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Deriv Compl Full Rewri 33144 pair #381922076
details
property
value
status
complete
benchmark
z107.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
Zantema_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
129.366747856 seconds
cpu usage
219.537280791
max memory
5.66083584E8
stage attributes
key
value
output-size
5693
starexec-result
WORST_CASE(?,O(n^1))
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^1)) * Step 1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a(a(x1)) -> b(b(b(x1))) b(x1) -> d(d(x1)) b(b(x1)) -> c(c(c(x1))) c(c(x1)) -> d(d(d(x1))) c(d(d(x1))) -> a(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 + [39] p(b) = [1] x1 + [26] p(c) = [1] x1 + [17] p(d) = [1] x1 + [11] Following rules are strictly oriented: b(x1) = [1] x1 + [26] > [1] x1 + [22] = d(d(x1)) b(b(x1)) = [1] x1 + [52] > [1] x1 + [51] = c(c(c(x1))) c(c(x1)) = [1] x1 + [34] > [1] x1 + [33] = d(d(d(x1))) Following rules are (at-least) weakly oriented: a(a(x1)) = [1] x1 + [78] >= [1] x1 + [78] = b(b(b(x1))) c(d(d(x1))) = [1] x1 + [39] >= [1] x1 + [39] = a(x1) * Step 2: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: a(a(x1)) -> b(b(b(x1))) c(d(d(x1))) -> a(x1) - Weak TRS: b(x1) -> d(d(x1)) b(b(x1)) -> c(c(c(x1))) c(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 + [27] p(b) = [1] x1 + [18] p(c) = [1] x1 + [12] p(d) = [1] x1 + [8] Following rules are strictly oriented: c(d(d(x1))) = [1] x1 + [28] > [1] x1 + [27] = a(x1) Following rules are (at-least) weakly oriented: a(a(x1)) = [1] x1 + [54] >= [1] x1 + [54] = b(b(b(x1))) b(x1) = [1] x1 + [18] >= [1] x1 + [16] = d(d(x1)) b(b(x1)) = [1] x1 + [36] >= [1] x1 + [36] = c(c(c(x1)))
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