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Deriv Compl Full Rewri 33144 pair #381922020
details
property
value
status
complete
benchmark
023.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n055.star.cs.uiowa.edu
space
AotoYamada_05
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.0880260468 seconds
cpu usage
91.844313821
max memory
6.752256E7
stage attributes
key
value
output-size
4542
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: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y)) app(id(),x) -> x app(plus(),0()) -> id() - Signature: {app/2} / {0/0,id/0,plus/0,s/0} - Obligation: derivational complexity wrt. signature {0,app,id,plus,s} + 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(0) = [11] p(app) = [1] x1 + [1] x2 + [0] p(id) = [8] p(plus) = [4] p(s) = [5] Following rules are strictly oriented: app(id(),x) = [1] x + [8] > [1] x + [0] = x app(plus(),0()) = [15] > [8] = id() Following rules are (at-least) weakly oriented: app(app(plus(),app(s(),x)),y) = [1] x + [1] y + [9] >= [1] x + [1] y + [9] = app(s(),app(app(plus(),x),y)) * Step 2: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y)) - Weak TRS: app(id(),x) -> x app(plus(),0()) -> id() - Signature: {app/2} / {0/0,id/0,plus/0,s/0} - Obligation: derivational complexity wrt. signature {0,app,id,plus,s} + 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(0) = [1] [2] p(app) = [1 2] x1 + [1 0] x2 + [0] [0 1] [0 1] [0] p(id) = [3] [2] p(plus) = [2] [0] p(s) = [0] [2] Following rules are strictly oriented: app(app(plus(),app(s(),x)),y) = [1 2] x + [1 0] y + [10] [0 1] [0 1] [2] > [1 2] x + [1 0] y + [6] [0 1] [0 1] [2] = app(s(),app(app(plus(),x),y)) Following rules are (at-least) weakly oriented: app(id(),x) = [1 0] x + [7] [0 1] [2] >= [1 0] x + [0] [0 1] [0] = x app(plus(),0()) = [3] [2] >= [3] [2] = id() * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS:
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