Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Deriv Compl Full Rewri 33144 pair #381922168
details
property
value
status
complete
benchmark
#3.7.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n052.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.1168520451 seconds
cpu usage
76.280915437
max memory
5.9097088E7
stage attributes
key
value
output-size
6137
starexec-result
WORST_CASE(?,O(n^2))
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^2)) * Step 1: WeightGap WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: half(0()) -> 0() half(s(s(x))) -> s(half(x)) log(s(0())) -> 0() log(s(s(x))) -> s(log(s(half(x)))) - Signature: {half/1,log/1} / {0/0,s/1} - Obligation: derivational complexity wrt. signature {0,half,log,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) = [7] p(half) = [1] x1 + [11] p(log) = [1] x1 + [4] p(s) = [1] x1 + [0] Following rules are strictly oriented: half(0()) = [18] > [7] = 0() log(s(0())) = [11] > [7] = 0() Following rules are (at-least) weakly oriented: half(s(s(x))) = [1] x + [11] >= [1] x + [11] = s(half(x)) log(s(s(x))) = [1] x + [4] >= [1] x + [15] = s(log(s(half(x)))) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 2: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: half(s(s(x))) -> s(half(x)) log(s(s(x))) -> s(log(s(half(x)))) - Weak TRS: half(0()) -> 0() log(s(0())) -> 0() - Signature: {half/1,log/1} / {0/0,s/1} - Obligation: derivational complexity wrt. signature {0,half,log,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) = [2] p(half) = [1] x1 + [0] p(log) = [1] x1 + [0] p(s) = [1] x1 + [8] Following rules are strictly oriented: half(s(s(x))) = [1] x + [16] > [1] x + [8] = s(half(x)) Following rules are (at-least) weakly oriented: half(0()) = [2] >= [2] = 0() log(s(0())) = [10] >= [2] = 0() log(s(s(x))) = [1] x + [16] >= [1] x + [16] = s(log(s(half(x)))) * Step 3: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: log(s(s(x))) -> s(log(s(half(x))))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Deriv Compl Full Rewri 33144