/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: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: active(c(X)) -> mark(d(X)) active(f(f(X))) -> mark(c(f(g(f(X))))) active(h(X)) -> mark(c(d(X))) c(active(X)) -> c(X) c(mark(X)) -> c(X) d(active(X)) -> d(X) d(mark(X)) -> d(X) f(active(X)) -> f(X) f(mark(X)) -> f(X) g(active(X)) -> g(X) g(mark(X)) -> g(X) h(active(X)) -> h(X) h(mark(X)) -> h(X) mark(c(X)) -> active(c(X)) mark(d(X)) -> active(d(X)) mark(f(X)) -> active(f(mark(X))) mark(g(X)) -> active(g(X)) mark(h(X)) -> active(h(mark(X))) - Signature: {active/1,c/1,d/1,f/1,g/1,h/1,mark/1} / {} - Obligation: derivational complexity wrt. signature {active,c,d,f,g,h,mark} + 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(active) = [1] x1 + [0] p(c) = [1] x1 + [0] p(d) = [1] x1 + [0] p(f) = [1] x1 + [64] p(g) = [1] x1 + [0] p(h) = [1] x1 + [145] p(mark) = [1] x1 + [0] Following rules are strictly oriented: active(h(X)) = [1] X + [145] > [1] X + [0] = mark(c(d(X))) Following rules are (at-least) weakly oriented: active(c(X)) = [1] X + [0] >= [1] X + [0] = mark(d(X)) active(f(f(X))) = [1] X + [128] >= [1] X + [128] = mark(c(f(g(f(X))))) c(active(X)) = [1] X + [0] >= [1] X + [0] = c(X) c(mark(X)) = [1] X + [0] >= [1] X + [0] = c(X) d(active(X)) = [1] X + [0] >= [1] X + [0] = d(X) d(mark(X)) = [1] X + [0] >= [1] X + [0] = d(X) f(active(X)) = [1] X + [64] >= [1] X + [64] = f(X) f(mark(X)) = [1] X + [64] >= [1] X + [64] = f(X) g(active(X)) = [1] X + [0] >= [1] X + [0] = g(X) g(mark(X)) = [1] X + [0] >= [1] X + [0] = g(X) h(active(X)) = [1] X + [145] >= [1] X + [145] = h(X) h(mark(X)) = [1] X + [145] >= [1] X + [145] = h(X) mark(c(X)) = [1] X + [0] >= [1] X + [0] = active(c(X)) mark(d(X)) = [1] X + [0] >= [1] X + [0] = active(d(X)) mark(f(X)) = [1] X + [64] >= [1] X + [64] = active(f(mark(X))) mark(g(X)) = [1] X + [0] >= [1] X + [0] = active(g(X)) mark(h(X)) = [1] X + [145] >= [1] X + [145] = active(h(mark(X))) * Step 2: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: active(c(X)) -> mark(d(X)) active(f(f(X))) -> mark(c(f(g(f(X))))) c(active(X)) -> c(X) c(mark(X)) -> c(X) d(active(X)) -> d(X) d(mark(X)) -> d(X) f(active(X)) -> f(X) f(mark(X)) -> f(X) g(active(X)) -> g(X) g(mark(X)) -> g(X) h(active(X)) -> h(X) h(mark(X)) -> h(X) mark(c(X)) -> active(c(X)) mark(d(X)) -> active(d(X)) mark(f(X)) -> active(f(mark(X))) mark(g(X)) -> active(g(X)) mark(h(X)) -> active(h(mark(X))) - Weak TRS: active(h(X)) -> mark(c(d(X))) - Signature: {active/1,c/1,d/1,f/1,g/1,h/1,mark/1} / {} - Obligation: derivational complexity wrt. signature {active,c,d,f,g,h,mark} + 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(active) = [1 64] x1 + [0] [0 0] [0] p(c) = [1 0] x1 + [0] [0 0] [5] p(d) = [1 0] x1 + [157] [0 0] [0] p(f) = [1 64] x1 + [1] [0 0] [3] p(g) = [1 0] x1 + [0] [0 0] [0] p(h) = [1 64] x1 + [25] [0 0] [8] p(mark) = [1 64] x1 + [60] [0 0] [0] Following rules are strictly oriented: active(c(X)) = [1 0] X + [320] [0 0] [0] > [1 0] X + [217] [0 0] [0] = mark(d(X)) active(f(f(X))) = [1 64] X + [386] [0 0] [0] > [1 64] X + [382] [0 0] [0] = mark(c(f(g(f(X))))) c(mark(X)) = [1 64] X + [60] [0 0] [5] > [1 0] X + [0] [0 0] [5] = c(X) d(mark(X)) = [1 64] X + [217] [0 0] [0] > [1 0] X + [157] [0 0] [0] = d(X) f(mark(X)) = [1 64] X + [61] [0 0] [3] > [1 64] X + [1] [0 0] [3] = f(X) g(mark(X)) = [1 64] X + [60] [0 0] [0] > [1 0] X + [0] [0 0] [0] = g(X) h(mark(X)) = [1 64] X + [85] [0 0] [8] > [1 64] X + [25] [0 0] [8] = h(X) mark(c(X)) = [1 0] X + [380] [0 0] [0] > [1 0] X + [320] [0 0] [0] = active(c(X)) mark(d(X)) = [1 0] X + [217] [0 0] [0] > [1 0] X + [157] [0 0] [0] = active(d(X)) mark(g(X)) = [1 0] X + [60] [0 0] [0] > [1 0] X + [0] [0 0] [0] = active(g(X)) Following rules are (at-least) weakly oriented: active(h(X)) = [1 64] X + [537] [0 0] [0] >= [1 0] X + [537] [0 0] [0] = mark(c(d(X))) c(active(X)) = [1 64] X + [0] [0 0] [5] >= [1 0] X + [0] [0 0] [5] = c(X) d(active(X)) = [1 64] X + [157] [0 0] [0] >= [1 0] X + [157] [0 0] [0] = d(X) f(active(X)) = [1 64] X + [1] [0 0] [3] >= [1 64] X + [1] [0 0] [3] = f(X) g(active(X)) = [1 64] X + [0] [0 0] [0] >= [1 0] X + [0] [0 0] [0] = g(X) h(active(X)) = [1 64] X + [25] [0 0] [8] >= [1 64] X + [25] [0 0] [8] = h(X) mark(f(X)) = [1 64] X + [253] [0 0] [0] >= [1 64] X + [253] [0 0] [0] = active(f(mark(X))) mark(h(X)) = [1 64] X + [597] [0 0] [0] >= [1 64] X + [597] [0 0] [0] = active(h(mark(X))) * Step 3: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: c(active(X)) -> c(X) d(active(X)) -> d(X) f(active(X)) -> f(X) g(active(X)) -> g(X) h(active(X)) -> h(X) mark(f(X)) -> active(f(mark(X))) mark(h(X)) -> active(h(mark(X))) - Weak TRS: active(c(X)) -> mark(d(X)) active(f(f(X))) -> mark(c(f(g(f(X))))) active(h(X)) -> mark(c(d(X))) c(mark(X)) -> c(X) d(mark(X)) -> d(X) f(mark(X)) -> f(X) g(mark(X)) -> g(X) h(mark(X)) -> h(X) mark(c(X)) -> active(c(X)) mark(d(X)) -> active(d(X)) mark(g(X)) -> active(g(X)) - Signature: {active/1,c/1,d/1,f/1,g/1,h/1,mark/1} / {} - Obligation: derivational complexity wrt. signature {active,c,d,f,g,h,mark} + 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(active) = [1 10] x1 + [0] [0 0] [1] p(c) = [1 4] x1 + [0] [0 0] [0] p(d) = [1 0] x1 + [0] [0 0] [0] p(f) = [1 0] x1 + [16] [0 0] [0] p(g) = [1 0] x1 + [0] [0 0] [0] p(h) = [1 0] x1 + [251] [0 0] [0] p(mark) = [1 0] x1 + [0] [0 1] [1] Following rules are strictly oriented: c(active(X)) = [1 10] X + [4] [0 0] [0] > [1 4] X + [0] [0 0] [0] = c(X) Following rules are (at-least) weakly oriented: active(c(X)) = [1 4] X + [0] [0 0] [1] >= [1 0] X + [0] [0 0] [1] = mark(d(X)) active(f(f(X))) = [1 0] X + [32] [0 0] [1] >= [1 0] X + [32] [0 0] [1] = mark(c(f(g(f(X))))) active(h(X)) = [1 0] X + [251] [0 0] [1] >= [1 0] X + [0] [0 0] [1] = mark(c(d(X))) c(mark(X)) = [1 4] X + [4] [0 0] [0] >= [1 4] X + [0] [0 0] [0] = c(X) d(active(X)) = [1 10] X + [0] [0 0] [0] >= [1 0] X + [0] [0 0] [0] = d(X) d(mark(X)) = [1 0] X + [0] [0 0] [0] >= [1 0] X + [0] [0 0] [0] = d(X) f(active(X)) = [1 10] X + [16] [0 0] [0] >= [1 0] X + [16] [0 0] [0] = f(X) f(mark(X)) = [1 0] X + [16] [0 0] [0] >= [1 0] X + [16] [0 0] [0] = f(X) g(active(X)) = [1 10] X + [0] [0 0] [0] >= [1 0] X + [0] [0 0] [0] = g(X) g(mark(X)) = [1 0] X + [0] [0 0] [0] >= [1 0] X + [0] [0 0] [0] = g(X) h(active(X)) = [1 10] X + [251] [0 0] [0] >= [1 0] X + [251] [0 0] [0] = h(X) h(mark(X)) = [1 0] X + [251] [0 0] [0] >= [1 0] X + [251] [0 0] [0] = h(X) mark(c(X)) = [1 4] X + [0] [0 0] [1] >= [1 4] X + [0] [0 0] [1] = active(c(X)) mark(d(X)) = [1 0] X + [0] [0 0] [1] >= [1 0] X + [0] [0 0] [1] = active(d(X)) mark(f(X)) = [1 0] X + [16] [0 0] [1] >= [1 0] X + [16] [0 0] [1] = active(f(mark(X))) mark(g(X)) = [1 0] X + [0] [0 0] [1] >= [1 0] X + [0] [0 0] [1] = active(g(X)) mark(h(X)) = [1 0] X + [251] [0 0] [1] >= [1 0] X + [251] [0 0] [1] = active(h(mark(X))) * Step 4: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: d(active(X)) -> d(X) f(active(X)) -> f(X) g(active(X)) -> g(X) h(active(X)) -> h(X) mark(f(X)) -> active(f(mark(X))) mark(h(X)) -> active(h(mark(X))) - Weak TRS: active(c(X)) -> mark(d(X)) active(f(f(X))) -> mark(c(f(g(f(X))))) active(h(X)) -> mark(c(d(X))) c(active(X)) -> c(X) c(mark(X)) -> c(X) d(mark(X)) -> d(X) f(mark(X)) -> f(X) g(mark(X)) -> g(X) h(mark(X)) -> h(X) mark(c(X)) -> active(c(X)) mark(d(X)) -> active(d(X)) mark(g(X)) -> active(g(X)) - Signature: {active/1,c/1,d/1,f/1,g/1,h/1,mark/1} / {} - Obligation: derivational complexity wrt. signature {active,c,d,f,g,h,mark} + 