* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: r(xs,ys,zs,nil()) -> xs r(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> r(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws))) r(xs,cons(y,ys),nil(),cons(w,ws)) -> r(xs,xs,cons(succ(zero()),nil()),ws) r(xs,nil(),zs,cons(w,ws)) -> r(xs,xs,cons(succ(zero()),zs),ws) - Signature: {r/4} / {cons/2,nil/0,succ/1,zero/0} - Obligation: innermost runtime complexity wrt. defined symbols {r} and constructors {cons,nil,succ,zero} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: r(xs,ys,zs,nil()) -> xs r(xs,cons(y,ys),cons(z,zs),cons(w,ws)) -> r(ys,cons(y,ys),zs,cons(succ(zero()),cons(w,ws))) r(xs,cons(y,ys),nil(),cons(w,ws)) -> r(xs,xs,cons(succ(zero()),nil()),ws) r(xs,nil(),zs,cons(w,ws)) -> r(xs,xs,cons(succ(zero()),zs),ws) - Signature: {r/4} / {cons/2,nil/0,succ/1,zero/0} - Obligation: innermost runtime complexity wrt. defined symbols {r} and constructors {cons,nil,succ,zero} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: r(x,cons(y,z),v,cons(w,x_6)){v -> cons(u,v)} = r(x,cons(y,z),cons(u,v),cons(w,x_6)) ->^+ r(z,cons(y,z),v,cons(succ(zero()),cons(w,x_6))) = C[r(z,cons(y,z),v,cons(succ(zero()),cons(w,x_6))) = r(x,cons(y,z),v,cons(w,x_6)){x -> z ,w -> succ(zero()) ,x_6 -> cons(w,x_6)}] WORST_CASE(Omega(n^1),?)