/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: a() -> n__a() activate(X) -> X activate(n__a()) -> a() activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) f(X) -> n__f(X) f(f(a())) -> c(n__f(n__g(n__f(n__a())))) g(X) -> n__g(X) - Signature: {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {a,activate,c,f,g,n__a,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(a) = [0] p(activate) = [1] x1 + [0] p(c) = [1] x1 + [0] p(f) = [1] x1 + [0] p(g) = [1] x1 + [1] p(n__a) = [0] p(n__f) = [1] x1 + [0] p(n__g) = [1] x1 + [0] Following rules are strictly oriented: g(X) = [1] X + [1] > [1] X + [0] = n__g(X) Following rules are (at-least) weakly oriented: a() = [0] >= [0] = n__a() activate(X) = [1] X + [0] >= [1] X + [0] = X activate(n__a()) = [0] >= [0] = a() activate(n__f(X)) = [1] X + [0] >= [1] X + [0] = f(activate(X)) activate(n__g(X)) = [1] X + [0] >= [1] X + [1] = g(activate(X)) f(X) = [1] X + [0] >= [1] X + [0] = n__f(X) f(f(a())) = [0] >= [0] = c(n__f(n__g(n__f(n__a())))) 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: a() -> n__a() activate(X) -> X activate(n__a()) -> a() activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) f(X) -> n__f(X) f(f(a())) -> c(n__f(n__g(n__f(n__a())))) - Weak TRS: g(X) -> n__g(X) - Signature: {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {a,activate,c,f,g,n__a,n__f,n__g} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, 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(a) = [13] p(activate) = [1] x1 + [8] p(c) = [1] x1 + [5] p(f) = [1] x1 + [5] p(g) = [1] x1 + [3] p(n__a) = [5] p(n__f) = [1] x1 + [5] p(n__g) = [1] x1 + [3] Following rules are strictly oriented: a() = [13] > [5] = n__a() activate(X) = [1] X + [8] > [1] X + [0] = X Following rules are (at-least) weakly oriented: activate(n__a()) = [13] >= [13] = a() activate(n__f(X)) = [1] X + [13] >= [1] X + [13] = f(activate(X)) activate(n__g(X)) = [1] X + [11] >= [1] X + [11] = g(activate(X)) f(X) = [1] X + [5] >= [1] X + [5] = n__f(X) f(f(a())) = [23] >= [23] = c(n__f(n__g(n__f(n__a())))) g(X) = [1] X + [3] >= [1] X + [3] = n__g(X) * Step 3: NaturalMI. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: activate(n__a()) -> a() activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) f(X) -> n__f(X) f(f(a())) -> c(n__f(n__g(n__f(n__a())))) - Weak TRS: a() -> n__a() activate(X) -> X g(X) -> n__g(X) - Signature: {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {a,activate,c,f,g,n__a,n__f,n__g} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, 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(a) = [11] p(activate) = [1] x1 + [1] p(c) = [1] x1 + [0] p(f) = [1] x1 + [0] p(g) = [1] x1 + [0] p(n__a) = [10] p(n__f) = [1] x1 + [0] p(n__g) = [1] x1 + [0] Following rules are strictly oriented: f(f(a())) = [11] > [10] = c(n__f(n__g(n__f(n__a())))) Following rules are (at-least) weakly oriented: a() = [11] >= [10] = n__a() activate(X) = [1] X + [1] >= [1] X + [0] = X activate(n__a()) = [11] >= [11] = a() activate(n__f(X)) = [1] X + [1] >= [1] X + [1] = f(activate(X)) activate(n__g(X)) = [1] X + [1] >= [1] X + [1] = g(activate(X)) f(X) = [1] X + [0] >= [1] X + [0] = n__f(X) g(X) = [1] X + [0] >= [1] X + [0] = n__g(X) * Step 4: WeightGap. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: activate(n__a()) -> a() activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) f(X) -> n__f(X) - Weak TRS: a() -> n__a() activate(X) -> X f(f(a())) -> c(n__f(n__g(n__f(n__a())))) g(X) -> n__g(X) - Signature: {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {a,activate,c,f,g,n__a,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(a) = [11] p(activate) = [1] x1 + [0] p(c) = [1] x1 + [2] p(f) = [1] x1 + [1] p(g) = [1] x1 + [0] p(n__a) = [11] p(n__f) = [1] x1 + [0] p(n__g) = [1] x1 + [0] Following rules are strictly oriented: f(X) = [1] X + [1] > [1] X + [0] = n__f(X) Following rules are (at-least) weakly oriented: a() = [11] >= [11] = n__a() activate(X) = [1] X + [0] >= [1] X + [0] = X activate(n__a()) = [11] >= [11] = a() activate(n__f(X)) = [1] X + [0] >= [1] X + [1] = f(activate(X)) activate(n__g(X)) = [1] X + [0] >= [1] X + [0] = g(activate(X)) f(f(a())) = [13] >= [13] = c(n__f(n__g(n__f(n__a())))) 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 5: NaturalMI. