details

property	value
status	complete
benchmark	ExProp7_Luc06_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n069.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_dc
runtime (wallclock)	293.043688059 seconds
cpu usage	1142.66184064
max memory	6.17160704E8

stage attributes

key	value
output-size	29092
starexec-result	WORST_CASE(?,O(n^12))

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^12)) * Step 1: DecomposeCP WORST_CASE(?,O(n^12)) + Considered Problem: - Strict TRS: a__f(X) -> f(X) a__f(0()) -> cons(0(),f(s(0()))) a__f(s(0())) -> a__f(a__p(s(0()))) a__p(X) -> p(X) a__p(s(X)) -> mark(X) mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) mark(s(X)) -> s(mark(X)) - Signature: {a__f/1,a__p/1,mark/1} / {0/0,cons/2,f/1,p/1,s/1} - Obligation: derivational complexity wrt. signature {0,a__f,a__p,cons,f,mark,p,s} + Applied Processor: DecomposeCP {onSelectionCP_ = any strict-rules, withBoundCP_ = RelativeComp, withCP_ = NaturalMI {miDimension = 4, miDegree = 4, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Nothing}} + Details: We first use the processor NaturalMI {miDimension = 4, miDegree = 4, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Nothing} to orient following rules strictly: a__f(0()) -> cons(0(),f(s(0()))) a__f(s(0())) -> a__f(a__p(s(0()))) mark(s(X)) -> s(mark(X)) The Processor induces the complexity certificate TIME (?,O(n^4)) SPACE(?,?) Observe that weak rules from Problem (R) are non-size-increasing. Once the complexity of (R) has been assessed, it suffices to consider only rules whose complexity has not been estimated in (R) resulting in the following Problem (S). Overall the certificate is obtained by composition. Problem (S) - Strict TRS: a__f(X) -> f(X) a__p(X) -> p(X) a__p(s(X)) -> mark(X) mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) - Signature: {a__f/1,a__p/1,mark/1} / {0/0,cons/2,f/1,p/1,s/1} - Obligation: derivational complexity wrt. signature {0,a__f,a__p,cons,f,mark,p,s} ** Step 1.a:1: NaturalMI WORST_CASE(?,O(n^4)) + Considered Problem: - Strict TRS: a__f(X) -> f(X) a__f(0()) -> cons(0(),f(s(0()))) a__f(s(0())) -> a__f(a__p(s(0()))) a__p(X) -> p(X) a__p(s(X)) -> mark(X) mark(0()) -> 0() mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(f(X)) -> a__f(mark(X)) mark(p(X)) -> a__p(mark(X)) mark(s(X)) -> s(mark(X)) - Signature: {a__f/1,a__p/1,mark/1} / {0/0,cons/2,f/1,p/1,s/1} - Obligation: derivational complexity wrt. signature {0,a__f,a__p,cons,f,mark,p,s} + Applied Processor: NaturalMI {miDimension = 4, miDegree = 4, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just first alternative for decompose on 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) = [0] [0] [1] [0] p(a__f) = [1 0 1 0] [0] [0 1 0 1] x1 + [0] [0 0 0 0] [1] [0 0 0 1] [1] p(a__p) = [1 0 0 0] [0] [0 1 0 0] x1 + [0] [0 0 0 1] [0] [0 0 0 1] [0] p(cons) = [1 1 0 1] [1 0 0 0] [0] [0 1 0 1] x1 + [0 0 0 0] x2 + [0] [0 0 0 0] [0 0 0 0] [1] [0 0 0 0] [0 0 0 0] [0] p(f) = [1 0 0 0] [0] [0 1 0 1] x1 + [0] [0 0 0 0] [0] [0 0 0 1] [1] p(mark) = [1 1 0 1] [0] [0 1 0 0] x1 + [0] [0 0 0 1] [1] [0 0 0 1] [0] popout

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

job log

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actions

all output return to Deriv Compl Full Rewri 33144