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Runti Compl Full Rewri 10127 pair #381902908
details
property
value
status
complete
benchmark
gen-1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n077.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
2.54143691063 seconds
cpu usage
7.657998668
max memory
1.46591744E8
stage attributes
key
value
output-size
15173
starexec-result
WORST_CASE(?,O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^1)) * Step 1: Sum WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: b(x,b(z,y)) -> f(b(f(f(z)),c(x,z,y))) b(y,z) -> z f(c(a(),z,x)) -> b(a(),z) - Signature: {b/2,f/1} / {a/0,c/3} - Obligation: runtime complexity wrt. defined symbols {b,f} and constructors {a,c} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DependencyPairs WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: b(x,b(z,y)) -> f(b(f(f(z)),c(x,z,y))) b(y,z) -> z f(c(a(),z,x)) -> b(a(),z) - Signature: {b/2,f/1} / {a/0,c/3} - Obligation: runtime complexity wrt. defined symbols {b,f} and constructors {a,c} + Applied Processor: DependencyPairs {dpKind_ = WIDP} + Details: We add the following weak dependency pairs: Strict DPs b#(x,b(z,y)) -> c_1(f#(b(f(f(z)),c(x,z,y)))) b#(y,z) -> c_2(z) f#(c(a(),z,x)) -> c_3(b#(a(),z)) Weak DPs and mark the set of starting terms. * Step 3: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: b#(x,b(z,y)) -> c_1(f#(b(f(f(z)),c(x,z,y)))) b#(y,z) -> c_2(z) f#(c(a(),z,x)) -> c_3(b#(a(),z)) - Strict TRS: b(x,b(z,y)) -> f(b(f(f(z)),c(x,z,y))) b(y,z) -> z f(c(a(),z,x)) -> b(a(),z) - Signature: {b/2,f/1,b#/2,f#/1} / {a/0,c/3,c_1/1,c_2/1,c_3/1} - Obligation: runtime complexity wrt. defined symbols {b#,f#} and constructors {a,c} + Applied Processor: NaturalMI {miDimension = 2, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any intersect of strict-rules and rewrite-rules} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima): The following argument positions are considered usable: uargs(b) = {1,2}, uargs(c) = {1,2,3}, uargs(f) = {1}, uargs(b#) = {2}, uargs(f#) = {1}, uargs(c_1) = {1}, uargs(c_2) = {1}, uargs(c_3) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(a) = [0] [0] p(b) = [2 0] x1 + [1 1] x2 + [0] [4 2] [1 3] [1] p(c) = [1 0] x1 + [1 1] x2 + [1 0] x3 + [0] [0 0] [0 0] [0 0] [0] p(f) = [1 0] x1 + [0] [4 0] [2] p(b#) = [2 0] x1 + [1 1] x2 + [1] [1 1] [0 2] [0] p(f#) = [1 0] x1 + [1] [0 0] [1] p(c_1) = [2 0] x1 + [0] [0 2] [0] p(c_2) = [1 0] x1 + [1] [0 2] [0] p(c_3) = [1 0] x1 + [0] [0 0] [0] Following rules are strictly oriented: b(x,b(z,y)) = [2 0] x + [2 4] y + [ 6 2] z + [1] [4 2] [4 10] [14 6] [4] > [1 0] x + [1 0] y + [ 3 1] z + [0] [4 0] [4 0] [12 4] [2] = f(b(f(f(z)),c(x,z,y)))
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