MAYBE * Step 1: NaturalPI MAYBE + Considered Problem: - Strict TRS: d(0()) -> 0() d(s(x)) -> s(s(d(x))) exp(0()) -> s(0()) exp(s(x)) -> d(exp(x)) - Signature: {d/1,exp/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {d,exp} and constructors {0,s} + 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(d) = {1}, uargs(s) = {1} Following symbols are considered usable: {d,exp} TcT has computed the following interpretation: p(0) = 2 p(d) = x1 p(exp) = 1 + 2*x1 + 5*x1^2 p(s) = x1 Following rules are strictly oriented: exp(0()) = 25 > 2 = s(0()) Following rules are (at-least) weakly oriented: d(0()) = 2 >= 2 = 0() d(s(x)) = x >= x = s(s(d(x))) exp(s(x)) = 1 + 2*x + 5*x^2 >= 1 + 2*x + 5*x^2 = d(exp(x)) * Step 2: Failure MAYBE + Considered Problem: - Strict TRS: d(0()) -> 0() d(s(x)) -> s(s(d(x))) exp(s(x)) -> d(exp(x)) - Weak TRS: exp(0()) -> s(0()) - Signature: {d/1,exp/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {d,exp} and constructors {0,s} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE