/export/starexec/sandbox/solver/bin/starexec_run_tct_dc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^2)) * Step 1: WeightGap. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(n__g(n__f(X)))) g(X) -> n__g(X) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {activate,c,d,f,g,h,n__d,n__f,n__g} + 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(activate) = [1] x1 + [0] p(c) = [1] x1 + [0] p(d) = [1] x1 + [0] p(f) = [1] x1 + [0] p(g) = [1] x1 + [0] p(h) = [1] x1 + [1] p(n__d) = [1] x1 + [0] p(n__f) = [1] x1 + [11] p(n__g) = [1] x1 + [0] Following rules are strictly oriented: activate(n__f(X)) = [1] X + [11] > [1] X + [0] = f(activate(X)) h(X) = [1] X + [1] > [1] X + [0] = c(n__d(X)) Following rules are (at-least) weakly oriented: activate(X) = [1] X + [0] >= [1] X + [0] = X activate(n__d(X)) = [1] X + [0] >= [1] X + [0] = d(X) activate(n__g(X)) = [1] X + [0] >= [1] X + [0] = g(X) c(X) = [1] X + [0] >= [1] X + [0] = d(activate(X)) d(X) = [1] X + [0] >= [1] X + [0] = n__d(X) f(X) = [1] X + [0] >= [1] X + [11] = n__f(X) f(f(X)) = [1] X + [0] >= [1] X + [22] = c(n__f(n__g(n__f(X)))) g(X) = [1] X + [0] >= [1] X + [0] = n__g(X) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 2: WeightGap. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__g(X)) -> g(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(n__g(n__f(X)))) g(X) -> n__g(X) - Weak TRS: activate(n__f(X)) -> f(activate(X)) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {activate,c,d,f,g,h,n__d,n__f,n__g} + 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(activate) = [1] x1 + [15] p(c) = [1] x1 + [1] p(d) = [1] x1 + [0] p(f) = [1] x1 + [12] p(g) = [1] x1 + [0] p(h) = [1] x1 + [3] p(n__d) = [1] x1 + [1] p(n__f) = [1] x1 + [12] p(n__g) = [1] x1 + [1] Following rules are strictly oriented: activate(X) = [1] X + [15] > [1] X + [0] = X activate(n__d(X)) = [1] X + [16] > [1] X + [0] = d(X) activate(n__g(X)) = [1] X + [16] > [1] X + [0] = g(X) Following rules are (at-least) weakly oriented: activate(n__f(X)) = [1] X + [27] >= [1] X + [27] = f(activate(X)) c(X) = [1] X + [1] >= [1] X + [15] = d(activate(X)) d(X) = [1] X + [0] >= [1] X + [1] = n__d(X) f(X) = [1] X + [12] >= [1] X + [12] = n__f(X) f(f(X)) = [1] X + [24] >= [1] X + [26] = c(n__f(n__g(n__f(X)))) g(X) = [1] X + [0] >= [1] X + [1] = n__g(X) h(X) = [1] X + [3] >= [1] X + [2] = c(n__d(X)) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 3: WeightGap. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(n__g(n__f(X)))) g(X) -> n__g(X) - Weak TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(X) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {activate,c,d,f,g,h,n__d,n__f,n__g} + 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(activate) = [1] x1 + [0] p(c) = [1] x1 + [3] p(d) = [1] x1 + [0] p(f) = [1] x1 + [0] p(g) = [1] x1 + [0] p(h) = [1] x1 + [13] p(n__d) = [1] x1 + [8] p(n__f) = [1] x1 + [1] p(n__g) = [1] x1 + [5] Following rules are strictly oriented: c(X) = [1] X + [3] > [1] X + [0] = d(activate(X)) Following rules are (at-least) weakly oriented: activate(X) = [1] X + [0] >= [1] X + [0] = X activate(n__d(X)) = [1] X + [8] >= [1] X + [0] = d(X) activate(n__f(X)) = [1] X + [1] >= [1] X + [0] = f(activate(X)) activate(n__g(X)) = [1] X + [5] >= [1] X + [0] = g(X) d(X) = [1] X + [0] >= [1] X + [8] = n__d(X) f(X) = [1] X + [0] >= [1] X + [1] = n__f(X) f(f(X)) = [1] X + [0] >= [1] X + [10] = c(n__f(n__g(n__f(X)))) g(X) = [1] X + [0] >= [1] X + [5] = n__g(X) h(X) = [1] X + [13] >= [1] X + [11] = c(n__d(X)) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 4: WeightGap. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(n__g(n__f(X)))) g(X) -> n__g(X) - Weak TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(X) c(X) -> d(activate(X)) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {activate,c,d,f,g,h,n__d,n__f,n__g} + 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(activate) = [1] x1 + [8] p(c) = [1] x1 + [11] p(d) = [1] x1 + [1] p(f) = [1] x1 + [6] p(g) = [1] x1 + [0] p(h) = [1] x1 + [11] p(n__d) = [1] x1 + [0] p(n__f) = [1] x1 + [6] p(n__g) = [1] x1 + [4] Following rules are strictly oriented: d(X) = [1] X + [1] > [1] X + [0] = n__d(X) Following rules are (at-least) weakly oriented: activate(X) = [1] X + [8] >= [1] X + [0] = X activate(n__d(X)) = [1] X + [8] >= [1] X + [1] = d(X) activate(n__f(X)) = [1] X + [14] >= [1] X + [14] = f(activate(X)) activate(n__g(X)) = [1] X + [12] >= [1] X + [0] = g(X) c(X) = [1] X + [11] >= [1] X + [9] = d(activate(X)) f(X) = [1] X + [6] >= [1] X + [6] = n__f(X) f(f(X)) = [1] X + [12] >= [1] X + [27] = c(n__f(n__g(n__f(X)))) g(X) = [1] X + [0] >= [1] X + [4] = n__g(X) h(X) = [1] X + [11] >= [1] X + [11] = c(n__d(X)) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 5: WeightGap. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(X) -> n__f(X) f(f(X)) -> c(n__f(n__g(n__f(X)))) g(X) -> n__g(X) - Weak TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(X) c(X) -> d(activate(X)) d(X) -> n__d(X) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {activate,c,d,f,g,h,n__d,n__f,n__g} + 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(activate) = [1] x1 + [4] p(c) = [1] x1 + [8] p(d) = [1] x1 + [0] p(f) = [1] x1 + [0] p(g) = [1] x1 + [6] p(h) = [1] x1 + [8] p(n__d) = [1] x1 + [0] p(n__f) = [1] x1 + [2] p(n__g) = [1] x1 + [5] Following rules are strictly oriented: g(X) = [1] X + [6] > [1] X + [5] = n__g(X) Following rules are (at-least) weakly oriented: activate(X) = [1] X + [4] >= [1] X + [0] = X activate(n__d(X)) = [1] X + [4] >= [1] X + [0] = d(X) activate(n__f(X)) = [1] X + [6] >= [1] X + [4] = f(activate(X)) activate(n__g(X)) = [1] X + [9] >= [1] X + [6] = g(X) c(X) = [1] X + [8] >= [1] X + [4] = d(activate(X)) d(X) = [1] X + [0] >= [1] X + [0] = n__d(X) f(X) = [1] X + [0] >= [1] X + [2] = n__f(X) f(f(X)) = [1] X + [0] >= [1] X + [17] = c(n__f(n__g(n__f(X)))) h(X) = [1] X + [8] >= [1] X + [8] = c(n__d(X)) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 6: NaturalMI. