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Deriv Compl Full Rewri 33144 pair #381922337
details
property
value
status
complete
benchmark
PEANO_nosorts-noand_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n039.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.1073710918 seconds
cpu usage
76.035757995
max memory
5.8236928E7
stage attributes
key
value
output-size
11878
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: U11(tt(),M,N) -> U12(tt(),activate(M),activate(N)) U12(tt(),M,N) -> s(plus(activate(N),activate(M))) activate(X) -> X plus(N,0()) -> N plus(N,s(M)) -> U11(tt(),M,N) - Signature: {U11/3,U12/3,activate/1,plus/2} / {0/0,s/1,tt/0} - Obligation: derivational complexity wrt. signature {0,U11,U12,activate,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(U11) = [1] x1 + [1] x2 + [1] x3 + [0] p(U12) = [1] x1 + [1] x2 + [1] x3 + [0] p(activate) = [1] x1 + [0] p(plus) = [1] x1 + [1] x2 + [7] p(s) = [1] x1 + [0] p(tt) = [0] Following rules are strictly oriented: plus(N,0()) = [1] N + [7] > [1] N + [0] = N plus(N,s(M)) = [1] M + [1] N + [7] > [1] M + [1] N + [0] = U11(tt(),M,N) Following rules are (at-least) weakly oriented: U11(tt(),M,N) = [1] M + [1] N + [0] >= [1] M + [1] N + [0] = U12(tt(),activate(M),activate(N)) U12(tt(),M,N) = [1] M + [1] N + [0] >= [1] M + [1] N + [7] = s(plus(activate(N),activate(M))) activate(X) = [1] X + [0] >= [1] X + [0] = X Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 2: WeightGap WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: U11(tt(),M,N) -> U12(tt(),activate(M),activate(N)) U12(tt(),M,N) -> s(plus(activate(N),activate(M))) activate(X) -> X - Weak TRS: plus(N,0()) -> N plus(N,s(M)) -> U11(tt(),M,N) - Signature: {U11/3,U12/3,activate/1,plus/2} / {0/0,s/1,tt/0} - Obligation: derivational complexity wrt. signature {0,U11,U12,activate,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(U11) = [1] x1 + [1] x2 + [1] x3 + [0] p(U12) = [1] x1 + [1] x2 + [1] x3 + [9] p(activate) = [1] x1 + [11] p(plus) = [1] x1 + [1] x2 + [0] p(s) = [1] x1 + [0] p(tt) = [0] Following rules are strictly oriented: activate(X) = [1] X + [11] > [1] X + [0] = X Following rules are (at-least) weakly oriented: U11(tt(),M,N) = [1] M + [1] N + [0] >= [1] M + [1] N + [31] = U12(tt(),activate(M),activate(N))
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