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Deriv Compl Full Rewri 33144 pair #381922201
details
property
value
status
complete
benchmark
6.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n073.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.1112341881 seconds
cpu usage
83.943412345
max memory
1.75894528E8
stage attributes
key
value
output-size
6831
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: a(y,x) -> y a(y,c(b(a(0(),x),0()))) -> b(a(c(b(0(),y)),x),0()) b(x,y) -> c(a(c(y),a(0(),x))) - Signature: {a/2,b/2} / {0/0,c/1} - Obligation: derivational complexity wrt. signature {0,a,b,c} + 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(a) = [1] x1 + [1] x2 + [0] p(b) = [1] x1 + [1] x2 + [1] p(c) = [1] x1 + [0] Following rules are strictly oriented: b(x,y) = [1] x + [1] y + [1] > [1] x + [1] y + [0] = c(a(c(y),a(0(),x))) Following rules are (at-least) weakly oriented: a(y,x) = [1] x + [1] y + [0] >= [1] y + [0] = y a(y,c(b(a(0(),x),0()))) = [1] x + [1] y + [1] >= [1] x + [1] y + [2] = b(a(c(b(0(),y)),x),0()) 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: a(y,x) -> y a(y,c(b(a(0(),x),0()))) -> b(a(c(b(0(),y)),x),0()) - Weak TRS: b(x,y) -> c(a(c(y),a(0(),x))) - Signature: {a/2,b/2} / {0/0,c/1} - Obligation: derivational complexity wrt. signature {0,a,b,c} + 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(a) = [1] x1 + [1] x2 + [2] p(b) = [1] x1 + [1] x2 + [4] p(c) = [1] x1 + [0] Following rules are strictly oriented: a(y,x) = [1] x + [1] y + [2] > [1] y + [0] = y Following rules are (at-least) weakly oriented: a(y,c(b(a(0(),x),0()))) = [1] x + [1] y + [8] >= [1] x + [1] y + [10] = b(a(c(b(0(),y)),x),0()) b(x,y) = [1] x + [1] y + [4] >= [1] x + [1] y + [4] = c(a(c(y),a(0(),x))) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 3: MI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: a(y,c(b(a(0(),x),0()))) -> b(a(c(b(0(),y)),x),0()) - Weak TRS: a(y,x) -> y b(x,y) -> c(a(c(y),a(0(),x))) - Signature: {a/2,b/2} / {0/0,c/1} - Obligation: derivational complexity wrt. signature {0,a,b,c} + Applied Processor:
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