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(X) -> n__f(X) f(f(X)) -> c(n__f(n__g(n__f(X)))) - Weak TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(X) c(X) -> d(activate(X)) d(X) -> n__d(X) g(X) -> n__g(X) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {activate,c,d,f,g,h,n__d,n__f,n__g} + 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(activate) = [1 0] x1 + [0] [0 1] [0] p(c) = [1 0] x1 + [1] [0 1] [0] p(d) = [1 0] x1 + [0] [0 1] [0] p(f) = [1 1] x1 + [0] [0 0] [2] p(g) = [1 0] x1 + [0] [0 0] [0] p(h) = [1 5] x1 + [5] [0 1] [0] p(n__d) = [1 0] x1 + [0] [0 1] [0] p(n__f) = [1 1] x1 + [0] [0 0] [2] p(n__g) = [1 0] x1 + [0] [0 0] [0] Following rules are strictly oriented: f(f(X)) = [1 1] X + [2] [0 0] [2] > [1 1] X + [1] [0 0] [2] = c(n__f(n__g(n__f(X)))) Following rules are (at-least) weakly oriented: activate(X) = [1 0] X + [0] [0 1] [0] >= [1 0] X + [0] [0 1] [0] = X activate(n__d(X)) = [1 0] X + [0] [0 1] [0] >= [1 0] X + [0] [0 1] [0] = d(X) activate(n__f(X)) = [1 1] X + [0] [0 0] [2] >= [1 1] X + [0] [0 0] [2] = f(activate(X)) activate(n__g(X)) = [1 0] X + [0] [0 0] [0] >= [1 0] X + [0] [0 0] [0] = g(X) c(X) = [1 0] X + [1] [0 1] [0] >= [1 0] X + [0] [0 1] [0] = d(activate(X)) d(X) = [1 0] X + [0] [0 1] [0] >= [1 0] X + [0] [0 1] [0] = n__d(X) f(X) = [1 1] X + [0] [0 0] [2] >= [1 1] X + [0] [0 0] [2] = n__f(X) g(X) = [1 0] X + [0] [0 0] [0] >= [1 0] X + [0] [0 0] [0] = n__g(X) h(X) = [1 5] X + [5] [0 1] [0] >= [1 0] X + [1] [0 1] [0] = c(n__d(X)) * Step 7: NaturalMI. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(X) -> n__f(X) - Weak TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(f(X)) -> c(n__f(n__g(n__f(X)))) g(X) -> n__g(X) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {activate,c,d,f,g,h,n__d,n__f,n__g} + 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(activate) = [1 6] x1 + [2] [0 1] [0] p(c) = [1 6] x1 + [3] [0 0] [0] p(d) = [1 0] x1 + [0] [0 0] [0] p(f) = [1 0] x1 + [7] [0 1] [1] p(g) = [1 0] x1 + [0] [0 0] [0] p(h) = [1 1] x1 + [5] [0 1] [5] p(n__d) = [1 0] x1 + [0] [0 0] [0] p(n__f) = [1 0] x1 + [1] [0 1] [1] p(n__g) = [1 0] x1 + [0] [0 0] [0] Following rules are strictly oriented: f(X) = [1 0] X + [7] [0 1] [1] > [1 0] X + [1] [0 1] [1] = n__f(X) Following rules are (at-least) weakly oriented: activate(X) = [1 6] X + [2] [0 1] [0] >= [1 0] X + [0] [0 1] [0] = X activate(n__d(X)) = [1 0] X + [2] [0 0] [0] >= [1 0] X + [0] [0 0] [0] = d(X) activate(n__f(X)) = [1 6] X + [9] [0 1] [1] >= [1 6] X + [9] [0 1] [1] = f(activate(X)) activate(n__g(X)) = [1 0] X + [2] [0 0] [0] >= [1 0] X + [0] [0 0] [0] = g(X) c(X) = [1 6] X + [3] [0 0] [0] >= [1 6] X + [2] [0 0] [0] = d(activate(X)) d(X) = [1 0] X + [0] [0 0] [0] >= [1 0] X + [0] [0 0] [0] = n__d(X) f(f(X)) = [1 0] X + [14] [0 1] [2] >= [1 0] X + [11] [0 0] [0] = c(n__f(n__g(n__f(X)))) g(X) = [1 0] X + [0] [0 0] [0] >= [1 0] X + [0] [0 0] [0] = n__g(X) h(X) = [1 1] X + [5] [0 1] [5] >= [1 0] X + [3] [0 0] [0] = c(n__d(X)) * Step 8: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(n__g(n__f(X)))) g(X) -> n__g(X) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,g/1,h/1} / {n__d/1,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {activate,c,d,f,g,h,n__d,n__f,n__g} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^2))