/export/starexec/sandbox2/solver/bin/starexec_run_tct_dci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^1)) * Step 1: NaturalMI. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) b(b(x1)) -> d(d(d(d(x1)))) b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) c(c(d(d(d(d(x1)))))) -> a(a(x1)) - Signature: {a/1,b/1,c/1} / {d/1} - Obligation: innermost derivational complexity wrt. signature {a,b,c,d} + 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) = [1] x1 + [18] p(b) = [1] x1 + [12] p(c) = [1] x1 + [8] p(d) = [1] x1 + [5] Following rules are strictly oriented: b(b(x1)) = [1] x1 + [24] > [1] x1 + [20] = d(d(d(d(x1)))) c(c(c(c(x1)))) = [1] x1 + [32] > [1] x1 + [30] = d(d(d(d(d(d(x1)))))) Following rules are (at-least) weakly oriented: a(a(a(a(x1)))) = [1] x1 + [72] >= [1] x1 + [72] = b(b(b(b(b(b(x1)))))) b(b(b(b(x1)))) = [1] x1 + [48] >= [1] x1 + [48] = c(c(c(c(c(c(x1)))))) c(c(d(d(d(d(x1)))))) = [1] x1 + [36] >= [1] x1 + [36] = a(a(x1)) * Step 2: NaturalMI. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) c(c(d(d(d(d(x1)))))) -> a(a(x1)) - Weak TRS: b(b(x1)) -> d(d(d(d(x1)))) c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) - Signature: {a/1,b/1,c/1} / {d/1} - Obligation: innermost derivational complexity wrt. signature {a,b,c,d} + 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) = [1] x1 + [144] p(b) = [1] x1 + [96] p(c) = [1] x1 + [64] p(d) = [1] x1 + [42] Following rules are strictly oriented: c(c(d(d(d(d(x1)))))) = [1] x1 + [296] > [1] x1 + [288] = a(a(x1)) Following rules are (at-least) weakly oriented: a(a(a(a(x1)))) = [1] x1 + [576] >= [1] x1 + [576] = b(b(b(b(b(b(x1)))))) b(b(x1)) = [1] x1 + [192] >= [1] x1 + [168] = d(d(d(d(x1)))) b(b(b(b(x1)))) = [1] x1 + [384] >= [1] x1 + [384] = c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) = [1] x1 + [256] >= [1] x1 + [252] = d(d(d(d(d(d(x1)))))) * Step 3: NaturalMI. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) - Weak TRS: b(b(x1)) -> d(d(d(d(x1)))) c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) c(c(d(d(d(d(x1)))))) -> a(a(x1)) - Signature: {a/1,b/1,c/1} / {d/1} - Obligation: innermost derivational complexity wrt. signature {a,b,c,d} + 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) = [1] x1 + [75] p(b) = [1] x1 + [50] p(c) = [1] x1 + [33] p(d) = [1] x1 + [22] Following rules are strictly oriented: b(b(b(b(x1)))) = [1] x1 + [200] > [1] x1 + [198] = c(c(c(c(c(c(x1)))))) Following rules are (at-least) weakly oriented: a(a(a(a(x1)))) = [1] x1 + [300] >= [1] x1 + [300] = b(b(b(b(b(b(x1)))))) b(b(x1)) = [1] x1 + [100] >= [1] x1 + [88] = d(d(d(d(x1)))) c(c(c(c(x1)))) = [1] x1 + [132] >= [1] x1 + [132] = d(d(d(d(d(d(x1)))))) c(c(d(d(d(d(x1)))))) = [1] x1 + [154] >= [1] x1 + [150] = a(a(x1)) * Step 4: NaturalMI. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) - Weak TRS: b(b(x1)) -> d(d(d(d(x1)))) b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) c(c(d(d(d(d(x1)))))) -> a(a(x1)) - Signature: {a/1,b/1,c/1} / {d/1} - Obligation: innermost derivational complexity wrt. signature {a,b,c,d} + 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) = [1] x1 + [146] p(b) = [1] x1 + [96] p(c) = [1] x1 + [64] p(d) = [1] x1 + [41] Following rules are strictly oriented: a(a(a(a(x1)))) = [1] x1 + [584] > [1] x1 + [576] = b(b(b(b(b(b(x1)))))) Following rules are (at-least) weakly oriented: b(b(x1)) = [1] x1 + [192] >= [1] x1 + [164] = d(d(d(d(x1)))) b(b(b(b(x1)))) = [1] x1 + [384] >= [1] x1 + [384] = c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) = [1] x1 + [256] >= [1] x1 + [246] = d(d(d(d(d(d(x1)))))) c(c(d(d(d(d(x1)))))) = [1] x1 + [292] >= [1] x1 + [292] = a(a(x1)) * Step 5: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) b(b(x1)) -> d(d(d(d(x1)))) b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) c(c(d(d(d(d(x1)))))) -> a(a(x1)) - Signature: {a/1,b/1,c/1} / {d/1} - Obligation: innermost derivational complexity wrt. signature {a,b,c,d} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))