details

property	value
status	complete
benchmark	Ex4_4_Luc96b_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.05338 seconds
cpu usage	4.6308
user time	4.41169
system time	0.219117
max virtual memory	1.8411988E7
max residence set size	333788.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) QDPQMonotonicMRRProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 1 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) QDPOrderProof [EQUIVALENT, 13 ms] (16) QDP (17) PisEmptyProof [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(g(X), Y) -> a__f(mark(X), f(g(X), Y)) mark(f(X1, X2)) -> a__f(mark(X1), X2) mark(g(X)) -> g(mark(X)) a__f(X1, X2) -> f(X1, X2) The set Q consists of the following terms: mark(f(x0, x1)) mark(g(x0)) a__f(x0, x1) ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: A__F(g(X), Y) -> A__F(mark(X), f(g(X), Y)) A__F(g(X), Y) -> MARK(X) MARK(f(X1, X2)) -> A__F(mark(X1), X2) MARK(f(X1, X2)) -> MARK(X1) MARK(g(X)) -> MARK(X) The TRS R consists of the following rules: a__f(g(X), Y) -> a__f(mark(X), f(g(X), Y)) mark(f(X1, X2)) -> a__f(mark(X1), X2) mark(g(X)) -> g(mark(X)) a__f(X1, X2) -> f(X1, X2) The set Q consists of the following terms: mark(f(x0, x1)) mark(g(x0)) a__f(x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) QDPQMonotonicMRRProof (EQUIVALENT) By using the Q-monotonic rule removal processor with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented such that it always occurs at a strongly monotonic position in a (P,Q,R)-chain. Strictly oriented dependency pairs: MARK(f(X1, X2)) -> A__F(mark(X1), X2) MARK(f(X1, X2)) -> MARK(X1) Used ordering: Polynomial interpretation [POLO]: POL(A__F(x_1, x_2)) = 2*x_1 POL(MARK(x_1)) = 2*x_1 POL(a__f(x_1, x_2)) = 2 + 2*x_1 POL(f(x_1, x_2)) = 2 + 2*x_1 POL(g(x_1)) = x_1 POL(mark(x_1)) = x_1 ---------------------------------------- popout

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

job log

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actions

all output return to TRS Innermost