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SRS_Standard 2019-03-29 03.29 pair #432295081
details
property
value
status
complete
benchmark
01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n007.star.cs.uiowa.edu
space
Zantema_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
11.8322 seconds
cpu usage
28.0988
user time
27.0524
system time
1.04637
max virtual memory
6.1978528E7
max residence set size
3700268.0
stage attributes
key
value
starexec-result
YES
output
25.77/7.54 YES 27.62/8.00 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 27.62/8.00 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 27.62/8.00 27.62/8.00 27.62/8.00 Termination w.r.t. Q of the given QTRS could be proven: 27.62/8.00 27.62/8.00 (0) QTRS 27.62/8.00 (1) DependencyPairsProof [EQUIVALENT, 7 ms] 27.62/8.00 (2) QDP 27.62/8.00 (3) MRRProof [EQUIVALENT, 68 ms] 27.62/8.00 (4) QDP 27.62/8.00 (5) DependencyGraphProof [EQUIVALENT, 1 ms] 27.62/8.00 (6) AND 27.62/8.00 (7) QDP 27.62/8.00 (8) UsableRulesProof [EQUIVALENT, 0 ms] 27.62/8.00 (9) QDP 27.62/8.00 (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] 27.62/8.00 (11) YES 27.62/8.00 (12) QDP 27.62/8.00 (13) UsableRulesProof [EQUIVALENT, 0 ms] 27.62/8.00 (14) QDP 27.62/8.00 (15) QDPSizeChangeProof [EQUIVALENT, 0 ms] 27.62/8.00 (16) YES 27.62/8.00 27.62/8.00 27.62/8.00 ---------------------------------------- 27.62/8.00 27.62/8.00 (0) 27.62/8.00 Obligation: 27.62/8.00 Q restricted rewrite system: 27.62/8.00 The TRS R consists of the following rules: 27.62/8.00 27.62/8.00 a(b(x1)) -> b(r(x1)) 27.62/8.00 r(a(x1)) -> d(r(x1)) 27.62/8.00 r(x1) -> d(x1) 27.62/8.00 d(a(x1)) -> a(a(d(x1))) 27.62/8.00 d(x1) -> a(x1) 27.62/8.00 27.62/8.00 Q is empty. 27.62/8.00 27.62/8.00 ---------------------------------------- 27.62/8.00 27.62/8.00 (1) DependencyPairsProof (EQUIVALENT) 27.62/8.00 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 27.62/8.00 ---------------------------------------- 27.62/8.00 27.62/8.00 (2) 27.62/8.00 Obligation: 27.62/8.00 Q DP problem: 27.62/8.00 The TRS P consists of the following rules: 27.62/8.00 27.62/8.00 A(b(x1)) -> R(x1) 27.62/8.00 R(a(x1)) -> D(r(x1)) 27.62/8.00 R(a(x1)) -> R(x1) 27.62/8.00 R(x1) -> D(x1) 27.62/8.00 D(a(x1)) -> A(a(d(x1))) 27.62/8.00 D(a(x1)) -> A(d(x1)) 27.62/8.00 D(a(x1)) -> D(x1) 27.62/8.00 D(x1) -> A(x1) 27.62/8.00 27.62/8.00 The TRS R consists of the following rules: 27.62/8.00 27.62/8.00 a(b(x1)) -> b(r(x1)) 27.62/8.00 r(a(x1)) -> d(r(x1)) 27.62/8.00 r(x1) -> d(x1) 27.62/8.00 d(a(x1)) -> a(a(d(x1))) 27.62/8.00 d(x1) -> a(x1) 27.62/8.00 27.62/8.00 Q is empty. 27.62/8.00 We have to consider all minimal (P,Q,R)-chains. 27.62/8.00 ---------------------------------------- 27.62/8.00 27.62/8.00 (3) MRRProof (EQUIVALENT) 27.62/8.00 By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. 27.62/8.00 27.62/8.00 Strictly oriented dependency pairs: 27.62/8.00 27.62/8.00 A(b(x1)) -> R(x1) 27.62/8.00 27.62/8.00 27.62/8.00 Used ordering: Polynomial interpretation [POLO]: 27.62/8.00 27.62/8.00 POL(A(x_1)) = x_1 27.62/8.00 POL(D(x_1)) = 2*x_1 27.62/8.00 POL(R(x_1)) = 3*x_1 27.62/8.00 POL(a(x_1)) = x_1 27.62/8.00 POL(b(x_1)) = 1 + 3*x_1 27.62/8.00 POL(d(x_1)) = x_1 27.62/8.00 POL(r(x_1)) = x_1 27.62/8.00 27.62/8.00 27.62/8.00 ---------------------------------------- 27.62/8.00 27.62/8.00 (4) 27.62/8.00 Obligation: 27.62/8.00 Q DP problem: 27.62/8.00 The TRS P consists of the following rules: 27.62/8.00 27.62/8.00 R(a(x1)) -> D(r(x1))
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