MAYBE * Step 1: NaturalPI MAYBE + Considered Problem: - Strict TRS: ack(Cons(x,xs),Nil()) -> ack(xs,Cons(Nil(),Nil())) ack(Cons(x',xs'),Cons(x,xs)) -> ack(xs',ack(Cons(x',xs'),xs)) ack(Nil(),n) -> Cons(Cons(Nil(),Nil()),n) goal(m,n) -> ack(m,n) - Signature: {ack/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {ack,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(ack) = {2} Following symbols are considered usable: {ack,goal} TcT has computed the following interpretation: p(Cons) = x2 p(Nil) = 2 p(ack) = x2 p(goal) = 1 + 2*x2 Following rules are strictly oriented: goal(m,n) = 1 + 2*n > n = ack(m,n) Following rules are (at-least) weakly oriented: ack(Cons(x,xs),Nil()) = 2 >= 2 = ack(xs,Cons(Nil(),Nil())) ack(Cons(x',xs'),Cons(x,xs)) = xs >= xs = ack(xs',ack(Cons(x',xs'),xs)) ack(Nil(),n) = n >= n = Cons(Cons(Nil(),Nil()),n) * Step 2: Failure MAYBE + Considered Problem: - Strict TRS: ack(Cons(x,xs),Nil()) -> ack(xs,Cons(Nil(),Nil())) ack(Cons(x',xs'),Cons(x,xs)) -> ack(xs',ack(Cons(x',xs'),xs)) ack(Nil(),n) -> Cons(Cons(Nil(),Nil()),n) - Weak TRS: goal(m,n) -> ack(m,n) - Signature: {ack/2,goal/2} / {Cons/2,Nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {ack,goal} and constructors {Cons,Nil} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE