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Deriv Compl Full Rewri 33144 pair #381922013
details
property
value
status
complete
benchmark
z106.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n047.star.cs.uiowa.edu
space
Zantema_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.1273889542 seconds
cpu usage
97.303654097
max memory
4.1046016E8
stage attributes
key
value
output-size
6323
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: a(a(x1)) -> b(b(b(x1))) b(x1) -> c(c(d(x1))) b(c(x1)) -> c(b(x1)) b(c(d(x1))) -> a(x1) c(x1) -> d(d(d(x1))) - Signature: {a/1,b/1,c/1} / {d/1} - Obligation: derivational complexity wrt. signature {a,b,c,d} + 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) = [1] x1 + [220] p(b) = [1] x1 + [144] p(c) = [1] x1 + [64] p(d) = [1] x1 + [16] Following rules are strictly oriented: a(a(x1)) = [1] x1 + [440] > [1] x1 + [432] = b(b(b(x1))) b(c(d(x1))) = [1] x1 + [224] > [1] x1 + [220] = a(x1) c(x1) = [1] x1 + [64] > [1] x1 + [48] = d(d(d(x1))) Following rules are (at-least) weakly oriented: b(x1) = [1] x1 + [144] >= [1] x1 + [144] = c(c(d(x1))) b(c(x1)) = [1] x1 + [208] >= [1] x1 + [208] = c(b(x1)) * Step 2: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: b(x1) -> c(c(d(x1))) b(c(x1)) -> c(b(x1)) - Weak TRS: a(a(x1)) -> b(b(b(x1))) b(c(d(x1))) -> a(x1) c(x1) -> d(d(d(x1))) - Signature: {a/1,b/1,c/1} / {d/1} - Obligation: derivational complexity wrt. signature {a,b,c,d} + 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) = [1] x1 + [48] p(b) = [1] x1 + [32] p(c) = [1] x1 + [14] p(d) = [1] x1 + [2] Following rules are strictly oriented: b(x1) = [1] x1 + [32] > [1] x1 + [30] = c(c(d(x1))) Following rules are (at-least) weakly oriented: a(a(x1)) = [1] x1 + [96] >= [1] x1 + [96] = b(b(b(x1))) b(c(x1)) = [1] x1 + [46] >= [1] x1 + [46] = c(b(x1)) b(c(d(x1))) = [1] x1 + [48] >= [1] x1 + [48] = a(x1)
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