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