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SRS_Standard 2019-03-29 03.29 pair #432295009
details
property
value
status
complete
benchmark
random-488.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n122.star.cs.uiowa.edu
space
Waldmann_19
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.76548 seconds
cpu usage
10.6882
user time
10.068
system time
0.620223
max virtual memory
7.9170784E7
max residence set size
1722328.0
stage attributes
key
value
starexec-result
YES
output
10.24/3.64 YES 10.39/3.71 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 10.39/3.71 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.39/3.71 10.39/3.71 10.39/3.71 Termination w.r.t. Q of the given QTRS could be proven: 10.39/3.71 10.39/3.71 (0) QTRS 10.39/3.71 (1) FlatCCProof [EQUIVALENT, 0 ms] 10.39/3.71 (2) QTRS 10.39/3.71 (3) RootLabelingProof [EQUIVALENT, 0 ms] 10.39/3.71 (4) QTRS 10.39/3.71 (5) QTRSRRRProof [EQUIVALENT, 25 ms] 10.39/3.71 (6) QTRS 10.39/3.71 (7) DependencyPairsProof [EQUIVALENT, 0 ms] 10.39/3.71 (8) QDP 10.39/3.71 (9) DependencyGraphProof [EQUIVALENT, 0 ms] 10.39/3.71 (10) QDP 10.39/3.71 (11) QDPOrderProof [EQUIVALENT, 5 ms] 10.39/3.71 (12) QDP 10.39/3.71 (13) PisEmptyProof [EQUIVALENT, 0 ms] 10.39/3.71 (14) YES 10.39/3.71 10.39/3.71 10.39/3.71 ---------------------------------------- 10.39/3.71 10.39/3.71 (0) 10.39/3.71 Obligation: 10.39/3.71 Q restricted rewrite system: 10.39/3.71 The TRS R consists of the following rules: 10.39/3.71 10.39/3.71 b(a(a(a(x1)))) -> a(b(b(b(x1)))) 10.39/3.71 b(a(a(a(x1)))) -> b(b(b(a(x1)))) 10.39/3.71 a(b(b(a(x1)))) -> a(a(a(a(x1)))) 10.39/3.71 10.39/3.71 Q is empty. 10.39/3.71 10.39/3.71 ---------------------------------------- 10.39/3.71 10.39/3.71 (1) FlatCCProof (EQUIVALENT) 10.39/3.71 We used flat context closure [ROOTLAB] 10.39/3.71 As Q is empty the flat context closure was sound AND complete. 10.39/3.71 10.39/3.71 ---------------------------------------- 10.39/3.71 10.39/3.71 (2) 10.39/3.71 Obligation: 10.39/3.71 Q restricted rewrite system: 10.39/3.71 The TRS R consists of the following rules: 10.39/3.71 10.39/3.71 b(a(a(a(x1)))) -> b(b(b(a(x1)))) 10.39/3.71 a(b(b(a(x1)))) -> a(a(a(a(x1)))) 10.39/3.71 b(b(a(a(a(x1))))) -> b(a(b(b(b(x1))))) 10.39/3.71 a(b(a(a(a(x1))))) -> a(a(b(b(b(x1))))) 10.39/3.71 10.39/3.71 Q is empty. 10.39/3.71 10.39/3.71 ---------------------------------------- 10.39/3.71 10.39/3.71 (3) RootLabelingProof (EQUIVALENT) 10.39/3.71 We used plain root labeling [ROOTLAB] with the following heuristic: 10.39/3.71 LabelAll: All function symbols get labeled 10.39/3.71 10.39/3.71 As Q is empty the root labeling was sound AND complete. 10.39/3.71 10.39/3.71 ---------------------------------------- 10.39/3.71 10.39/3.71 (4) 10.39/3.71 Obligation: 10.39/3.71 Q restricted rewrite system: 10.39/3.71 The TRS R consists of the following rules: 10.39/3.71 10.39/3.71 b_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) 10.39/3.71 b_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1)))) 10.39/3.71 a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1)))) 10.39/3.71 a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1)))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1)))) 10.39/3.71 b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))) 10.39/3.71 b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))) 10.39/3.71 a_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))) 10.39/3.71 a_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1))))) 10.39/3.71 10.39/3.71 Q is empty. 10.39/3.71 10.39/3.71 ---------------------------------------- 10.39/3.71 10.39/3.71 (5) QTRSRRRProof (EQUIVALENT) 10.39/3.71 Used ordering: 10.39/3.71 Polynomial interpretation [POLO]: 10.39/3.71 10.39/3.71 POL(a_{a_1}(x_1)) = 1 + x_1 10.39/3.71 POL(a_{b_1}(x_1)) = 2 + x_1 10.39/3.71 POL(b_{a_1}(x_1)) = 1 + x_1 10.39/3.71 POL(b_{b_1}(x_1)) = x_1 10.39/3.71 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 10.39/3.71 10.39/3.71 b_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) 10.39/3.71 b_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1)))) 10.39/3.71 b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> b_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))) 10.39/3.71 a_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1))))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1))))) 10.39/3.71 a_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1))))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))))
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