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Deriv Compl Full Rewri 33144 pair #381921988
details
property
value
status
complete
benchmark
#3.35.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n069.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.1054799557 seconds
cpu usage
87.948938087
max memory
1.68615936E8
stage attributes
key
value
output-size
5557
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(0()) -> s(0()) f(s(x)) -> s(s(g(x))) g(0()) -> 0() g(s(x)) -> f(x) - Signature: {f/1,g/1} / {0/0,s/1} - Obligation: derivational complexity wrt. signature {0,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(0) = [8] p(f) = [1] x1 + [4] p(g) = [1] x1 + [4] p(s) = [1] x1 + [0] Following rules are strictly oriented: f(0()) = [12] > [8] = s(0()) g(0()) = [12] > [8] = 0() Following rules are (at-least) weakly oriented: f(s(x)) = [1] x + [4] >= [1] x + [4] = s(s(g(x))) g(s(x)) = [1] x + [4] >= [1] x + [4] = f(x) * Step 2: WeightGap WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(s(x)) -> s(s(g(x))) g(s(x)) -> f(x) - Weak TRS: f(0()) -> s(0()) g(0()) -> 0() - Signature: {f/1,g/1} / {0/0,s/1} - Obligation: derivational complexity wrt. signature {0,f,g,s} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = NoUArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following nonconstant growth matrix-interpretation: We apply a matrix interpretation of kind triangular matrix interpretation: Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [0] p(f) = [1] x1 + [2] p(g) = [1] x1 + [1] p(s) = [1] x1 + [2] Following rules are strictly oriented: g(s(x)) = [1] x + [3] > [1] x + [2] = f(x) Following rules are (at-least) weakly oriented: f(0()) = [2] >= [2] = s(0()) f(s(x)) = [1] x + [4] >= [1] x + [5] = s(s(g(x))) g(0()) = [1] >= [0] = 0() Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 3: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(s(x)) -> s(s(g(x)))
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