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Deriv Compl Full Rewri 33144 pair #381921920
details
property
value
status
complete
benchmark
t011.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n037.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.1137189865 seconds
cpu usage
102.097203267
max memory
2.38628864E8
stage attributes
key
value
output-size
3628
starexec-result
WORST_CASE(?,O(n^2))
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^2)) * Step 1: WeightGap WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: g(f(x),y) -> f(h(x,y)) h(x,y) -> g(x,f(y)) - Signature: {g/2,h/2} / {f/1} - Obligation: derivational complexity wrt. signature {f,g,h} + 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(f) = [1] x1 + [0] p(g) = [1] x1 + [1] x2 + [0] p(h) = [1] x1 + [1] x2 + [5] Following rules are strictly oriented: h(x,y) = [1] x + [1] y + [5] > [1] x + [1] y + [0] = g(x,f(y)) Following rules are (at-least) weakly oriented: g(f(x),y) = [1] x + [1] y + [0] >= [1] x + [1] y + [5] = f(h(x,y)) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 2: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: g(f(x),y) -> f(h(x,y)) - Weak TRS: h(x,y) -> g(x,f(y)) - Signature: {g/2,h/2} / {f/1} - Obligation: derivational complexity wrt. signature {f,g,h} + Applied Processor: NaturalMI {miDimension = 2, miDegree = 2, 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(f) = [1 0] x1 + [0] [0 1] [1] p(g) = [1 9] x1 + [1 6] x2 + [4] [0 1] [0 0] [0] p(h) = [1 9] x1 + [1 6] x2 + [10] [0 1] [0 0] [0] Following rules are strictly oriented: g(f(x),y) = [1 9] x + [1 6] y + [13] [0 1] [0 0] [1] > [1 9] x + [1 6] y + [10] [0 1] [0 0] [1] = f(h(x,y)) Following rules are (at-least) weakly oriented: h(x,y) = [1 9] x + [1 6] y + [10] [0 1] [0 0] [0] >= [1 9] x + [1 6] y + [10] [0 1] [0 0] [0] = g(x,f(y)) * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: g(f(x),y) -> f(h(x,y)) h(x,y) -> g(x,f(y)) - Signature: {g/2,h/2} / {f/1} - Obligation: derivational complexity wrt. signature {f,g,h} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^2))
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