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Deriv Compl Full Rewri 33144 pair #381921929
details
property
value
status
complete
benchmark
jones1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n055.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.0253520012 seconds
cpu usage
86.538301994
max memory
5.1924992E7
stage attributes
key
value
output-size
6051
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: r1(cons(x,k),a) -> r1(k,cons(x,a)) r1(empty(),a) -> a rev(ls) -> r1(ls,empty()) - Signature: {r1/2,rev/1} / {cons/2,empty/0} - Obligation: derivational complexity wrt. signature {cons,empty,r1,rev} + 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(cons) = [1] x1 + [1] x2 + [12] p(empty) = [8] p(r1) = [1] x1 + [1] x2 + [4] p(rev) = [1] x1 + [12] Following rules are strictly oriented: r1(empty(),a) = [1] a + [12] > [1] a + [0] = a Following rules are (at-least) weakly oriented: r1(cons(x,k),a) = [1] a + [1] k + [1] x + [16] >= [1] a + [1] k + [1] x + [16] = r1(k,cons(x,a)) rev(ls) = [1] ls + [12] >= [1] ls + [12] = r1(ls,empty()) * Step 2: WeightGap WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: r1(cons(x,k),a) -> r1(k,cons(x,a)) rev(ls) -> r1(ls,empty()) - Weak TRS: r1(empty(),a) -> a - Signature: {r1/2,rev/1} / {cons/2,empty/0} - Obligation: derivational complexity wrt. signature {cons,empty,r1,rev} + 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(cons) = [1] x1 + [1] x2 + [0] p(empty) = [9] p(r1) = [1] x1 + [1] x2 + [0] p(rev) = [1] x1 + [11] Following rules are strictly oriented: rev(ls) = [1] ls + [11] > [1] ls + [9] = r1(ls,empty()) Following rules are (at-least) weakly oriented: r1(cons(x,k),a) = [1] a + [1] k + [1] x + [0] >= [1] a + [1] k + [1] x + [0] = r1(k,cons(x,a)) r1(empty(),a) = [1] a + [9] >= [1] a + [0] = a 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: r1(cons(x,k),a) -> r1(k,cons(x,a)) - Weak TRS: r1(empty(),a) -> a rev(ls) -> r1(ls,empty()) - Signature: {r1/2,rev/1} / {cons/2,empty/0} - Obligation: derivational complexity wrt. signature {cons,empty,r1,rev} + Applied Processor: NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just any strict-rules} + Details:
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