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	n152.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.10749 seconds
cpu usage	4.70457
user time	4.49708
system time	0.207488
max virtual memory	1.8411964E7
max residence set size	329892.0

stage attributes

key	value
starexec-result	YES

output

4.27/2.01 YES 4.54/2.08 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 4.54/2.08 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.54/2.08 4.54/2.08 4.54/2.08 Termination w.r.t. Q of the given QTRS could be proven: 4.54/2.08 4.54/2.08 (0) QTRS 4.54/2.08 (1) DependencyPairsProof [EQUIVALENT, 0 ms] 4.54/2.08 (2) QDP 4.54/2.08 (3) QDPQMonotonicMRRProof [EQUIVALENT, 30 ms] 4.54/2.08 (4) QDP 4.54/2.08 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 4.54/2.08 (6) AND 4.54/2.08 (7) QDP 4.54/2.08 (8) UsableRulesProof [EQUIVALENT, 0 ms] 4.54/2.08 (9) QDP 4.54/2.08 (10) QReductionProof [EQUIVALENT, 0 ms] 4.54/2.08 (11) QDP 4.54/2.08 (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] 4.54/2.08 (13) YES 4.54/2.08 (14) QDP 4.54/2.08 (15) QDPOrderProof [EQUIVALENT, 0 ms] 4.54/2.08 (16) QDP 4.54/2.08 (17) PisEmptyProof [EQUIVALENT, 0 ms] 4.54/2.08 (18) YES 4.54/2.08 4.54/2.08 4.54/2.08 ---------------------------------------- 4.54/2.08 4.54/2.08 (0) 4.54/2.08 Obligation: 4.54/2.08 Q restricted rewrite system: 4.54/2.08 The TRS R consists of the following rules: 4.54/2.08 4.54/2.08 a__f(g(X), Y) -> a__f(mark(X), f(g(X), Y)) 4.54/2.08 mark(f(X1, X2)) -> a__f(mark(X1), X2) 4.54/2.08 mark(g(X)) -> g(mark(X)) 4.54/2.08 a__f(X1, X2) -> f(X1, X2) 4.54/2.08 4.54/2.08 The set Q consists of the following terms: 4.54/2.08 4.54/2.08 mark(f(x0, x1)) 4.54/2.08 mark(g(x0)) 4.54/2.08 a__f(x0, x1) 4.54/2.08 4.54/2.08 4.54/2.08 ---------------------------------------- 4.54/2.08 4.54/2.08 (1) DependencyPairsProof (EQUIVALENT) 4.54/2.08 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 4.54/2.08 ---------------------------------------- 4.54/2.08 4.54/2.08 (2) 4.54/2.08 Obligation: 4.54/2.08 Q DP problem: 4.54/2.08 The TRS P consists of the following rules: 4.54/2.08 4.54/2.08 A__F(g(X), Y) -> A__F(mark(X), f(g(X), Y)) 4.54/2.08 A__F(g(X), Y) -> MARK(X) 4.54/2.08 MARK(f(X1, X2)) -> A__F(mark(X1), X2) 4.54/2.08 MARK(f(X1, X2)) -> MARK(X1) 4.54/2.08 MARK(g(X)) -> MARK(X) 4.54/2.08 4.54/2.08 The TRS R consists of the following rules: 4.54/2.08 4.54/2.08 a__f(g(X), Y) -> a__f(mark(X), f(g(X), Y)) 4.54/2.08 mark(f(X1, X2)) -> a__f(mark(X1), X2) 4.54/2.08 mark(g(X)) -> g(mark(X)) 4.54/2.08 a__f(X1, X2) -> f(X1, X2) 4.54/2.08 4.54/2.08 The set Q consists of the following terms: 4.54/2.08 4.54/2.08 mark(f(x0, x1)) 4.54/2.08 mark(g(x0)) 4.54/2.08 a__f(x0, x1) 4.54/2.08 4.54/2.08 We have to consider all minimal (P,Q,R)-chains. 4.54/2.08 ---------------------------------------- 4.54/2.08 4.54/2.08 (3) QDPQMonotonicMRRProof (EQUIVALENT) 4.54/2.08 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. 4.54/2.08 4.54/2.08 Strictly oriented dependency pairs: 4.54/2.08 4.54/2.08 MARK(f(X1, X2)) -> A__F(mark(X1), X2) 4.54/2.08 MARK(f(X1, X2)) -> MARK(X1) 4.54/2.08 4.54/2.08 4.54/2.08 Used ordering: Polynomial interpretation [POLO]: 4.54/2.08 4.54/2.08 POL(A__F(x_1, x_2)) = 2*x_1 4.54/2.08 POL(MARK(x_1)) = 2*x_1 4.54/2.08 POL(a__f(x_1, x_2)) = 2 + 2*x_1 4.54/2.08 POL(f(x_1, x_2)) = 2 + 2*x_1 4.54/2.08 POL(g(x_1)) = x_1 4.54/2.08 POL(mark(x_1)) = x_1 4.54/2.08 4.54/2.08 4.54/2.08 ---------------------------------------- popout

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all output return to TRS_Innermost 2019-03-28 22.12