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Deriv Compl Full Rewri 33144 pair #381922706
details
property
value
status
complete
benchmark
z124.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
Zantema_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
294.130545855 seconds
cpu usage
860.024170068
max memory
7.22833408E8
stage attributes
key
value
output-size
41356
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: a(q1(b(x1))) -> q2(a(y(x1))) a(q2(a(x1))) -> q2(a(a(x1))) a(q2(y(x1))) -> q2(a(y(x1))) q0(a(x1)) -> x(q1(x1)) q0(y(x1)) -> y(q3(x1)) q1(a(x1)) -> a(q1(x1)) q1(y(x1)) -> y(q1(x1)) q2(x(x1)) -> x(q0(x1)) q3(bl(x1)) -> bl(q4(x1)) q3(y(x1)) -> y(q3(x1)) y(q1(b(x1))) -> q2(y(y(x1))) y(q2(a(x1))) -> q2(y(a(x1))) y(q2(y(x1))) -> q2(y(y(x1))) - Signature: {a/1,q0/1,q1/1,q2/1,q3/1,y/1} / {b/1,bl/1,q4/1,x/1} - Obligation: derivational complexity wrt. signature {a,b,bl,q0,q1,q2,q3,q4,x,y} + 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(a) = [1] x1 + [0] p(b) = [1] x1 + [2] p(bl) = [1] x1 + [8] p(q0) = [1] x1 + [3] p(q1) = [1] x1 + [0] p(q2) = [1] x1 + [0] p(q3) = [1] x1 + [0] p(q4) = [1] x1 + [0] p(x) = [1] x1 + [0] p(y) = [1] x1 + [1] Following rules are strictly oriented: a(q1(b(x1))) = [1] x1 + [2] > [1] x1 + [1] = q2(a(y(x1))) q0(a(x1)) = [1] x1 + [3] > [1] x1 + [0] = x(q1(x1)) q0(y(x1)) = [1] x1 + [4] > [1] x1 + [1] = y(q3(x1)) y(q1(b(x1))) = [1] x1 + [3] > [1] x1 + [2] = q2(y(y(x1))) Following rules are (at-least) weakly oriented: a(q2(a(x1))) = [1] x1 + [0] >= [1] x1 + [0] = q2(a(a(x1))) a(q2(y(x1))) = [1] x1 + [1] >= [1] x1 + [1] = q2(a(y(x1))) q1(a(x1)) = [1] x1 + [0] >= [1] x1 + [0] = a(q1(x1)) q1(y(x1)) = [1] x1 + [1] >= [1] x1 + [1] = y(q1(x1)) q2(x(x1)) = [1] x1 + [0] >= [1] x1 + [3] = x(q0(x1)) q3(bl(x1)) = [1] x1 + [8] >= [1] x1 + [8] = bl(q4(x1)) q3(y(x1)) = [1] x1 + [1] >= [1] x1 + [1] = y(q3(x1)) y(q2(a(x1))) = [1] x1 + [1] >= [1] x1 + [1] = q2(y(a(x1))) y(q2(y(x1))) = [1] x1 + [2] >= [1] x1 + [2]
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