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: activate(n__a()) -> a() activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) - Weak TRS: a() -> n__a() activate(X) -> X f(X) -> n__f(X) f(f(a())) -> c(n__f(n__g(n__f(n__a())))) g(X) -> n__g(X) - Signature: {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {a,activate,c,f,g,n__a,n__f,n__g} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, 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(a) = [0] p(activate) = [1] x1 + [1] p(c) = [1] x1 + [0] p(f) = [1] x1 + [0] p(g) = [1] x1 + [0] p(n__a) = [0] p(n__f) = [1] x1 + [0] p(n__g) = [1] x1 + [0] Following rules are strictly oriented: activate(n__a()) = [1] > [0] = a() Following rules are (at-least) weakly oriented: a() = [0] >= [0] = n__a() activate(X) = [1] X + [1] >= [1] X + [0] = X activate(n__f(X)) = [1] X + [1] >= [1] X + [1] = f(activate(X)) activate(n__g(X)) = [1] X + [1] >= [1] X + [1] = g(activate(X)) f(X) = [1] X + [0] >= [1] X + [0] = n__f(X) f(f(a())) = [0] >= [0] = c(n__f(n__g(n__f(n__a())))) g(X) = [1] X + [0] >= [1] X + [0] = n__g(X) * Step 6: NaturalMI. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) - Weak TRS: a() -> n__a() activate(X) -> X activate(n__a()) -> a() f(X) -> n__f(X) f(f(a())) -> c(n__f(n__g(n__f(n__a())))) g(X) -> n__g(X) - Signature: {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {a,activate,c,f,g,n__a,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(a) = [4] [1] p(activate) = [1 1] x1 + [0] [0 1] [0] p(c) = [1 0] x1 + [0] [0 0] [1] p(f) = [1 0] x1 + [0] [0 1] [0] p(g) = [1 1] x1 + [0] [0 1] [4] p(n__a) = [3] [1] p(n__f) = [1 0] x1 + [0] [0 1] [0] p(n__g) = [1 1] x1 + [0] [0 1] [4] Following rules are strictly oriented: activate(n__g(X)) = [1 2] X + [4] [0 1] [4] > [1 2] X + [0] [0 1] [4] = g(activate(X)) Following rules are (at-least) weakly oriented: a() = [4] [1] >= [3] [1] = n__a() activate(X) = [1 1] X + [0] [0 1] [0] >= [1 0] X + [0] [0 1] [0] = X activate(n__a()) = [4] [1] >= [4] [1] = a() activate(n__f(X)) = [1 1] X + [0] [0 1] [0] >= [1 1] X + [0] [0 1] [0] = f(activate(X)) f(X) = [1 0] X + [0] [0 1] [0] >= [1 0] X + [0] [0 1] [0] = n__f(X) f(f(a())) = [4] [1] >= [4] [1] = c(n__f(n__g(n__f(n__a())))) g(X) = [1 1] X + [0] [0 1] [4] >= [1 1] X + [0] [0 1] [4] = n__g(X) * Step 7: NaturalMI. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: activate(n__f(X)) -> f(activate(X)) - Weak TRS: a() -> n__a() activate(X) -> X activate(n__a()) -> a() activate(n__g(X)) -> g(activate(X)) f(X) -> n__f(X) f(f(a())) -> c(n__f(n__g(n__f(n__a())))) g(X) -> n__g(X) - Signature: {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {a,activate,c,f,g,n__a,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(a) = [0] [2] p(activate) = [1 4] x1 + [0] [0 1] [4] p(c) = [1 0] x1 + [0] [0 1] [0] p(f) = [1 1] x1 + [4] [0 1] [2] p(g) = [1 0] x1 + [0] [0 1] [0] p(n__a) = [0] [2] p(n__f) = [1 1] x1 + [4] [0 1] [2] p(n__g) = [1 0] x1 + [0] [0 1] [0] Following rules are strictly oriented: activate(n__f(X)) = [1 5] X + [12] [0 1] [6] > [1 5] X + [8] [0 1] [6] = f(activate(X)) Following rules are (at-least) weakly oriented: a() = [0] [2] >= [0] [2] = n__a() activate(X) = [1 4] X + [0] [0 1] [4] >= [1 0] X + [0] [0 1] [0] = X activate(n__a()) = [8] [6] >= [0] [2] = a() activate(n__g(X)) = [1 4] X + [0] [0 1] [4] >= [1 4] X + [0] [0 1] [4] = g(activate(X)) f(X) = [1 1] X + [4] [0 1] [2] >= [1 1] X + [4] [0 1] [2] = n__f(X) f(f(a())) = [14] [6] >= [14] [6] = c(n__f(n__g(n__f(n__a())))) g(X) = [1 0] X + [0] [0 1] [0] >= [1 0] X + [0] [0 1] [0] = n__g(X) * Step 8: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: a() -> n__a() activate(X) -> X activate(n__a()) -> a() activate(n__f(X)) -> f(activate(X)) activate(n__g(X)) -> g(activate(X)) f(X) -> n__f(X) f(f(a())) -> c(n__f(n__g(n__f(n__a())))) g(X) -> n__g(X) - Signature: {a/0,activate/1,f/1,g/1} / {c/1,n__a/0,n__f/1,n__g/1} - Obligation: derivational complexity wrt. signature {a,activate,c,f,g,n__a,n__f,n__g} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^2))