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(active) = [1 32] x1 + [0] [0 0] [16] p(c) = [1 17] x1 + [0] [0 0] [0] p(d) = [1 0] x1 + [0] [0 0] [0] p(f) = [1 0] x1 + [193] [0 0] [0] p(g) = [1 32] x1 + [0] [0 0] [0] p(h) = [1 0] x1 + [83] [0 0] [0] p(mark) = [1 0] x1 + [0] [0 1] [16] Following rules are strictly oriented: g(active(X)) = [1 32] X + [512] [0 0] [0] > [1 32] X + [0] [0 0] [0] = g(X) Following rules are (at-least) weakly oriented: active(c(X)) = [1 17] X + [0] [0 0] [16] >= [1 0] X + [0] [0 0] [16] = mark(d(X)) active(f(f(X))) = [1 0] X + [386] [0 0] [16] >= [1 0] X + [386] [0 0] [16] = mark(c(f(g(f(X))))) active(h(X)) = [1 0] X + [83] [0 0] [16] >= [1 0] X + [0] [0 0] [16] = mark(c(d(X))) c(active(X)) = [1 32] X + [272] [0 0] [0] >= [1 17] X + [0] [0 0] [0] = c(X) c(mark(X)) = [1 17] X + [272] [0 0] [0] >= [1 17] X + [0] [0 0] [0] = c(X) d(active(X)) = [1 32] X + [0] [0 0] [0] >= [1 0] X + [0] [0 0] [0] = d(X) d(mark(X)) = [1 0] X + [0] [0 0] [0] >= [1 0] X + [0] [0 0] [0] = d(X) f(active(X)) = [1 32] X + [193] [0 0] [0] >= [1 0] X + [193] [0 0] [0] = f(X) f(mark(X)) = [1 0] X + [193] [0 0] [0] >= [1 0] X + [193] [0 0] [0] = f(X) g(mark(X)) = [1 32] X + [512] [0 0] [0] >= [1 32] X + [0] [0 0] [0] = g(X) h(active(X)) = [1 32] X + [83] [0 0] [0] >= [1 0] X + [83] [0 0] [0] = h(X) h(mark(X)) = [1 0] X + [83] [0 0] [0] >= [1 0] X + [83] [0 0] [0] = h(X) mark(c(X)) = [1 17] X + [0] [0 0] [16] >= [1 17] X + [0] [0 0] [16] = active(c(X)) mark(d(X)) = [1 0] X + [0] [0 0] [16] >= [1 0] X + [0] [0 0] [16] = active(d(X)) mark(f(X)) = [1 0] X + [193] [0 0] [16] >= [1 0] X + [193] [0 0] [16] = active(f(mark(X))) mark(g(X)) = [1 32] X + [0] [0 0] [16] >= [1 32] X + [0] [0 0] [16] = active(g(X)) mark(h(X)) = [1 0] X + [83] [0 0] [16] >= [1 0] X + [83] [0 0] [16] = active(h(mark(X))) * Step 5: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: d(active(X)) -> d(X) f(active(X)) -> f(X) h(active(X)) -> h(X) mark(f(X)) -> active(f(mark(X))) mark(h(X)) -> active(h(mark(X))) - Weak TRS: active(c(X)) -> mark(d(X)) active(f(f(X))) -> mark(c(f(g(f(X))))) active(h(X)) -> mark(c(d(X))) c(active(X)) -> c(X) c(mark(X)) -> c(X) d(mark(X)) -> d(X) f(mark(X)) -> f(X) g(active(X)) -> g(X) g(mark(X)) -> g(X) h(mark(X)) -> h(X) mark(c(X)) -> active(c(X)) mark(d(X)) -> active(d(X)) mark(g(X)) -> active(g(X)) - Signature: {active/1,c/1,d/1,f/1,g/1,h/1,mark/1} / {} - Obligation: derivational complexity wrt. signature {active,c,d,f,g,h,mark} + 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(active) = [1 