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Deriv Compl Full Rewri 33144 pair #381922160
details
property
value
status
complete
benchmark
#4.20.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.0718579292 seconds
cpu usage
89.085228173
max memory
7.284736E7
stage attributes
key
value
output-size
3413
starexec-result
WORST_CASE(?,O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_tct_dc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^1)) * Step 1: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(f(x)) -> f(x) g(0()) -> g(f(0())) - Signature: {f/1,g/1} / {0/0} - Obligation: derivational complexity wrt. signature {0,f,g} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = NoUArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following nonconstant growth matrix-interpretation: We apply a matrix interpretation of kind triangular matrix interpretation: Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [3] p(f) = [1] x1 + [4] p(g) = [1] x1 + [0] Following rules are strictly oriented: f(f(x)) = [1] x + [8] > [1] x + [4] = f(x) Following rules are (at-least) weakly oriented: g(0()) = [3] >= [7] = g(f(0())) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 2: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: g(0()) -> g(f(0())) - Weak TRS: f(f(x)) -> f(x) - Signature: {f/1,g/1} / {0/0} - Obligation: derivational complexity wrt. signature {0,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(0) = [0] [4] p(f) = [1 4] x1 + [0] [0 0] [0] p(g) = [1 6] x1 + [1] [0 0] [1] Following rules are strictly oriented: g(0()) = [25] [1] > [17] [1] = g(f(0())) Following rules are (at-least) weakly oriented: f(f(x)) = [1 4] x + [0] [0 0] [0] >= [1 4] x + [0] [0 0] [0] = f(x) * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(f(x)) -> f(x) g(0()) -> g(f(0())) - Signature: {f/1,g/1} / {0/0} - Obligation: derivational complexity wrt. signature {0,f,g} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))
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