MAYBE * Step 1: NaturalPI MAYBE + Considered Problem: - Strict TRS: badd(x,Nil()) -> x badd(x',Cons(x,xs)) -> badd(Cons(Nil(),Nil()),badd(x',xs)) goal(x,y) -> badd(x,y) - Signature: {badd/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {badd,goal} and constructors {Cons,Nil} + Applied Processor: NaturalPI {shape = Mixed 2, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(mixed(2)): The following argument positions are considered usable: uargs(badd) = {2} Following symbols are considered usable: {badd,goal} TcT has computed the following interpretation: p(Cons) = x2 p(Nil) = 0 p(badd) = x1 + x2 p(goal) = 2 + 2*x1 + x1^2 + x2 + 7*x2^2 Following rules are strictly oriented: goal(x,y) = 2 + 2*x + x^2 + y + 7*y^2 > x + y = badd(x,y) Following rules are (at-least) weakly oriented: badd(x,Nil()) = x >= x = x badd(x',Cons(x,xs)) = x' + xs >= x' + xs = badd(Cons(Nil(),Nil()),badd(x',xs)) * Step 2: Failure MAYBE + Considered Problem: - Strict TRS: badd(x,Nil()) -> x badd(x',Cons(x,xs)) -> badd(Cons(Nil(),Nil()),badd(x',xs)) - Weak TRS: goal(x,y) -> badd(x,y) - Signature: {badd/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {badd,goal} and constructors {Cons,Nil} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE