Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Deriv Compl Full Rewri 33144 pair #381922043
details
property
value
status
complete
benchmark
#4.20a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n038.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.0376260281 seconds
cpu usage
89.161806884
max memory
7.510016E7
stage attributes
key
value
output-size
5645
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: f(f(x)) -> f(x) f(s(x)) -> f(x) g(s(0())) -> g(f(s(0()))) - 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) = [0] p(f) = [1] x1 + [0] p(g) = [1] x1 + [2] p(s) = [1] x1 + [1] Following rules are strictly oriented: f(s(x)) = [1] x + [1] > [1] x + [0] = f(x) Following rules are (at-least) weakly oriented: f(f(x)) = [1] x + [0] >= [1] x + [0] = f(x) g(s(0())) = [3] >= [3] = g(f(s(0()))) * Step 2: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(f(x)) -> f(x) g(s(0())) -> g(f(s(0()))) - Weak TRS: f(s(x)) -> f(x) - 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) = [1] p(f) = [1] x1 + [1] p(g) = [1] x1 + [0] p(s) = [1] x1 + [1] Following rules are strictly oriented: f(f(x)) = [1] x + [2] > [1] x + [1] = f(x) Following rules are (at-least) weakly oriented: f(s(x)) = [1] x + [2] >= [1] x + [1] = f(x) g(s(0())) = [2] >= [3] = g(f(s(0()))) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 3: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: g(s(0())) -> g(f(s(0()))) - Weak TRS: f(f(x)) -> f(x) f(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 = 3, miDegree = 1, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just any strict-rules} + Details:
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Deriv Compl Full Rewri 33144