/export/starexec/sandbox/solver/bin/starexec_run_tct_dci /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: 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: innermost derivational complexity wrt. signature {active,c,d,f,g,h,mark} + 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(active) = [1] x1 + [0] p(c) = [1] x1 + [0] p(d) = [1] x1 + [5] p(f) = [1] x1 + [0] p(g) = [1] x1 + [0] p(h) = [1] x1 + [0] p(mark) = [1] x1 + [1] Following rules are strictly oriented: c(mark(X)) = [1] X + [1] > [1] X + [0] = c(X) d(mark(X)) = [1] X + [6] > [1] X + [5] = d(X) f(mark(X)) = [1] X + [1] > [1] X + [0] = f(X) g(mark(X)) = [1] X + [1] > [1] X + [0] = g(X) h(mark(X)) = [1] X + [1] > [1] X + [0] = h(X) mark(c(X)) = [1] X + [1] > [1] X + [0] = active(c(X)) mark(d(X)) = [1] X + [6] > [1] X + [5] = active(d(X)) mark(g(X)) = [1] X + [1] > [1] X + [0] = active(g(X)) Following rules are (at-least) weakly oriented: active(c(X)) = [1] X + [0] >= [1] X + [6] = mark(d(X)) active(f(f(X))) = [1] X + [0] >= [1] X + [1] = mark(c(f(g(f(X))))) active(h(X)) = [1] X + [0] >= [1] X + [6] = mark(c(d(X))) c(active(X)) = [1] X + [0] >= [1] X + [0] = c(X) d(active(X)) = [1] X + [5] >= [1] X + [5] = d(X) f(active(X)) = [1] X + [0] >= [1] X + [0] = f(X) g(active(X)) = [1] X + [0] >= [1] X + [0] = g(X) h(active(X)) = [1] X + [0] >= [1] X + [0] = h(X) mark(f(X)) = [1] X + [1] >= [1] X + [1] = active(f(mark(X))) mark(h(X)) = [1] X + [1] >= [1] X + [1] = active(h(mark(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: 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) 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: 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: innermost derivational complexity wrt. signature {active,c,d,f,g,h,mark} + 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(active) = [1] x1 + [1] p(c) = [1] x1 + [0] p(d) = [1] x1 + [0] p(f) = [1] x1 + [0] p(g) = [1] x1 + [0] p(h) = [1] x1 + [0] p(mark) = [1] x1 + [4] Following rules are strictly oriented: c(active(X)) = [1] X + [1] > [1] X + [0] = c(X) d(active(X)) = [1] X + [1] > [1] X + [0] = d(X) f(active(X)) = [1] X + [1] > [1] X + [0] = f(X) g(active(X)) = [1] X + [1] > [1] X + [0] = g(X) h(active(X)) = [1] X + [1] > [1] X + [0] = h(X) Following rules are (at-least) weakly oriented: active(c(X)) = [1] X + [1] >= [1] X + [4] = mark(d(X)) active(f(f(X))) = [1] X + [1] >= [1] X + [4] = mark(c(f(g(f(X))))) active(h(X)) = [1] X + [1] >= [1] X + [4] = mark(c(d(X))) c(mark(X)) = [1] X + [4] >= [1] X + [0] = c(X) d(mark(X)) = [1] X + [4] >= [1] X + [0] = d(X) f(mark(X)) = [1] X + [4] >= [1] X + [0] = f(X) g(mark(X)) = [1] X + [4] >= [1] X + [0] = g(X) h(mark(X)) = [1] X + [4] >= [1] X + [0] = h(X) mark(c(X)) = [1] X + [4] >= [1] X + [1] = active(c(X)) mark(d(X)) = [1] X + [4] >= [1] X + [1] = active(d(X)) mark(f(X)) = [1] X + [4] >= [1] X + [5] = active(f(mark(X))) mark(g(X)) = [1] X + [4] >= [1] X + [1] = active(g(X)) mark(h(X)) = [1] X + [4] >= [1] X + [5] = active(h(mark(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: active(c(X)) -> mark(d(X)) active(f(f(X))) -> mark(c(f(g(f(X))))) active(h(X)) -> mark(c(d(X))) mark(f(X)) -> active(f(mark(X))) mark(h(X)) -> active(h(mark(X))) - Weak TRS: 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)) - Signature: {active/1,c/1,d/1,f/1,g/1,h/1,mark/1} / {} - Obligation: innermost derivational complexity wrt. signature {active,c,d,f,g,h,mark} + 