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Deriv Compl Full Rewri 33144 pair #381922794
details
property
value
status
complete
benchmark
Ex15_Luc06_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n029.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.7402989864 seconds
cpu usage
108.571603779
max memory
8.7420928E7
stage attributes
key
value
output-size
8958
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: a__f(X) -> f(X) a__f(f(a())) -> a__f(g(f(a()))) mark(a()) -> a() mark(f(X)) -> a__f(X) mark(g(X)) -> g(mark(X)) - Signature: {a__f/1,mark/1} / {a/0,f/1,g/1} - Obligation: derivational complexity wrt. signature {a,a__f,f,g,mark} + 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) = [15] p(a__f) = [1] x1 + [1] p(f) = [1] x1 + [1] p(g) = [1] x1 + [0] p(mark) = [1] x1 + [12] Following rules are strictly oriented: mark(a()) = [27] > [15] = a() mark(f(X)) = [1] X + [13] > [1] X + [1] = a__f(X) Following rules are (at-least) weakly oriented: a__f(X) = [1] X + [1] >= [1] X + [1] = f(X) a__f(f(a())) = [17] >= [17] = a__f(g(f(a()))) mark(g(X)) = [1] X + [12] >= [1] X + [12] = g(mark(X)) * Step 2: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: a__f(X) -> f(X) a__f(f(a())) -> a__f(g(f(a()))) mark(g(X)) -> g(mark(X)) - Weak TRS: mark(a()) -> a() mark(f(X)) -> a__f(X) - Signature: {a__f/1,mark/1} / {a/0,f/1,g/1} - Obligation: derivational complexity wrt. signature {a,a__f,f,g,mark} + 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) = [12] p(a__f) = [1] x1 + [1] p(f) = [1] x1 + [0] p(g) = [1] x1 + [0] p(mark) = [1] x1 + [1] Following rules are strictly oriented: a__f(X) = [1] X + [1] > [1] X + [0] = f(X) Following rules are (at-least) weakly oriented: a__f(f(a())) = [13] >= [13] = a__f(g(f(a()))) mark(a()) = [13] >= [12] = a() mark(f(X)) = [1] X + [1] >= [1] X + [1]
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