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Deriv Compl Full Rewri 33144 pair #381922322
details
property
value
status
complete
benchmark
2.38.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n026.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.0410959721 seconds
cpu usage
91.225616132
max memory
3.51727616E8
stage attributes
key
value
output-size
7335
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: ++(x,nil()) -> x ++(++(x,y),z) -> ++(x,++(y,z)) ++(.(x,y),z) -> .(x,++(y,z)) ++(nil(),y) -> y - Signature: {++/2} / {./2,nil/0} - Obligation: derivational complexity wrt. signature {++,.,nil} + 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(++) = [1] x1 + [1] x2 + [2] p(.) = [1] x1 + [1] x2 + [0] p(nil) = [0] Following rules are strictly oriented: ++(x,nil()) = [1] x + [2] > [1] x + [0] = x ++(nil(),y) = [1] y + [2] > [1] y + [0] = y Following rules are (at-least) weakly oriented: ++(++(x,y),z) = [1] x + [1] y + [1] z + [4] >= [1] x + [1] y + [1] z + [4] = ++(x,++(y,z)) ++(.(x,y),z) = [1] x + [1] y + [1] z + [2] >= [1] x + [1] y + [1] z + [2] = .(x,++(y,z)) 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: ++(++(x,y),z) -> ++(x,++(y,z)) ++(.(x,y),z) -> .(x,++(y,z)) - Weak TRS: ++(x,nil()) -> x ++(nil(),y) -> y - Signature: {++/2} / {./2,nil/0} - Obligation: derivational complexity wrt. signature {++,.,nil} + 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(++) = [1 6] x1 + [1 0] x2 + [0] [0 1] [0 1] [2] p(.) = [1 0] x1 + [1 0] x2 + [1] [0 0] [0 1] [0] p(nil) = [7] [0] Following rules are strictly oriented: ++(++(x,y),z) = [1 12] x + [1 6] y + [1 0] z + [12] [0 1] [0 1] [0 1] [4] > [1 6] x + [1 6] y + [1 0] z + [0] [0 1] [0 1] [0 1] [4] = ++(x,++(y,z)) Following rules are (at-least) weakly oriented: ++(x,nil()) = [1 6] x + [7] [0 1] [2] >= [1 0] x + [0] [0 1] [0] = x ++(.(x,y),z) = [1 0] x + [1 6] y + [1 0] z + [1] [0 0] [0 1] [0 1] [2] >= [1 0] x + [1 6] y + [1 0] z + [1] [0 0] [0 1] [0 1] [2] = .(x,++(y,z)) ++(nil(),y) = [1 0] y + [7]
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