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(active) = [1] x1 + [0] p(c) = [1] x1 + [2] p(d) = [1] x1 + [0] p(f) = [1] x1 + [0] p(g) = [1] x1 + [4] p(h) = [1] x1 + [4] p(mark) = [1] x1 + [0] Following rules are strictly oriented: active(c(X)) = [1] X + [2] > [1] X + [0] = mark(d(X)) active(h(X)) = [1] X + [4] > [1] X + [2] = mark(c(d(X))) Following rules are (at-least) weakly oriented: active(f(f(X))) = [1] X + [0] >= [1] X + [6] = mark(c(f(g(f(X))))) c(active(X)) = [1] X + [2] >= [1] X + [2] = c(X) c(mark(X)) = [1] X + [2] >= [1] X + [2] = 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 + [0] >= [1] X + [0] = f(X) f(mark(X)) = [1] X + [0] >= [1] X + [0] = f(X) g(active(X)) = [1] X + [4] >= [1] X + [4] = g(X) g(mark(X)) = [1] X + [4] >= [1] X + [4] = g(X) h(active(X)) = [1] X + [4] >= [1] X + [4] = h(X) h(mark(X)) = [1] X + [4] >= [1] X + [4] = h(X) mark(c(X)) = [1] X + [2] >= [1] X + [2] = active(c(X)) mark(d(X)) = [1] X + [0] >= [1] X + [0] = active(d(X)) mark(f(X)) = [1] X + [0] >= [1] X + [0] = active(f(mark(X))) mark(g(X)) = [1] X + [4] >= [1] X + [4] = active(g(X)) mark(h(X)) = [1] X + [4] >= [1] X + [4] = active(h(mark(X))) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 4: NaturalMI. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: active(f(f(X))) -> mark(c(f(g(f(X))))) mark(f(X)) -> active(f(mark(X))) mark(h(X)) -> active(h(mark(X))) - Weak TRS: active(c(X)) -> mark(d(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)) - Signature: {active/1,c/1,d/1,f/1,g/1,h/1,mark/1} / {} - Obligation: innermost derivational complexity wrt. signature {active,c,d,f,g,h,mark} + Applied Processor: NaturalMI {miDimension = 3, miDegree = 1, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind triangular matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima): Following symbols are considered usable: all TcT has computed the following interpretation: p(active) = [1 0 1] [0] [0 0 0] x1 + [0] [0 0 0] [0] p(c) = [1 0 0] [0] [0 0 0] x1 + [1] [0 0 0] [0] p(d) = [1 0 0] [0] [0 0 0] x1 + [1] [0 0 0] [0] p(f) = [1 0 1] [0] [0 0 0] x1 + [0] [0 0 0] [1] p(g) = [1 0 0] [0] [0 0 0] x1 + [0] [0 0 0] [0] p(h) = [1 0 1] [0] [0 0 0] x1 + [0] [0 0 0] [0] p(mark) = [1 0 1] [0] [0 0 0] x1 + [0] [0 0 0] [0] Following rules are strictly oriented: active(f(f(X))) = [1 0 1] [2] [0 0 0] X + [0] [0 0 0] [0] > [1 0 1] [0] [0 0 0] X + [0] [0 0 0] [0] = mark(c(f(g(f(X))))) Following rules are (at-least) weakly oriented: active(c(X)) = [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [0] = mark(d(X)) active(h(X)) = [1 0 1] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [0] = mark(c(d(X))) c(active(X)) = [1 0 1] [0] [0 0 0] X + [1] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [1] [0 0 0] [0] = c(X) c(mark(X)) = [1 0 1] [0] [0 0 0] X + [1] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [1] [0 0 0] [0] = c(X) d(active(X)) = [1 0 1] [0] [0 0 0] X + [1] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [1] [0 0 0] [0] = d(X) d(mark(X)) = [1 0 1] [0] [0 0 0] X + [1] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [1] [0 0 0] [0] = d(X) f(active(X)) = [1 0 1] [0] [0 0 0] X + [0] [0 0 0] [1] >= [1 0 1] [0] [0 0 0] X + [0] [0 0 0] [1] = f(X) f(mark(X)) = [1 0 1] [0] [0 0 0] X + [0] [0 0 0] [1] >= [1 0 1] [0] [0 0 0] X + [0] [0 0 0] [1] = f(X) g(active(X)) = [1 0 1] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [0] = g(X) g(mark(X)) = [1 0 1] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [0] = g(X) h(active(X)) = [1 