* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: empty(cons(x,l)) -> false() empty(nil()) -> true() head(cons(x,l)) -> x if(false(),x,l) -> last(head(l),tail(l)) if(true(),x,l) -> x last(x,l) -> if(empty(l),x,l) rev(cons(x,l)) -> cons(rev1(x,l),rev2(x,l)) rev(nil()) -> nil() rev2(x,cons(y,l)) -> rev(cons(x,rev2(y,l))) rev2(x,nil()) -> nil() tail(cons(x,l)) -> l tail(nil()) -> nil() - Signature: {empty/1,head/1,if/3,last/2,rev/1,rev2/2,tail/1} / {cons/2,false/0,nil/0,rev1/2,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {empty,head,if,last,rev,rev2,tail} and constructors {cons ,false,nil,rev1,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: empty(cons(x,l)) -> false() empty(nil()) -> true() head(cons(x,l)) -> x if(false(),x,l) -> last(head(l),tail(l)) if(true(),x,l) -> x last(x,l) -> if(empty(l),x,l) rev(cons(x,l)) -> cons(rev1(x,l),rev2(x,l)) rev(nil()) -> nil() rev2(x,cons(y,l)) -> rev(cons(x,rev2(y,l))) rev2(x,nil()) -> nil() tail(cons(x,l)) -> l tail(nil()) -> nil() - Signature: {empty/1,head/1,if/3,last/2,rev/1,rev2/2,tail/1} / {cons/2,false/0,nil/0,rev1/2,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {empty,head,if,last,rev,rev2,tail} and constructors {cons ,false,nil,rev1,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: rev2(x,z){z -> cons(y,z)} = rev2(x,cons(y,z)) ->^+ rev(cons(x,rev2(y,z))) = C[rev2(y,z) = rev2(x,z){x -> y}] WORST_CASE(Omega(n^1),?)