}] WORST_CASE(Omega(n^1),?)