/export/starexec/sandbox2/solver/bin/starexec_run_tct_dc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^2)) * Step 1: WeightGap. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: g(x,y) -> h(x,y) h(f(x),y) -> f(g(x,y)) - Signature: {g/2,h/2} / {f/1} - Obligation: derivational complexity wrt. signature {f,g,h} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = NoUArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following nonconstant growth matrix-interpretation: We apply a matrix interpretation of kind triangular matrix interpretation: Following symbols are considered usable: all TcT has computed the following interpretation: p(f) = [1] x1 + [8] p(g) = [1] x1 + [1] x2 + [0] p(h) = [1] x1 + [1] x2 + [5] Following rules are strictly oriented: h(f(x),y) = [1] x + [1] y + [13] > [1] x + [1] y + [8] = f(g(x,y)) Following rules are (at-least) weakly oriented: g(x,y) = [1] x + [1] y + [0] >= [1] x + [1] y + [5] = h(x,y) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 2: NaturalMI. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: g(x,y) -> h(x,y) - Weak TRS: h(f(x),y) -> f(g(x,y)) - Signature: {g/2,h/2} / {f/1} - Obligation: derivational complexity wrt. signature {f,g,h} + Applied Processor: NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind triangular matrix interpretation: Following symbols are considered usable: all TcT has computed the following interpretation: p(f) = [1 0] x1 + [0] [0 1] [2] p(g) = [1 1] x1 + [1 0] x2 + [10] [0 1] [0 1] [2] p(h) = [1 1] x1 + [1 0] x2 + [8] [0 1] [0 1] [2] Following rules are strictly oriented: g(x,y) = [1 1] x + [1 0] y + [10] [0 1] [0 1] [2] > [1 1] x + [1 0] y + [8] [0 1] [0 1] [2] = h(x,y) Following rules are (at-least) weakly oriented: h(f(x),y) = [1 1] x + [1 0] y + [10] [0 1] [0 1] [4] >= [1 1] x + [1 0] y + [10] [0 1] [0 1] [4] = f(g(x,y)) * Step 3: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: g(x,y) -> h(x,y) h(f(x),y) -> f(g(x,y)) - Signature: {g/2,h/2} / {f/1} - Obligation: derivational complexity wrt. signature {f,g,h} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^2))