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TRS_Innermost 2019-03-28 22.12 pair #432271390
details
property
value
status
complete
benchmark
#4.31.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n052.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
4.49108 seconds
cpu usage
14.313
user time
13.756
system time
0.557003
max virtual memory
5.9602936E7
max residence set size
1446040.0
stage attributes
key
value
starexec-result
YES
output
13.81/4.34 YES 14.05/4.41 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 14.05/4.41 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 14.05/4.41 14.05/4.41 14.05/4.41 Termination w.r.t. Q of the given QTRS could be proven: 14.05/4.41 14.05/4.41 (0) QTRS 14.05/4.41 (1) FlatCCProof [SOUND, 0 ms] 14.05/4.41 (2) QTRS 14.05/4.41 (3) RootLabelingProof [EQUIVALENT, 0 ms] 14.05/4.41 (4) QTRS 14.05/4.41 (5) QTRSRRRProof [EQUIVALENT, 151 ms] 14.05/4.41 (6) QTRS 14.05/4.41 (7) QTRSRRRProof [EQUIVALENT, 26 ms] 14.05/4.41 (8) QTRS 14.05/4.41 (9) DependencyPairsProof [EQUIVALENT, 10 ms] 14.05/4.41 (10) QDP 14.05/4.41 (11) QDPOrderProof [EQUIVALENT, 220 ms] 14.05/4.41 (12) QDP 14.05/4.41 (13) DependencyGraphProof [EQUIVALENT, 0 ms] 14.05/4.41 (14) TRUE 14.05/4.41 14.05/4.41 14.05/4.41 ---------------------------------------- 14.05/4.41 14.05/4.41 (0) 14.05/4.41 Obligation: 14.05/4.41 Q restricted rewrite system: 14.05/4.41 The TRS R consists of the following rules: 14.05/4.41 14.05/4.41 a(d(x)) -> d(c(b(a(x)))) 14.05/4.41 b(c(x)) -> c(d(a(b(x)))) 14.05/4.41 a(c(x)) -> x 14.05/4.41 b(d(x)) -> x 14.05/4.41 14.05/4.41 The set Q consists of the following terms: 14.05/4.41 14.05/4.41 a(d(x0)) 14.05/4.41 b(c(x0)) 14.05/4.41 a(c(x0)) 14.05/4.41 b(d(x0)) 14.05/4.41 14.05/4.41 14.05/4.41 ---------------------------------------- 14.05/4.41 14.05/4.41 (1) FlatCCProof (SOUND) 14.05/4.41 We used flat context closure [ROOTLAB] 14.05/4.41 14.05/4.41 ---------------------------------------- 14.05/4.41 14.05/4.41 (2) 14.05/4.41 Obligation: 14.05/4.41 Q restricted rewrite system: 14.05/4.41 The TRS R consists of the following rules: 14.05/4.41 14.05/4.41 a(a(d(x))) -> a(d(c(b(a(x))))) 14.05/4.41 d(a(d(x))) -> d(d(c(b(a(x))))) 14.05/4.41 c(a(d(x))) -> c(d(c(b(a(x))))) 14.05/4.41 b(a(d(x))) -> b(d(c(b(a(x))))) 14.05/4.41 a(b(c(x))) -> a(c(d(a(b(x))))) 14.05/4.41 d(b(c(x))) -> d(c(d(a(b(x))))) 14.05/4.41 c(b(c(x))) -> c(c(d(a(b(x))))) 14.05/4.41 b(b(c(x))) -> b(c(d(a(b(x))))) 14.05/4.41 a(a(c(x))) -> a(x) 14.05/4.41 d(a(c(x))) -> d(x) 14.05/4.41 c(a(c(x))) -> c(x) 14.05/4.41 b(a(c(x))) -> b(x) 14.05/4.41 a(b(d(x))) -> a(x) 14.05/4.41 d(b(d(x))) -> d(x) 14.05/4.41 c(b(d(x))) -> c(x) 14.05/4.41 b(b(d(x))) -> b(x) 14.05/4.41 14.05/4.41 Q is empty. 14.05/4.41 14.05/4.41 ---------------------------------------- 14.05/4.41 14.05/4.41 (3) RootLabelingProof (EQUIVALENT) 14.05/4.41 We used plain root labeling [ROOTLAB] with the following heuristic: 14.05/4.41 LabelAll: All function symbols get labeled 14.05/4.41 14.05/4.41 As Q is empty the root labeling was sound AND complete. 14.05/4.41 14.05/4.41 ---------------------------------------- 14.05/4.41 14.05/4.41 (4) 14.05/4.41 Obligation: 14.05/4.41 Q restricted rewrite system: 14.05/4.41 The TRS R consists of the following rules: 14.05/4.41 14.05/4.41 a_{a_1}(a_{d_1}(d_{a_1}(x))) -> a_{d_1}(d_{c_1}(c_{b_1}(b_{a_1}(a_{a_1}(x))))) 14.05/4.41 a_{a_1}(a_{d_1}(d_{d_1}(x))) -> a_{d_1}(d_{c_1}(c_{b_1}(b_{a_1}(a_{d_1}(x))))) 14.05/4.41 a_{a_1}(a_{d_1}(d_{c_1}(x))) -> a_{d_1}(d_{c_1}(c_{b_1}(b_{a_1}(a_{c_1}(x))))) 14.05/4.41 a_{a_1}(a_{d_1}(d_{b_1}(x))) -> a_{d_1}(d_{c_1}(c_{b_1}(b_{a_1}(a_{b_1}(x))))) 14.05/4.41 d_{a_1}(a_{d_1}(d_{a_1}(x))) -> d_{d_1}(d_{c_1}(c_{b_1}(b_{a_1}(a_{a_1}(x))))) 14.05/4.41 d_{a_1}(a_{d_1}(d_{d_1}(x))) -> d_{d_1}(d_{c_1}(c_{b_1}(b_{a_1}(a_{d_1}(x))))) 14.05/4.41 d_{a_1}(a_{d_1}(d_{c_1}(x))) -> d_{d_1}(d_{c_1}(c_{b_1}(b_{a_1}(a_{c_1}(x))))) 14.05/4.41 d_{a_1}(a_{d_1}(d_{b_1}(x))) -> d_{d_1}(d_{c_1}(c_{b_1}(b_{a_1}(a_{b_1}(x))))) 14.05/4.41 c_{a_1}(a_{d_1}(d_{a_1}(x))) -> c_{d_1}(d_{c_1}(c_{b_1}(b_{a_1}(a_{a_1}(x))))) 14.05/4.41 c_{a_1}(a_{d_1}(d_{d_1}(x))) -> c_{d_1}(d_{c_1}(c_{b_1}(b_{a_1}(a_{d_1}(x)))))
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