* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: eq(X,Y) -> false() eq(0(),0()) -> true() eq(s(X),s(Y)) -> eq(X,Y) inf(X) -> cons(X,inf(s(X))) length(cons(X,L)) -> s(length(L)) length(nil()) -> 0() take(0(),X) -> nil() take(s(X),cons(Y,L)) -> cons(Y,take(X,L)) - Signature: {eq/2,inf/1,length/1,take/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {eq,inf,length,take} and constructors {0,cons,false,nil,s ,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: eq(X,Y) -> false() eq(0(),0()) -> true() eq(s(X),s(Y)) -> eq(X,Y) inf(X) -> cons(X,inf(s(X))) length(cons(X,L)) -> s(length(L)) length(nil()) -> 0() take(0(),X) -> nil() take(s(X),cons(Y,L)) -> cons(Y,take(X,L)) - Signature: {eq/2,inf/1,length/1,take/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {eq,inf,length,take} and constructors {0,cons,false,nil,s ,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: eq(x,y){x -> s(x),y -> s(y)} = eq(s(x),s(y)) ->^+ eq(x,y) = C[eq(x,y) = eq(x,y){}] WORST_CASE(Omega(n^1),?)