/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: NaturalMI. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: 0(1(2(3(4(x1))))) -> 0(2(1(3(4(x1))))) 0(5(1(2(4(3(x1)))))) -> 0(5(2(1(4(3(x1)))))) 0(5(2(4(1(3(x1)))))) -> 0(1(5(2(4(3(x1)))))) 0(5(3(1(2(4(x1)))))) -> 0(1(5(3(2(4(x1)))))) 0(5(4(1(3(2(x1)))))) -> 0(5(4(3(1(2(x1)))))) - Signature: {0/1} / {1/1,2/1,3/1,4/1,5/1} - Obligation: derivational complexity wrt. signature {0,1,2,3,4,5} + Applied Processor: NaturalMI {miDimension = 2, 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(0) = [1 0] x1 + [0] [0 0] [1] p(1) = [1 0] x1 + [1] [0 0] [0] p(2) = [1 1] x1 + [0] [0 0] [0] p(3) = [1 0] x1 + [0] [0 0] [1] p(4) = [1 0] x1 + [0] [0 0] [0] p(5) = [1 1] x1 + [0] [0 0] [1] Following rules are strictly oriented: 0(1(2(3(4(x1))))) = [1 0] x1 + [2] [0 0] [1] > [1 0] x1 + [1] [0 0] [1] = 0(2(1(3(4(x1))))) Following rules are (at-least) weakly oriented: 0(5(1(2(4(3(x1)))))) = [1 0] x1 + [1] [0 0] [1] >= [1 0] x1 + [1] [0 0] [1] = 0(5(2(1(4(3(x1)))))) 0(5(2(4(1(3(x1)))))) = [1 0] x1 + [1] [0 0] [1] >= [1 0] x1 + [1] [0 0] [1] = 0(1(5(2(4(3(x1)))))) 0(5(3(1(2(4(x1)))))) = [1 0] x1 + [2] [0 0] [1] >= [1 0] x1 + [2] [0 0] [1] = 0(1(5(3(2(4(x1)))))) 0(5(4(1(3(2(x1)))))) = [1 1] x1 + [1] [0 0] [1] >= [1 1] x1 + [1] [0 0] [1] = 0(5(4(3(1(2(x1)))))) * Step 2: NaturalMI. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: 0(5(1(2(4(3(x1)))))) -> 0(5(2(1(4(3(x1)))))) 0(5(2(4(1(3(x1)))))) -> 0(1(5(2(4(3(x1)))))) 0(5(3(1(2(4(x1)))))) -> 0(1(5(3(2(4(x1)))))) 0(5(4(1(3(2(x1)))))) -> 0(5(4(3(1(2(x1)))))) - Weak TRS: 0(1(2(3(4(x1))))) -> 0(2(1(3(4(x1))))) - Signature: {0/1} / {1/1,2/1,3/1,4/1,5/1} - Obligation: derivational complexity wrt. signature {0,1,2,3,4,5} + Applied Processor: NaturalMI {miDimension = 2, 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(0) = [1 0] x1 + [1] [0 0] [0] p(1) = [1 1] x1 + [0] [0 0] [0] p(2) = [1 0] x1 + [1] [0 0] [1] p(3) = [1 0] x1 + [0] [0 0] [1] p(4) = [1 0] x1 + [0] [0 0] [0] p(5) = [1 0] x1 + [0] [0 0] [0] Following rules are strictly oriented: 0(5(1(2(4(3(x1)))))) = [1 0] x1 + [3] [0 0] [0] > [1 0] x1 + [2] [0 0] [0] = 0(5(2(1(4(3(x1)))))) 0(5(2(4(1(3(x1)))))) = [1 0] x1 + [3] [0 0] [0] > [1 0] x1 + [2] [0 0] [0] = 0(1(5(2(4(3(x1)))))) 0(5(3(1(2(4(x1)))))) = [1 0] x1 + [3] [0 0] [0] > [1 0] x1 + [2] [0 0] [0] = 0(1(5(3(2(4(x1)))))) Following rules are (at-least) weakly oriented: 0(1(2(3(4(x1))))) = [1 0] x1 + [3] [0 0] [0] >= [1 0] x1 + [3] [0 0] [0] = 0(2(1(3(4(x1))))) 0(5(4(1(3(2(x1)))))) = [1 0] x1 + [3] [0 0] [0] >= [1 0] x1 + [3] [0 0] [0] = 0(5(4(3(1(2(x1)))))) * Step 3: NaturalMI. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: 0(5(4(1(3(2(x1)))))) -> 0(5(4(3(1(2(x1)))))) - Weak TRS: 0(1(2(3(4(x1))))) -> 0(2(1(3(4(x1))))) 0(5(1(2(4(3(x1)))))) -> 0(5(2(1(4(3(x1)))))) 0(5(2(4(1(3(x1)))))) -> 0(1(5(2(4(3(x1)))))) 0(5(3(1(2(4(x1)))))) -> 0(1(5(3(2(4(x1)))))) - Signature: {0/1} / {1/1,2/1,3/1,4/1,5/1} - Obligation: derivational complexity wrt. signature {0,1,2,3,4,5} + Applied Processor: NaturalMI {miDimension = 2, 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(0) = [1 1] x1 + [0] [0 0] [1] p(1) = [1 0] x1 + [0] [0 0] [1] p(2) = [1 1] x1 + [0] [0 0] [0] p(3) = [1 0] x1 + [0] [0 0] [0] p(4) = [1 1] x1 + [0] [0 0] [1] p(5) = [1 0] x1 + [0] [0 0] [1] Following rules are strictly oriented: 0(5(4(1(3(2(x1)))))) = [1 1] x1 + [2] [0 0] [1] > [1 1] x1 + [1] [0 0] [1] = 0(5(4(3(1(2(x1)))))) Following rules are (at-least) weakly oriented: 0(1(2(3(4(x1))))) = [1 1] x1 + [1] [0 0] [1] >= [1 1] x1 + [1] [0 0] [1] = 0(2(1(3(4(x1))))) 0(5(1(2(4(3(x1)))))) = [1 0] x1 + [2] [0 0] [1] >= [1 0] x1 + [2] [0 0] [1] = 0(5(2(1(4(3(x1)))))) 0(5(2(4(1(3(x1)))))) = [1 0] x1 + [3] [0 0] [1] >= [1 0] x1 + [2] [0 0] [1] = 0(1(5(2(4(3(x1)))))) 0(5(3(1(2(4(x1)))))) = [1 1] x1 + [2] [0 0] [1] >= [1 1] x1 + [2] [0 0] [1] = 0(1(5(3(2(4(x1)))))) * Step 4: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: 0(1(2(3(4(x1))))) -> 0(2(1(3(4(x1))))) 0(5(1(2(4(3(x1)))))) -> 0(5(2(1(4(3(x1)))))) 0(5(2(4(1(3(x1)))))) -> 0(1(5(2(4(3(x1)))))) 0(5(3(1(2(4(x1)))))) -> 0(1(5(3(2(4(x1)))))) 0(5(4(1(3(2(x1)))))) -> 0(5(4(3(1(2(x1)))))) - Signature: {0/1} / {1/1,2/1,3/1,4/1,5/1} - Obligation: derivational complexity wrt. signature {0,1,2,3,4,5} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))