* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: empty(cons(n,x)) -> false() empty(nil()) -> true() head(cons(n,x)) -> n if(false(),b,x) -> if2(b,x) if(true(),b,x) -> weight_undefined_error() if2(false(),x) -> weight(sum(x,cons(0(),tail(tail(x))))) if2(true(),x) -> head(x) sum(cons(0(),x),y) -> sum(x,y) sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y)) sum(nil(),y) -> y tail(cons(n,x)) -> x tail(nil()) -> nil() weight(x) -> if(empty(x),empty(tail(x)),x) - Signature: {empty/1,head/1,if/3,if2/2,sum/2,tail/1,weight/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0 ,weight_undefined_error/0} - Obligation: innermost runtime complexity wrt. defined symbols {empty,head,if,if2,sum,tail,weight} and constructors {0 ,cons,false,nil,s,true,weight_undefined_error} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: empty(cons(n,x)) -> false() empty(nil()) -> true() head(cons(n,x)) -> n if(false(),b,x) -> if2(b,x) if(true(),b,x) -> weight_undefined_error() if2(false(),x) -> weight(sum(x,cons(0(),tail(tail(x))))) if2(true(),x) -> head(x) sum(cons(0(),x),y) -> sum(x,y) sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y)) sum(nil(),y) -> y tail(cons(n,x)) -> x tail(nil()) -> nil() weight(x) -> if(empty(x),empty(tail(x)),x) - Signature: {empty/1,head/1,if/3,if2/2,sum/2,tail/1,weight/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0 ,weight_undefined_error/0} - Obligation: innermost runtime complexity wrt. defined symbols {empty,head,if,if2,sum,tail,weight} and constructors {0 ,cons,false,nil,s,true,weight_undefined_error} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: sum(x,y){x -> cons(0(),x)} = sum(cons(0(),x),y) ->^+ sum(x,y) = C[sum(x,y) = sum(x,y){}] WORST_CASE(Omega(n^1),?)