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Deriv Compl Full Rewri 33144 pair #381922307
details
property
value
status
complete
benchmark
z084.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n029.star.cs.uiowa.edu
space
Zantema_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.0358459949 seconds
cpu usage
83.51197452
max memory
2.22208E8
stage attributes
key
value
output-size
6041
starexec-result
WORST_CASE(?,O(n^2))
output
/export/starexec/sandbox2/solver/bin/starexec_run_tct_dc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^2)) * Step 1: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: a(x1) -> c(b(x1)) b(b(x1)) -> a(c(x1)) b(c(x1)) -> a(x1) c(c(c(x1))) -> b(x1) - Signature: {a/1,b/1,c/1} / {} - Obligation: derivational complexity wrt. signature {a,b,c} + 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 + [26] p(b) = [1] x1 + [18] p(c) = [1] x1 + [8] Following rules are strictly oriented: b(b(x1)) = [1] x1 + [36] > [1] x1 + [34] = a(c(x1)) c(c(c(x1))) = [1] x1 + [24] > [1] x1 + [18] = b(x1) Following rules are (at-least) weakly oriented: a(x1) = [1] x1 + [26] >= [1] x1 + [26] = c(b(x1)) b(c(x1)) = [1] x1 + [26] >= [1] x1 + [26] = a(x1) * Step 2: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: a(x1) -> c(b(x1)) b(c(x1)) -> a(x1) - Weak TRS: b(b(x1)) -> a(c(x1)) c(c(c(x1))) -> b(x1) - Signature: {a/1,b/1,c/1} / {} - Obligation: derivational complexity wrt. signature {a,b,c} + 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(a) = [1 19] x1 + [254] [0 1] [73] p(b) = [1 14] x1 + [0] [0 1] [50] p(c) = [1 5] x1 + [4] [0 1] [23] Following rules are strictly oriented: b(c(x1)) = [1 19] x1 + [326] [0 1] [73] > [1 19] x1 + [254] [0 1] [73] = a(x1) Following rules are (at-least) weakly oriented: a(x1) = [1 19] x1 + [254] [0 1] [73] >= [1 19] x1 + [254] [0 1] [73] = c(b(x1)) b(b(x1)) = [1 28] x1 + [700] [0 1] [100] >= [1 24] x1 + [695] [0 1] [96] = a(c(x1)) c(c(c(x1))) = [1 15] x1 + [357] [0 1] [69] >= [1 14] x1 + [0]
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