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Deriv Compl Full Rewri 33144 pair #381922123
details
property
value
status
complete
benchmark
jones6.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n073.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.1036629677 seconds
cpu usage
85.084348275
max memory
9.730048E7
stage attributes
key
value
output-size
6598
starexec-result
WORST_CASE(?,O(n^2))
output
/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: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(a,cons(x,k)) -> f(cons(x,a),k) f(a,empty()) -> g(a,empty()) g(cons(x,k),d) -> g(k,cons(x,d)) g(empty(),d) -> d - Signature: {f/2,g/2} / {cons/2,empty/0} - Obligation: derivational complexity wrt. signature {cons,empty,f,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(cons) = [1] x1 + [1] x2 + [2] p(empty) = [8] p(f) = [1] x1 + [1] x2 + [0] p(g) = [1] x1 + [1] x2 + [0] Following rules are strictly oriented: g(empty(),d) = [1] d + [8] > [1] d + [0] = d Following rules are (at-least) weakly oriented: f(a,cons(x,k)) = [1] a + [1] k + [1] x + [2] >= [1] a + [1] k + [1] x + [2] = f(cons(x,a),k) f(a,empty()) = [1] a + [8] >= [1] a + [8] = g(a,empty()) g(cons(x,k),d) = [1] d + [1] k + [1] x + [2] >= [1] d + [1] k + [1] x + [2] = g(k,cons(x,d)) * Step 2: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(a,cons(x,k)) -> f(cons(x,a),k) f(a,empty()) -> g(a,empty()) g(cons(x,k),d) -> g(k,cons(x,d)) - Weak TRS: g(empty(),d) -> d - Signature: {f/2,g/2} / {cons/2,empty/0} - Obligation: derivational complexity wrt. signature {cons,empty,f,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(cons) = [1] x1 + [1] x2 + [2] p(empty) = [0] p(f) = [1] x1 + [1] x2 + [1] p(g) = [1] x1 + [1] x2 + [0] Following rules are strictly oriented: f(a,empty()) = [1] a + [1] > [1] a + [0] = g(a,empty()) Following rules are (at-least) weakly oriented: f(a,cons(x,k)) = [1] a + [1] k + [1] x + [3] >= [1] a + [1] k + [1] x + [3] = f(cons(x,a),k) g(cons(x,k),d) = [1] d + [1] k + [1] x + [2] >= [1] d + [1] k + [1] x + [2] = g(k,cons(x,d)) g(empty(),d) = [1] d + [0] >= [1] d + [0] = d * Step 3: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(a,cons(x,k)) -> f(cons(x,a),k) g(cons(x,k),d) -> g(k,cons(x,d)) - Weak TRS:
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