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Deriv Compl Full Rewri 33144 pair #381922171
details
property
value
status
complete
benchmark
t007.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n041.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.0200870037 seconds
cpu usage
95.370522123
max memory
4.216832E7
stage attributes
key
value
output-size
5627
starexec-result
WORST_CASE(?,O(n^1))
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^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x) -> g(x) f(a()) -> f(b()) g(b()) -> g(a()) - Signature: {f/1,g/1} / {a/0,b/0} - Obligation: derivational complexity wrt. signature {a,b,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(a) = [0] p(b) = [0] p(f) = [1] x1 + [9] p(g) = [1] x1 + [1] Following rules are strictly oriented: f(x) = [1] x + [9] > [1] x + [1] = g(x) Following rules are (at-least) weakly oriented: f(a()) = [9] >= [9] = f(b()) g(b()) = [1] >= [1] = g(a()) * Step 2: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(a()) -> f(b()) g(b()) -> g(a()) - Weak TRS: f(x) -> g(x) - Signature: {f/1,g/1} / {a/0,b/0} - Obligation: derivational complexity wrt. signature {a,b,f,g} + 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(a) = [6] [4] p(b) = [14] [2] p(f) = [1 4] x1 + [0] [0 0] [6] p(g) = [1 0] x1 + [0] [0 0] [1] Following rules are strictly oriented: g(b()) = [14] [1] > [6] [1] = g(a()) Following rules are (at-least) weakly oriented: f(x) = [1 4] x + [0] [0 0] [6] >= [1 0] x + [0] [0 0] [1] = g(x) f(a()) = [22] [6] >= [22] [6] = f(b()) * Step 3: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(a()) -> f(b()) - Weak TRS: f(x) -> g(x)
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