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SRS_Standard 2019-03-29 03.29 pair #432294709
details
property
value
status
complete
benchmark
random-436.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n104.star.cs.uiowa.edu
space
Waldmann_19
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
5.63585 seconds
cpu usage
16.3963
user time
15.5527
system time
0.843619
max virtual memory
1.19484952E8
max residence set size
2371880.0
stage attributes
key
value
starexec-result
YES
output
15.85/5.03 YES 16.19/5.05 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 16.19/5.05 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 16.19/5.05 16.19/5.05 16.19/5.05 Termination w.r.t. Q of the given QTRS could be proven: 16.19/5.05 16.19/5.05 (0) QTRS 16.19/5.05 (1) QTRSRRRProof [EQUIVALENT, 59 ms] 16.19/5.05 (2) QTRS 16.19/5.05 (3) DependencyPairsProof [EQUIVALENT, 25 ms] 16.19/5.05 (4) QDP 16.19/5.05 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 16.19/5.05 (6) AND 16.19/5.05 (7) QDP 16.19/5.05 (8) UsableRulesProof [EQUIVALENT, 1 ms] 16.19/5.05 (9) QDP 16.19/5.05 (10) DependencyGraphProof [EQUIVALENT, 0 ms] 16.19/5.05 (11) QDP 16.19/5.05 (12) UsableRulesProof [EQUIVALENT, 0 ms] 16.19/5.05 (13) QDP 16.19/5.05 (14) MRRProof [EQUIVALENT, 0 ms] 16.19/5.05 (15) QDP 16.19/5.05 (16) PisEmptyProof [EQUIVALENT, 0 ms] 16.19/5.05 (17) YES 16.19/5.05 (18) QDP 16.19/5.05 (19) QDPOrderProof [EQUIVALENT, 5 ms] 16.19/5.05 (20) QDP 16.19/5.05 (21) PisEmptyProof [EQUIVALENT, 0 ms] 16.19/5.05 (22) YES 16.19/5.05 16.19/5.05 16.19/5.05 ---------------------------------------- 16.19/5.05 16.19/5.05 (0) 16.19/5.05 Obligation: 16.19/5.05 Q restricted rewrite system: 16.19/5.05 The TRS R consists of the following rules: 16.19/5.05 16.19/5.05 a(b(b(a(x1)))) -> a(b(a(b(x1)))) 16.19/5.05 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 16.19/5.05 a(a(b(b(x1)))) -> b(b(a(a(x1)))) 16.19/5.05 16.19/5.05 Q is empty. 16.19/5.05 16.19/5.05 ---------------------------------------- 16.19/5.05 16.19/5.05 (1) QTRSRRRProof (EQUIVALENT) 16.19/5.05 Used ordering: 16.19/5.05 Polynomial interpretation [POLO]: 16.19/5.05 16.19/5.05 POL(a(x_1)) = 1 + x_1 16.19/5.05 POL(b(x_1)) = x_1 16.19/5.05 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 16.19/5.05 16.19/5.05 a(a(b(a(x1)))) -> a(b(b(a(x1)))) 16.19/5.05 16.19/5.05 16.19/5.05 16.19/5.05 16.19/5.05 ---------------------------------------- 16.19/5.05 16.19/5.05 (2) 16.19/5.05 Obligation: 16.19/5.05 Q restricted rewrite system: 16.19/5.05 The TRS R consists of the following rules: 16.19/5.05 16.19/5.05 a(b(b(a(x1)))) -> a(b(a(b(x1)))) 16.19/5.05 a(a(b(b(x1)))) -> b(b(a(a(x1)))) 16.19/5.05 16.19/5.05 Q is empty. 16.19/5.05 16.19/5.05 ---------------------------------------- 16.19/5.05 16.19/5.05 (3) DependencyPairsProof (EQUIVALENT) 16.19/5.05 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 16.19/5.05 ---------------------------------------- 16.19/5.05 16.19/5.05 (4) 16.19/5.05 Obligation: 16.19/5.05 Q DP problem: 16.19/5.05 The TRS P consists of the following rules: 16.19/5.05 16.19/5.05 A(b(b(a(x1)))) -> A(b(a(b(x1)))) 16.19/5.05 A(b(b(a(x1)))) -> A(b(x1)) 16.19/5.05 A(a(b(b(x1)))) -> A(a(x1)) 16.19/5.05 A(a(b(b(x1)))) -> A(x1) 16.19/5.05 16.19/5.05 The TRS R consists of the following rules: 16.19/5.05 16.19/5.05 a(b(b(a(x1)))) -> a(b(a(b(x1)))) 16.19/5.05 a(a(b(b(x1)))) -> b(b(a(a(x1)))) 16.19/5.05 16.19/5.05 Q is empty. 16.19/5.05 We have to consider all minimal (P,Q,R)-chains. 16.19/5.05 ---------------------------------------- 16.19/5.05 16.19/5.05 (5) DependencyGraphProof (EQUIVALENT) 16.19/5.05 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs. 16.19/5.05 ----------------------------------------
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