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Deriv Compl Full Rewri 33144 pair #381922476
details
property
value
status
complete
benchmark
PEANO_nosorts_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n074.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.0744760036 seconds
cpu usage
91.126620673
max memory
8.3140608E7
stage attributes
key
value
output-size
8677
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: activate(X) -> X and(tt(),X) -> activate(X) plus(N,0()) -> N plus(N,s(M)) -> s(plus(N,M)) - Signature: {activate/1,and/2,plus/2} / {0/0,s/1,tt/0} - Obligation: derivational complexity wrt. signature {0,activate,and,plus,s,tt} + 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(activate) = [1] x1 + [1] p(and) = [1] x1 + [1] x2 + [1] p(plus) = [1] x1 + [1] x2 + [0] p(s) = [1] x1 + [0] p(tt) = [0] Following rules are strictly oriented: activate(X) = [1] X + [1] > [1] X + [0] = X Following rules are (at-least) weakly oriented: and(tt(),X) = [1] X + [1] >= [1] X + [1] = activate(X) plus(N,0()) = [1] N + [0] >= [1] N + [0] = N plus(N,s(M)) = [1] M + [1] N + [0] >= [1] M + [1] N + [0] = s(plus(N,M)) 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: and(tt(),X) -> activate(X) plus(N,0()) -> N plus(N,s(M)) -> s(plus(N,M)) - Weak TRS: activate(X) -> X - Signature: {activate/1,and/2,plus/2} / {0/0,s/1,tt/0} - Obligation: derivational complexity wrt. signature {0,activate,and,plus,s,tt} + 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(activate) = [1] x1 + [0] p(and) = [1] x1 + [1] x2 + [8] p(plus) = [1] x1 + [1] x2 + [0] p(s) = [1] x1 + [0] p(tt) = [0] Following rules are strictly oriented: and(tt(),X) = [1] X + [8] > [1] X + [0] = activate(X) Following rules are (at-least) weakly oriented: activate(X) = [1] X + [0] >= [1] X + [0] = X plus(N,0()) = [1] N + [0] >= [1] N + [0] = N plus(N,s(M)) = [1] M + [1] N + [0] >= [1] M + [1] N + [0] = s(plus(N,M))
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