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Deriv Compl Full Rewri 33144 pair #381922203
details
property
value
status
complete
benchmark
torpa3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n050.star.cs.uiowa.edu
space
Secret_05_SRS
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.1859278679 seconds
cpu usage
101.223549203
max memory
3.503104E8
stage attributes
key
value
output-size
15213
starexec-result
WORST_CASE(?,O(n^1))
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^1)) * Step 1: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: b(b(x1)) -> c(d(x1)) c(x1) -> g(x1) c(c(x1)) -> d(d(d(x1))) d(d(x1)) -> c(f(x1)) d(d(d(x1))) -> g(c(x1)) f(x1) -> a(g(x1)) g(x1) -> d(a(b(x1))) g(g(x1)) -> b(c(x1)) - Signature: {b/1,c/1,d/1,f/1,g/1} / {a/1} - Obligation: derivational complexity wrt. signature {a,b,c,d,f,g} + 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 + [13] p(b) = [1] x1 + [0] p(c) = [1] x1 + [0] p(d) = [1] x1 + [0] p(f) = [1] x1 + [15] p(g) = [1] x1 + [0] Following rules are strictly oriented: f(x1) = [1] x1 + [15] > [1] x1 + [13] = a(g(x1)) Following rules are (at-least) weakly oriented: b(b(x1)) = [1] x1 + [0] >= [1] x1 + [0] = c(d(x1)) c(x1) = [1] x1 + [0] >= [1] x1 + [0] = g(x1) c(c(x1)) = [1] x1 + [0] >= [1] x1 + [0] = d(d(d(x1))) d(d(x1)) = [1] x1 + [0] >= [1] x1 + [15] = c(f(x1)) d(d(d(x1))) = [1] x1 + [0] >= [1] x1 + [0] = g(c(x1)) g(x1) = [1] x1 + [0] >= [1] x1 + [13] = d(a(b(x1))) g(g(x1)) = [1] x1 + [0] >= [1] x1 + [0] = b(c(x1)) Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 2: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: b(b(x1)) -> c(d(x1)) c(x1) -> g(x1) c(c(x1)) -> d(d(d(x1))) d(d(x1)) -> c(f(x1)) d(d(d(x1))) -> g(c(x1)) g(x1) -> d(a(b(x1))) g(g(x1)) -> b(c(x1)) - Weak TRS: f(x1) -> a(g(x1)) - Signature: {b/1,c/1,d/1,f/1,g/1} / {a/1} - Obligation: derivational complexity wrt. signature {a,b,c,d,f,g} + 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 + [9]
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