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Deriv Compl Full Rewri 33144 pair #381921953
details
property
value
status
complete
benchmark
#3.56.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
81.0361340046 seconds
cpu usage
157.739739565
max memory
1.17497856E8
stage attributes
key
value
output-size
7047
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: f(x) -> x f(c(s(x),y)) -> f(c(x,s(y))) f(f(x)) -> f(d(f(x))) g(c(x,s(y))) -> g(c(s(x),y)) - Signature: {f/1,g/1} / {c/2,d/1,s/1} - Obligation: derivational complexity wrt. signature {c,d,f,g,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(c) = [1] x1 + [1] x2 + [8] p(d) = [1] x1 + [0] p(f) = [1] x1 + [8] p(g) = [1] x1 + [0] p(s) = [1] x1 + [10] Following rules are strictly oriented: f(x) = [1] x + [8] > [1] x + [0] = x Following rules are (at-least) weakly oriented: f(c(s(x),y)) = [1] x + [1] y + [26] >= [1] x + [1] y + [26] = f(c(x,s(y))) f(f(x)) = [1] x + [16] >= [1] x + [16] = f(d(f(x))) g(c(x,s(y))) = [1] x + [1] y + [18] >= [1] x + [1] y + [18] = g(c(s(x),y)) * Step 2: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(c(s(x),y)) -> f(c(x,s(y))) f(f(x)) -> f(d(f(x))) g(c(x,s(y))) -> g(c(s(x),y)) - Weak TRS: f(x) -> x - Signature: {f/1,g/1} / {c/2,d/1,s/1} - Obligation: derivational complexity wrt. signature {c,d,f,g,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(c) = [1 2] x1 + [1 3] x2 + [4] [0 1] [0 0] [0] p(d) = [1 0] x1 + [5] [0 0] [2] p(f) = [1 2] x1 + [0] [0 1] [6] p(g) = [1 1] x1 + [0] [0 0] [4] p(s) = [1 0] x1 + [2] [0 1] [1] Following rules are strictly oriented: f(c(s(x),y)) = [1 4] x + [1 3] y + [10] [0 1] [0 0] [7] > [1 4] x + [1 3] y + [9] [0 1] [0 0] [6] = f(c(x,s(y))) f(f(x)) = [1 4] x + [12] [0 1] [12] > [1 2] x + [9] [0 0] [8] = f(d(f(x))) Following rules are (at-least) weakly oriented: f(x) = [1 2] x + [0] [0 1] [6] >= [1 0] x + [0]
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