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Deriv Compl Full Rewri 33144 pair #381922052
details
property
value
status
complete
benchmark
#3.15.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)
30.2387039661 seconds
cpu usage
83.04628925
max memory
1.063493632E9
stage attributes
key
value
output-size
7448
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: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: average(x,s(s(s(y)))) -> s(average(s(x),y)) average(0(),0()) -> 0() average(0(),s(0())) -> 0() average(0(),s(s(0()))) -> s(0()) average(s(x),y) -> average(x,s(y)) - Signature: {average/2} / {0/0,s/1} - Obligation: derivational complexity wrt. signature {0,average,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(average) = [1] x1 + [1] x2 + [0] p(s) = [1] x1 + [7] Following rules are strictly oriented: average(x,s(s(s(y)))) = [1] x + [1] y + [21] > [1] x + [1] y + [14] = s(average(s(x),y)) average(0(),s(0())) = [7] > [0] = 0() average(0(),s(s(0()))) = [14] > [7] = s(0()) Following rules are (at-least) weakly oriented: average(0(),0()) = [0] >= [0] = 0() average(s(x),y) = [1] x + [1] y + [7] >= [1] x + [1] y + [7] = average(x,s(y)) * Step 2: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: average(0(),0()) -> 0() average(s(x),y) -> average(x,s(y)) - Weak TRS: average(x,s(s(s(y)))) -> s(average(s(x),y)) average(0(),s(0())) -> 0() average(0(),s(s(0()))) -> s(0()) - Signature: {average/2} / {0/0,s/1} - Obligation: derivational complexity wrt. signature {0,average,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(average) = [1] x1 + [1] x2 + [0] p(s) = [1] x1 + [0] Following rules are strictly oriented: average(0(),0()) = [16] > [8] = 0() Following rules are (at-least) weakly oriented: average(x,s(s(s(y)))) = [1] x + [1] y + [0] >= [1] x + [1] y + [0] = s(average(s(x),y)) average(0(),s(0())) = [16] >= [8] = 0() average(0(),s(s(0()))) = [16] >= [8] = s(0()) average(s(x),y) = [1] x + [1] y + [0] >= [1] x + [1] y + [0]
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