0 1] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 1] [0] [0 0 0] X + [0] [0 0 0] [0] = h(X) h(mark(X)) = [1 0 1] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 1] [0] [0 0 0] X + [0] [0 0 0] [0] = h(X) mark(c(X)) = [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [0] = active(c(X)) mark(d(X)) = [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [0] = active(d(X)) mark(f(X)) = [1 0 1] [1] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 1] [1] [0 0 0] X + [0] [0 0 0] [0] = active(f(mark(X))) mark(g(X)) = [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [0] = active(g(X)) mark(h(X)) = [1 0 1] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 1] [0] [0 0 0] X + [0] [0 0 0] [0] = active(h(mark(X))) * Step 5: NaturalMI. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: 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(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)) - Signature: {active/1,c/1,d/1,f/1,g/1,h/1,mark/1} / {} - Obligation: innermost derivational complexity wrt. signature {active,c,d,f,g,h,mark} + Applied Processor: NaturalMI {miDimension = 3, miDegree = 2, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind triangular matrix interpretation (containing no more than 2 non-zero interpretation-entries in the diagonal of the component-wise maxima): Following symbols are considered usable: all TcT has computed the following interpretation: p(active) = [1 1 0] [0] [0 0 0] x1 + [0] [0 0 1] [0] p(c) = [1 1 1] [0] [0 0 1] x1 + [0] [0 0 0] [0] p(d) = [1 0 1] [0] [0 0 1] x1 + [0] [0 0 0] [0] p(f) = [1 1 0] [0] [0 0 0] x1 + [0] [0 0 1] [0] p(g) = [1 0 0] [0] [0 0 0] x1 + [0] [0 0 0] [0] p(h) = [1 1 1] [1] [0 0 1] x1 + [1] [0 0 1] [1] p(mark) = [1 1 1] [0] [0 0 0] x1 + [0] [0 0 1] [0] Following rules are strictly oriented: mark(h(X)) = [1 1 3] [3] [0 0 0] X + [0] [0 0 1] [1] > [1 1 3] [2] [0 0 0] X + [0] [0 0 1] [1] = active(h(mark(X))) Following rules are (at-least) weakly oriented: active(c(X)) = [1 1 2] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 2] [0] [0 0 0] X + [0] [0 0 0] [0] = mark(d(X)) active(f(f(X))) = [1 1 0] [0] [0 0 0] X + [0] [0 0 1] [0] >= [1 1 0] [0] [0 0 0] X + [0] [0 0 0] [0] = mark(c(f(g(f(X))))) active(h(X)) = [1 1 2] [2] [0 0 0] X + [0] [0 0 1] [1] >= [1 0 2] [0] [0 0 0] X + [0] [0 0 0] [0] = mark(c(d(X))) c(active(X)) = [1 1 1] [0] [0 0 1] X + [0] [0 0 0] [0] >= [1 1 1] [0] [0 0 1] X + [0] [0 0 0] [0] = c(X) c(mark(X)) = [1 1 2] [0] [0 0 1] X + [0] [0 0 0] [0] >= [1 1 1] [0] [0 0 1] X + [0] [0 0 0] [0] = c(X) d(active(X)) = [1 1 1] [0] [0 0 1] X + [0] [0 0 0] [0] >= [1 0 1] [0] [0 0 1] X + [0] [0 0 0] [0] = d(X) d(mark(X)) = [1 1 2] [0] [0 0 1] X + [0] [0 0 0] [0] >= [1 0 1] [0] [0 0 1] X + [0] [0 0 0] [0] = d(X) f(active(X)) = [1 1 0] [0] [0 0 0] X + [0] [0 0 1] [0] >= [1 1 0] [0] [0 0 0] X + [0] [0 0 1] [0] = f(X) f(mark(X)) = [1 1 1] [0] [0 0 0] X + [0] [0 0 1] [0] >= [1 1 0] [0] [0 0 0] X + [0] [0 0 1] [0] = f(X) g(active(X)) = [1 1 0] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [0] = g(X) g(mark(X)) = [1 1 1] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [0] = g(X) h(active(X)) = [1 1 1] [1] [0 0 1] X + [1] [0 0 1] [1] >= [1 1 1] [1] [0 0 1] X + [1] [0 0 1] [1] = h(X) h(mark(X)) = [1 1 2] [1] [0 0 1] X + [1] [0 0 1] [1] >= [1 1 1] [1] [0 0 1] X + [1] [0 0 1] [1] = h(X) mark(c(X)) = [1 1 2] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 1 2] [0] [0 0 0] X + [0] [0 