0] x1 + [34] [0 1] [0] p(c) = [1 0] x1 + [129] [0 0] [3] p(d) = [1 0] x1 + [12] [0 0] [0] p(f) = [1 17] x1 + [15] [0 1] [17] p(g) = [1 0] x1 + [113] [0 0] [0] p(h) = [1 24] x1 + [201] [0 1] [28] p(mark) = [1 4] x1 + [68] [0 1] [2] Following rules are strictly oriented: d(active(X)) = [1 0] X + [46] [0 0] [0] > [1 0] X + [12] [0 0] [0] = d(X) f(active(X)) = [1 17] X + [49] [0 1] [17] > [1 17] X + [15] [0 1] [17] = f(X) h(active(X)) = [1 24] X + [235] [0 1] [28] > [1 24] X + [201] [0 1] [28] = h(X) mark(h(X)) = [1 28] X + [381] [0 1] [30] > [1 28] X + [351] [0 1] [30] = active(h(mark(X))) Following rules are (at-least) weakly oriented: active(c(X)) = [1 0] X + [163] [0 0] [3] >= [1 0] X + [80] [0 0] [2] = mark(d(X)) active(f(f(X))) = [1 34] X + [353] [0 1] [34] >= [1 17] X + [352] [0 0] [5] = mark(c(f(g(f(X))))) active(h(X)) = [1 24] X + [235] [0 1] [28] >= [1 0] X + [221] [0 0] [5] = mark(c(d(X))) c(active(X)) = [1 0] X + [163] [0 0] [3] >= [1 0] X + [129] [0 0] [3] = c(X) c(mark(X)) = [1 4] X + [197] [0 0] [3] >= [1 0] X + [129] [0 0] [3] = c(X) d(mark(X)) = [1 4] X + [80] [0 0] [0] >= [1 0] X + [12] [0 0] [0] = d(X) f(mark(X)) = [1 21] X + [117] [0 1] [19] >= [1 17] X + [15] [0 1] [17] = f(X) g(active(X)) = [1 0] X + [147] [0 0] [0] >= [1 0] X + [113] [0 0] [0] = g(X) g(mark(X)) = [1 4] X + [181] [0 0] [0] >= [1 0] X + [113] [0 0] [0] = g(X) h(mark(X)) = [1 28] X + [317] [0 1] [30] >= [1 24] X + [201] [0 1] [28] = h(X) mark(c(X)) = [1 0] X + [209] [0 0] [5] >= [1 0] X + [163] [0 0] [3] = active(c(X)) mark(d(X)) = [1 0] X + [80] [0 0] [2] >= [1 0] X + [46] [0 0] [0] = active(d(X)) mark(f(X)) = [1 21] X + [151] [0 1] [19] >= [1 21] X + [151] [0 1] [19] = active(f(mark(X))) mark(g(X)) = [1 0] X + [181] [0 0] [2] >= [1 0] X + [147] [0 0] [0] = active(g(X)) * Step 6: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: mark(f(X)) -> active(f(mark(X))) - Weak TRS: active(c(X)) -> mark(d(X)) active(f(f(X))) -> mark(c(f(g(f(X))))) active(h(X)) -> mark(c(d(X))) c(active(X)) -> c(X) c(mark(X)) -> c(X) d(active(X)) -> d(X) d(mark(X)) -> d(X) f(active(X)) -> f(X) f(mark(X)) -> f(X) g(active(X)) -> g(X) g(mark(X)) -> g(X) h(active(X)) -> h(X) h(mark(X)) -> h(X) mark(c(X)) -> active(c(X)) mark(d(X)) -> active(d(X)) mark(g(X)) -> active(g(X)) mark(h(X)) -> active(h(mark(X))) - Signature: {active/1,c/1,d/1,f/1,g/1,h/1,mark/1} / {} - Obligation: derivational complexity wrt. signature {active,c,d,f,g,h,mark} + 