MAYBE * Step 1: WeightGap MAYBE + Considered Problem: - Strict TRS: c() -> d() g(X) -> h(X) h(d()) -> g(c()) - Signature: {c/0,g/1,h/1} / {d/0} - Obligation: innermost runtime complexity wrt. defined symbols {c,g,h} and constructors {d} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following nonconstant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(g) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(c) = [2] p(d) = [0] p(g) = [1] x1 + [0] p(h) = [0] Following rules are strictly oriented: c() = [2] > [0] = d() Following rules are (at-least) weakly oriented: g(X) = [1] X + [0] >= [0] = h(X) h(d()) = [0] >= [2] = g(c()) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 2: WeightGap MAYBE + Considered Problem: - Strict TRS: g(X) -> h(X) h(d()) -> g(c()) - Weak TRS: c() -> d() - Signature: {c/0,g/1,h/1} / {d/0} - Obligation: innermost runtime complexity wrt. defined symbols {c,g,h} and constructors {d} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following nonconstant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(g) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(c) = [0] p(d) = [0] p(g) = [1] x1 + [0] p(h) = [1] Following rules are strictly oriented: h(d()) = [1] > [0] = g(c()) Following rules are (at-least) weakly oriented: c() = [0] >= [0] = d() g(X) = [1] X + [0] >= [1] = h(X) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 3: Failure MAYBE + Considered Problem: - Strict TRS: g(X) -> h(X) - Weak TRS: c() -> d() h(d()) -> g(c()) - Signature: {c/0,g/1,h/1} / {d/0} - Obligation: innermost runtime complexity wrt. defined symbols {c,g,h} and constructors {d} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE