details

property	value
status	complete
benchmark	7.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n052.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_dc
runtime (wallclock)	65.2298340797 seconds
cpu usage	145.608128212
max memory	6.6424832E8

stage attributes

key	value
output-size	7644
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: c(c(a(a(y,0()),x))) -> c(y) c(c(b(c(y),0()))) -> a(0(),c(c(a(y,0())))) c(c(c(a(x,y)))) -> b(c(c(c(c(y)))),x) - Signature: {c/1} / {0/0,a/2,b/2} - 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) = [8] p(a) = [1] x1 + [1] x2 + [0] p(b) = [1] x1 + [1] x2 + [0] p(c) = [1] x1 + [0] Following rules are strictly oriented: c(c(a(a(y,0()),x))) = [1] x + [1] y + [8] > [1] y + [0] = c(y) Following rules are (at-least) weakly oriented: c(c(b(c(y),0()))) = [1] y + [8] >= [1] y + [16] = a(0(),c(c(a(y,0())))) c(c(c(a(x,y)))) = [1] x + [1] y + [0] >= [1] x + [1] y + [0] = b(c(c(c(c(y)))),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: c(c(b(c(y),0()))) -> a(0(),c(c(a(y,0())))) c(c(c(a(x,y)))) -> b(c(c(c(c(y)))),x) - Weak TRS: c(c(a(a(y,0()),x))) -> c(y) - Signature: {c/1} / {0/0,a/2,b/2} - 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) = [7] p(a) = [1] x1 + [1] x2 + [1] p(b) = [1] x1 + [1] x2 + [0] p(c) = [1] x1 + [0] Following rules are strictly oriented: c(c(c(a(x,y)))) = [1] x + [1] y + [1] > [1] x + [1] y + [0] = b(c(c(c(c(y)))),x) Following rules are (at-least) weakly oriented: c(c(a(a(y,0()),x))) = [1] x + [1] y + [9] >= [1] y + [0] = c(y) c(c(b(c(y),0()))) = [1] y + [7] >= [1] y + [16] = a(0(),c(c(a(y,0())))) 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: c(c(b(c(y),0()))) -> a(0(),c(c(a(y,0())))) - Weak TRS: c(c(a(a(y,0()),x))) -> c(y) c(c(c(a(x,y)))) -> b(c(c(c(c(y)))),x) - Signature: {c/1} / {0/0,a/2,b/2} - Obligation: derivational complexity wrt. signature {0,a,b,c} + Applied Processor: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Deriv Compl Full Rewri 33144