details

property	value
status	complete
benchmark	random-470.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n061.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.4398 seconds
cpu usage	13.9728
user time	13.302
system time	0.670791
max virtual memory	5.9611116E7
max residence set size	2064576.0

stage attributes

key	value
starexec-result	YES

output

13.04/4.24 YES 13.68/4.35 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 13.68/4.35 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 13.68/4.35 13.68/4.35 13.68/4.35 Termination w.r.t. Q of the given QTRS could be proven: 13.68/4.35 13.68/4.35 (0) QTRS 13.68/4.35 (1) FlatCCProof [EQUIVALENT, 0 ms] 13.68/4.35 (2) QTRS 13.68/4.35 (3) RootLabelingProof [EQUIVALENT, 0 ms] 13.68/4.35 (4) QTRS 13.68/4.35 (5) DependencyPairsProof [EQUIVALENT, 2 ms] 13.68/4.35 (6) QDP 13.68/4.35 (7) DependencyGraphProof [EQUIVALENT, 0 ms] 13.68/4.35 (8) AND 13.68/4.35 (9) QDP 13.68/4.35 (10) UsableRulesProof [EQUIVALENT, 3 ms] 13.68/4.35 (11) QDP 13.68/4.35 (12) QDPOrderProof [EQUIVALENT, 39 ms] 13.68/4.35 (13) QDP 13.68/4.35 (14) DependencyGraphProof [EQUIVALENT, 0 ms] 13.68/4.35 (15) TRUE 13.68/4.35 (16) QDP 13.68/4.35 (17) UsableRulesProof [EQUIVALENT, 2 ms] 13.68/4.35 (18) QDP 13.68/4.35 (19) QDPSizeChangeProof [EQUIVALENT, 1 ms] 13.68/4.35 (20) YES 13.68/4.35 13.68/4.35 13.68/4.35 ---------------------------------------- 13.68/4.35 13.68/4.35 (0) 13.68/4.35 Obligation: 13.68/4.35 Q restricted rewrite system: 13.68/4.35 The TRS R consists of the following rules: 13.68/4.35 13.68/4.35 a(b(a(a(x1)))) -> a(b(b(a(x1)))) 13.68/4.35 a(b(a(b(x1)))) -> a(b(b(a(x1)))) 13.68/4.35 b(b(a(a(x1)))) -> a(b(a(a(x1)))) 13.68/4.35 b(b(b(b(x1)))) -> a(a(a(a(x1)))) 13.68/4.35 13.68/4.35 Q is empty. 13.68/4.35 13.68/4.35 ---------------------------------------- 13.68/4.35 13.68/4.35 (1) FlatCCProof (EQUIVALENT) 13.68/4.35 We used flat context closure [ROOTLAB] 13.68/4.35 As Q is empty the flat context closure was sound AND complete. 13.68/4.35 13.68/4.35 ---------------------------------------- 13.68/4.35 13.68/4.35 (2) 13.68/4.35 Obligation: 13.68/4.35 Q restricted rewrite system: 13.68/4.35 The TRS R consists of the following rules: 13.68/4.35 13.68/4.35 a(b(a(a(x1)))) -> a(b(b(a(x1)))) 13.68/4.35 a(b(a(b(x1)))) -> a(b(b(a(x1)))) 13.68/4.35 a(b(b(a(a(x1))))) -> a(a(b(a(a(x1))))) 13.68/4.35 b(b(b(a(a(x1))))) -> b(a(b(a(a(x1))))) 13.68/4.35 a(b(b(b(b(x1))))) -> a(a(a(a(a(x1))))) 13.68/4.35 b(b(b(b(b(x1))))) -> b(a(a(a(a(x1))))) 13.68/4.35 13.68/4.35 Q is empty. 13.68/4.35 13.68/4.35 ---------------------------------------- 13.68/4.35 13.68/4.35 (3) RootLabelingProof (EQUIVALENT) 13.68/4.35 We used plain root labeling [ROOTLAB] with the following heuristic: 13.68/4.35 LabelAll: All function symbols get labeled 13.68/4.35 13.68/4.35 As Q is empty the root labeling was sound AND complete. 13.68/4.35 13.68/4.35 ---------------------------------------- 13.68/4.35 13.68/4.35 (4) 13.68/4.35 Obligation: 13.68/4.35 Q restricted rewrite system: 13.68/4.35 The TRS R consists of the following rules: 13.68/4.35 13.68/4.35 a_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1)))) 13.68/4.35 a_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) 13.68/4.35 a_{b_1}(b_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1)))) 13.68/4.35 a_{b_1}(b_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) 13.68/4.35 a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> a_{a_1}(a_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1))))) 13.68/4.35 a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> a_{a_1}(a_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1))))) 13.68/4.35 b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{a_1}(a_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1))))) 13.68/4.35 b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> b_{a_1}(a_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1))))) 13.68/4.35 a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1))))) 13.68/4.35 a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1))))) 13.68/4.35 b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))) -> b_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1))))) 13.68/4.35 b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))) -> b_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1))))) 13.68/4.35 13.68/4.35 Q is empty. 13.68/4.35 13.68/4.35 ---------------------------------------- 13.68/4.35 13.68/4.35 (5) DependencyPairsProof (EQUIVALENT) 13.68/4.35 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. popout

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