details

property	value
status	complete
benchmark	z024.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.30885 seconds
cpu usage	9.3792
user time	8.93787
system time	0.441326
max virtual memory	2.0870156E7
max residence set size	1468736.0

stage attributes

key	value
starexec-result	YES

output

8.83/3.17 YES 9.23/3.23 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 9.23/3.23 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 9.23/3.23 9.23/3.23 9.23/3.23 Termination w.r.t. Q of the given QTRS could be proven: 9.23/3.23 9.23/3.23 (0) QTRS 9.23/3.23 (1) RootLabelingProof [EQUIVALENT, 0 ms] 9.23/3.23 (2) QTRS 9.23/3.23 (3) DependencyPairsProof [EQUIVALENT, 2 ms] 9.23/3.23 (4) QDP 9.23/3.23 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 9.23/3.23 (6) QDP 9.23/3.23 (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] 9.23/3.23 (8) YES 9.23/3.23 9.23/3.23 9.23/3.23 ---------------------------------------- 9.23/3.23 9.23/3.23 (0) 9.23/3.23 Obligation: 9.23/3.23 Q restricted rewrite system: 9.23/3.23 The TRS R consists of the following rules: 9.23/3.23 9.23/3.23 a(b(a(x1))) -> a(a(b(b(a(a(x1)))))) 9.23/3.23 b(a(a(b(x1)))) -> b(a(b(x1))) 9.23/3.23 9.23/3.23 Q is empty. 9.23/3.23 9.23/3.23 ---------------------------------------- 9.23/3.23 9.23/3.23 (1) RootLabelingProof (EQUIVALENT) 9.23/3.23 We used plain root labeling [ROOTLAB] with the following heuristic: 9.23/3.23 LabelAll: All function symbols get labeled 9.23/3.23 9.23/3.23 As Q is empty the root labeling was sound AND complete. 9.23/3.23 9.23/3.23 ---------------------------------------- 9.23/3.23 9.23/3.23 (2) 9.23/3.23 Obligation: 9.23/3.23 Q restricted rewrite system: 9.23/3.23 The TRS R consists of the following rules: 9.23/3.23 9.23/3.23 a_{b_1}(b_{a_1}(a_{a_1}(x1))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))) 9.23/3.23 a_{b_1}(b_{a_1}(a_{b_1}(x1))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))) 9.23/3.23 b_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{a_1}(x1))) 9.23/3.23 b_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{b_1}(x1))) 9.23/3.23 9.23/3.23 Q is empty. 9.23/3.23 9.23/3.23 ---------------------------------------- 9.23/3.23 9.23/3.23 (3) DependencyPairsProof (EQUIVALENT) 9.23/3.23 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 9.23/3.23 ---------------------------------------- 9.23/3.23 9.23/3.23 (4) 9.23/3.23 Obligation: 9.23/3.23 Q DP problem: 9.23/3.23 The TRS P consists of the following rules: 9.23/3.23 9.23/3.23 A_{B_1}(b_{a_1}(a_{a_1}(x1))) -> A_{B_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1))))) 9.23/3.23 A_{B_1}(b_{a_1}(a_{a_1}(x1))) -> B_{A_1}(a_{a_1}(a_{a_1}(x1))) 9.23/3.23 A_{B_1}(b_{a_1}(a_{b_1}(x1))) -> A_{B_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1))))) 9.23/3.23 A_{B_1}(b_{a_1}(a_{b_1}(x1))) -> B_{A_1}(a_{a_1}(a_{b_1}(x1))) 9.23/3.23 B_{A_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> B_{A_1}(a_{b_1}(b_{a_1}(x1))) 9.23/3.23 B_{A_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> B_{A_1}(a_{b_1}(b_{b_1}(x1))) 9.23/3.23 9.23/3.23 The TRS R consists of the following rules: 9.23/3.23 9.23/3.23 a_{b_1}(b_{a_1}(a_{a_1}(x1))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))) 9.23/3.23 a_{b_1}(b_{a_1}(a_{b_1}(x1))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))) 9.23/3.23 b_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{a_1}(x1))) 9.23/3.23 b_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{b_1}(x1))) 9.23/3.23 9.23/3.23 Q is empty. 9.23/3.23 We have to consider all minimal (P,Q,R)-chains. 9.23/3.23 ---------------------------------------- 9.23/3.23 9.23/3.23 (5) DependencyGraphProof (EQUIVALENT) 9.23/3.23 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes. 9.23/3.23 ---------------------------------------- 9.23/3.23 9.23/3.23 (6) 9.23/3.23 Obligation: 9.23/3.23 Q DP problem: 9.23/3.23 The TRS P consists of the following rules: 9.23/3.23 9.23/3.23 B_{A_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> B_{A_1}(a_{b_1}(b_{a_1}(x1))) 9.23/3.23 9.23/3.23 The TRS R consists of the following rules: 9.23/3.23 9.23/3.23 a_{b_1}(b_{a_1}(a_{a_1}(x1))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))))) 9.23/3.23 a_{b_1}(b_{a_1}(a_{b_1}(x1))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))))) 9.23/3.23 b_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{a_1}(x1))) 9.23/3.23 b_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) -> b_{a_1}(a_{b_1}(b_{b_1}(x1))) 9.23/3.23 9.23/3.23 Q is empty. popout

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all output return to SRS_Standard 2019-03-29 03.29