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Deriv Compl Full Rewri 33144 pair #381922308
details
property
value
status
complete
benchmark
beans1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n027.star.cs.uiowa.edu
space
Zantema_06
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
294.026556015 seconds
cpu usage
735.511675404
max memory
5.86661888E8
stage attributes
key
value
output-size
13389
starexec-result
WORST_CASE(?,O(n^2))
output
/export/starexec/sandbox/solver/bin/starexec_run_tct_dc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^2)) * Step 1: WeightGap WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: 0(2(0(x1))) -> 1(0(1(x1))) 0(2(1(x1))) -> 1(0(2(x1))) 0(2(R(x1))) -> 1(0(1(R(x1)))) 1(2(0(x1))) -> 2(0(1(x1))) 1(2(1(x1))) -> 2(0(2(x1))) 1(2(R(x1))) -> 2(0(1(R(x1)))) L(2(0(x1))) -> L(1(0(1(x1)))) L(2(1(x1))) -> L(1(0(2(x1)))) - Signature: {0/1,1/1,L/1} / {2/1,R/1} - Obligation: derivational complexity wrt. signature {0,1,2,L,R} + 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) = [1] x1 + [8] p(1) = [1] x1 + [0] p(2) = [1] x1 + [9] p(L) = [1] x1 + [0] p(R) = [1] x1 + [0] Following rules are strictly oriented: 0(2(0(x1))) = [1] x1 + [25] > [1] x1 + [8] = 1(0(1(x1))) 0(2(R(x1))) = [1] x1 + [17] > [1] x1 + [8] = 1(0(1(R(x1)))) L(2(0(x1))) = [1] x1 + [17] > [1] x1 + [8] = L(1(0(1(x1)))) Following rules are (at-least) weakly oriented: 0(2(1(x1))) = [1] x1 + [17] >= [1] x1 + [17] = 1(0(2(x1))) 1(2(0(x1))) = [1] x1 + [17] >= [1] x1 + [17] = 2(0(1(x1))) 1(2(1(x1))) = [1] x1 + [9] >= [1] x1 + [26] = 2(0(2(x1))) 1(2(R(x1))) = [1] x1 + [9] >= [1] x1 + [17] = 2(0(1(R(x1)))) L(2(1(x1))) = [1] x1 + [9] >= [1] x1 + [17] = L(1(0(2(x1)))) 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: 0(2(1(x1))) -> 1(0(2(x1))) 1(2(0(x1))) -> 2(0(1(x1))) 1(2(1(x1))) -> 2(0(2(x1))) 1(2(R(x1))) -> 2(0(1(R(x1)))) L(2(1(x1))) -> L(1(0(2(x1)))) - Weak TRS: 0(2(0(x1))) -> 1(0(1(x1))) 0(2(R(x1))) -> 1(0(1(R(x1)))) L(2(0(x1))) -> L(1(0(1(x1)))) - Signature: {0/1,1/1,L/1} / {2/1,R/1} - Obligation: derivational complexity wrt. signature {0,1,2,L,R} + Applied Processor: NaturalMI {miDimension = 2, miDegree = 2, 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) = [1 0] x1 + [0] [0 0] [0] p(1) = [1 0] x1 + [0]
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