0 0] [0] = active(c(X)) mark(d(X)) = [1 0 2] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 2] [0] [0 0 0] X + [0] [0 0 0] [0] = active(d(X)) mark(f(X)) = [1 1 1] [0] [0 0 0] X + [0] [0 0 1] [0] >= [1 1 1] [0] [0 0 0] X + [0] [0 0 1] [0] = active(f(mark(X))) mark(g(X)) = [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [0] [0 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: innermost derivational complexity wrt. signature {active,c,d,f,g,h,mark} + Applied Processor: NaturalMI {miDimension = 3, miDegree = 2, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind triangular matrix interpretation (containing no more than 2 non-zero interpretation-entries in the diagonal of the component-wise maxima): Following symbols are considered usable: all TcT has computed the following interpretation: p(active) = [1 0 0] [0] [0 1 1] x1 + [0] [0 0 0] [0] p(c) = [1 0 0] [0] [0 0 0] x1 + [0] [0 0 0] [1] p(d) = [1 0 0] [0] [0 0 0] x1 + [0] [0 0 0] [1] p(f) = [1 0 0] [0] [0 1 0] x1 + [1] [0 0 0] [0] p(g) = [1 0 0] [0] [0 1 0] x1 + [0] [0 0 0] [0] p(h) = [1 0 0] [0] [0 1 0] x1 + [1] [0 0 0] [0] p(mark) = [1 1 0] [0] [0 1 0] x1 + [1] [0 0 0] [0] Following rules are strictly oriented: mark(f(X)) = [1 1 0] [1] [0 1 0] X + [2] [0 0 0] [0] > [1 1 0] [0] [0 1 0] X + [2] [0 0 0] [0] = active(f(mark(X))) Following rules are (at-least) weakly oriented: active(c(X)) = [1 0 0] [0] [0 0 0] X + [1] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [1] [0 0 0] [0] = mark(d(X)) active(f(f(X))) = [1 0 0] [0] [0 1 0] X + [2] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [1] [0 0 0] [0] = mark(c(f(g(f(X))))) active(h(X)) = [1 0 0] [0] [0 1 0] X + [1] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [1] [0 0 0] [0] = mark(c(d(X))) c(active(X)) = [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [1] >= [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [1] = c(X) c(mark(X)) = [1 1 0] [0] [0 0 0] X + [0] [0 0 0] [1] >= [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [1] = c(X) d(active(X)) = [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [1] >= [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [1] = d(X) d(mark(X)) = [1 1 0] [0] [0 0 0] X + [0] [0 0 0] [1] >= [1 0 0] [0] [0 0 0] X + [0] [0 0 0] [1] = d(X) f(active(X)) = [1 0 0] [0] [0 1 1] X + [1] [0 0 0] [0] >= [1 0 0] [0] [0 1 0] X + [1] [0 0 0] [0] = f(X) f(mark(X)) = [1 1 0] [0] [0 1 0] X + [2] [0 0 0] [0] >= [1 0 0] [0] [0 1 0] X + [1] [0 0 0] [0] = f(X) g(active(X)) = [1 0 0] [0] [0 1 1] X + [0] [0 0 0] [0] >= [1 0 0] [0] [0 1 0] X + [0] [0 0 0] [0] = g(X) g(mark(X)) = [1 1 0] [0] [0 1 0] X + [1] [0 0 0] [0] >= [1 0 0] [0] [0 1 0] X + [0] [0 0 0] [0] = g(X) h(active(X)) = [1 0 0] [0] [0 1 1] X + [1] [0 0 0] [0] >= [1 0 0] [0] [0 1 0] X + [1] [0 0 0] [0] = h(X) h(mark(X)) = [1 1 0] [0] [0 1 0] X + [2] [0 0 0] [0] >= [1 0 0] [0] [0 1 0] X + [1] [0 0 0] [0] = h(X) mark(c(X)) = [1 0 0] [0] [0 0 0] X + [1] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [1] [0 0 0] [0] = active(c(X)) mark(d(X)) = [1 0 0] [0] [0 0 0] X + [1] [0 0 0] [0] >= [1 0 0] [0] [0 0 0] X + [1] [0 0 0] [0] = active(d(X)) mark(g(X)) = [1 1 0] [0] [0 1 0] X + [1] [0 0 0] [0] >= [1 0 0] [0] [0 1 0] X + [0] [0 0 0] [0] = active(g(X)) mark(h(X)) = [1 1 0] [1] [0 1 0] X + [2] [0 0 0] [0] >= [1 1 0] [0] [0 1 0] X + [2] [0 0 0] [0] = 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: innermost 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))