/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^1)) * Step 1: WeightGap. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(g(n__f(X)))) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1} - Obligation: derivational complexity wrt. signature {activate,c,d,f,g,h,n__d,n__f} + 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 + [0] Following rules are strictly oriented: 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__f(X)) = [1] X + [0] >= [1] X + [0] = f(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 + [0] = n__f(X) f(f(X)) = [1] X + [0] >= [1] X + [0] = c(n__f(g(n__f(X)))) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 2: WeightGap. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(g(n__f(X)))) - Weak TRS: h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1} - Obligation: derivational complexity wrt. signature {activate,c,d,f,g,h,n__d,n__f} + 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 + [6] p(c) = [1] x1 + [0] p(d) = [1] x1 + [0] p(f) = [1] x1 + [2] p(g) = [1] x1 + [0] p(h) = [1] x1 + [10] p(n__d) = [1] x1 + [1] p(n__f) = [1] x1 + [0] Following rules are strictly oriented: activate(X) = [1] X + [6] > [1] X + [0] = X activate(n__d(X)) = [1] X + [7] > [1] X + [0] = d(X) activate(n__f(X)) = [1] X + [6] > [1] X + [2] = f(X) f(X) = [1] X + [2] > [1] X + [0] = n__f(X) f(f(X)) = [1] X + [4] > [1] X + [0] = c(n__f(g(n__f(X)))) Following rules are (at-least) weakly oriented: c(X) = [1] X + [0] >= [1] X + [6] = d(activate(X)) d(X) = [1] X + [0] >= [1] X + [1] = n__d(X) h(X) = [1] X + [10] >= [1] X + [1] = 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^1)) + Considered Problem: - Strict TRS: c(X) -> d(activate(X)) d(X) -> n__d(X) - Weak TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(g(n__f(X)))) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1} - Obligation: derivational complexity wrt. signature {activate,c,d,f,g,h,n__d,n__f} + 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 + [13] p(c) = [1] x1 + [0] p(d) = [1] x1 + [5] p(f) = [1] x1 + [9] p(g) = [1] x1 + [4] p(h) = [1] x1 + [4] p(n__d) = [1] x1 + [4] p(n__f) = [1] x1 + [7] Following rules are strictly oriented: d(X) = [1] X + [5] > [1] X + [4] = n__d(X) Following rules are (at-least) weakly oriented: activate(X) = [1] X + [13] >= [1] X + [0] = X activate(n__d(X)) = [1] X + [17] >= [1] X + [5] = d(X) activate(n__f(X)) = [1] X + [20] >= [1] X + [9] = f(X) c(X) = [1] X + [0] >= [1] X + [18] = d(activate(X)) f(X) = [1] X + [9] >= [1] X + [7] = n__f(X) f(f(X)) = [1] X + [18] >= [1] X + [18] = c(n__f(g(n__f(X)))) h(X) = [1] X + [4] >= [1] X + [4] = 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^1)) + Considered Problem: - Strict TRS: c(X) -> d(activate(X)) - Weak TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(X) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(g(n__f(X)))) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1} - Obligation: derivational complexity wrt. signature {activate,c,d,f,g,h,n__d,n__f} + 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 + [2] p(c) = [1] x1 + [3] p(d) = [1] x1 + [0] p(f) = [1] x1 + [2] p(g) = [1] x1 + [0] p(h) = [1] x1 + [3] p(n__d) = [1] x1 + [0] p(n__f) = [1] x1 + [0] Following rules are strictly oriented: c(X) = [1] X + [3] > [1] X + [2] = d(activate(X)) Following rules are (at-least) weakly oriented: activate(X) = [1] X + [2] >= [1] X + [0] = X activate(n__d(X)) = [1] X + [2] >= [1] X + [0] = d(X) activate(n__f(X)) = [1] X + [2] >= [1] X + [2] = f(X) d(X) = [1] X + [0] >= [1] X + [0] = n__d(X) f(X) = [1] X + [2] >= [1] X + [0] = n__f(X) f(f(X)) = [1] X + [4] >= [1] X + [3] = c(n__f(g(n__f(X)))) h(X) = [1] X + [3] >= [1] X + [3] = c(n__d(X)) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 5: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: activate(X) -> X activate(n__d(X)) -> d(X) activate(n__f(X)) -> f(X) c(X) -> d(activate(X)) d(X) -> n__d(X) f(X) -> n__f(X) f(f(X)) -> c(n__f(g(n__f(X)))) h(X) -> c(n__d(X)) - Signature: {activate/1,c/1,d/1,f/1,h/1} / {g/1,n__d/1,n__f/1} - Obligation: derivational complexity wrt. signature {activate,c,d,f,g,h,n__d,n__f} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))