* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y)))))) bsort(nil()) -> nil() bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z)))) bubble(.(x,nil())) -> .(x,nil()) bubble(nil()) -> nil() butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z))) butlast(.(x,nil())) -> nil() butlast(nil()) -> nil() last(.(x,.(y,z))) -> last(.(y,z)) last(.(x,nil())) -> x last(nil()) -> 0() - Signature: {bsort/1,bubble/1,butlast/1,last/1} / {./2,0/0,<=/2,if/3,nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {bsort,bubble,butlast,last} and constructors {.,0,<=,if ,nil} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: bsort(.(x,y)) -> last(.(bubble(.(x,y)),bsort(butlast(bubble(.(x,y)))))) bsort(nil()) -> nil() bubble(.(x,.(y,z))) -> if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z)))) bubble(.(x,nil())) -> .(x,nil()) bubble(nil()) -> nil() butlast(.(x,.(y,z))) -> .(x,butlast(.(y,z))) butlast(.(x,nil())) -> nil() butlast(nil()) -> nil() last(.(x,.(y,z))) -> last(.(y,z)) last(.(x,nil())) -> x last(nil()) -> 0() - Signature: {bsort/1,bubble/1,butlast/1,last/1} / {./2,0/0,<=/2,if/3,nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {bsort,bubble,butlast,last} and constructors {.,0,<=,if ,nil} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: bubble(.(x,z)){z -> .(y,z)} = bubble(.(x,.(y,z))) ->^+ if(<=(x,y),.(y,bubble(.(x,z))),.(x,bubble(.(y,z)))) = C[bubble(.(x,z)) = bubble(.(x,z)){}] WORST_CASE(Omega(n^1),?)