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(active) = [1 0] x1 + [15] [0 1] [0] p(c) = [1 0] x1 + [4] [0 0] [1] p(d) = [1 0] x1 + [3] [0 0] [0] p(f) = [1 8] x1 + [10] [0 1] [64] p(g) = [1 0] x1 + [246] [0 0] [32] p(h) = [1 0] x1 + [233] [0 1] [128] p(mark) = [1 2] x1 + [16] [0 1] [0] Following rules are strictly oriented: mark(f(X)) = [1 10] X + [154] [0 1] [64] > [1 10] X + [41] [0 1] [64] = active(f(mark(X))) Following rules are (at-least) weakly oriented: active(c(X)) = [1 0] X + [19] [0 0] [1] >= [1 0] X + [19] [0 0] [0] = mark(d(X)) active(f(f(X))) = [1 16] X + [547] [0 1] [128] >= [1 8] X + [544] [0 0] [1] = mark(c(f(g(f(X))))) active(h(X)) = [1 0] X + [248] [0 1] [128] >= [1 0] X + [25] [0 0] [1] = mark(c(d(X))) c(active(X)) = [1 0] X + [19] [0 0] [1] >= [1 0] X + [4] [0 0] [1] = c(X) c(mark(X)) = [1 2] X + [20] [0 0] [1] >= [1 0] X + [4] [0 0] [1] = c(X) d(active(X)) = [1 0] X + [18] [0 0] [0] >= [1 0] X + [3] [0 0] [0] = d(X) d(mark(X)) = [1 2] X + [19] [0 0] [0] >= [1 0] X + [3] [0 0] [0] = d(X) f(active(X)) = [1 8] X + [25] [0 1] [64] >= [1 8] X + [10] [0 1] [64] = f(X) f(mark(X)) = [1 10] X + [26] [0 1] [64] >= [1 8] X + [10] [0 1] [64] = f(X) g(active(X)) = [1 0] X + [261] [0 0] [32] >= [1 0] X + [246] [0 0] [32] = g(X) g(mark(X)) = [1 2] X + [262] [0 0] [32] >= [1 0] X + [246] [0 0] [32] = g(X) h(active(X)) = [1 0] X + [248] [0 1] [128] >= [1 0] X + [233] [0 1] [128] = h(X) h(mark(X)) = [1 2] X + [249] [0 1] [128] >= [1 0] X + [233] [0 1] [128] = h(X) mark(c(X)) = [1 0] X + [22] [0 0] [1] >= [1 0] X + [19] [0 0] [1] = active(c(X)) mark(d(X)) = [1 0] X + [19] [0 0] [0] >= [1 0] X + [18] [0 0] [0] = active(d(X)) mark(g(X)) = [1 0] X + [326] [0 0] [32] >= [1 0] X + [261] [0 0] [32] = active(g(X)) mark(h(X)) = [1 2] X + [505] [0 1] [128] >= [1 2] X + [264] [0 1] [128] = active(h(mark(X))) * Step 7: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: active(c(X)) -> mark(d(X)) active(f(f(X))) -> mark(c(f(g(f(X))))) active(h(X)) -> mark(c(d(X))) c(active(X)) -> c(X) c(mark(X)) -> c(X) d(active(X)) -> d(X) d(mark(X)) -> d(X) f(active(X)) -> f(X) f(mark(X)) -> f(X) g(active(X)) -> g(X) g(mark(X)) -> g(X) h(active(X)) -> h(X) h(mark(X)) -> h(X) mark(c(X)) -> active(c(X)) mark(d(X)) -> active(d(X)) mark(f(X)) -> active(f(mark(X))) mark(g(X)) -> active(g(X)) mark(h(X)) -> active(h(mark(X))) - Signature: {active/1,c/1,d/1,f/1,g/1,h/1,mark/1} / {} - Obligation: derivational complexity wrt. signature {active,c,d,f,g,h,mark} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^2))