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SRS Stand 10685 pair #381717810
details
property
value
status
complete
benchmark
beans7.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
Zantema_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
6.71068000793 seconds
cpu usage
18.28701132
max memory
1.79124224E9
stage attributes
key
value
output-size
7200
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 30 ms] (2) QDP (3) MRRProof [EQUIVALENT, 72 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 3 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 10 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) QDP (11) QDPOrderProof [EQUIVALENT, 37 ms] (12) QDP (13) PisEmptyProof [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: B(a(a(x1))) -> A(b(c(x1))) B(a(a(x1))) -> B(c(x1)) B(a(a(x1))) -> C(x1) C(a(x1)) -> A(c(x1)) C(a(x1)) -> C(x1) B(c(a(x1))) -> A(b(c(x1))) B(c(a(x1))) -> B(c(x1)) B(c(a(x1))) -> C(x1) C(b(x1)) -> D(x1) D(x1) -> B(a(x1)) D(x1) -> A(x1) A(d(x1)) -> D(a(x1)) A(d(x1)) -> A(x1) A(a(x1)) -> A(b(a(x1))) A(a(x1)) -> B(a(x1)) The TRS R consists of the following rules: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) MRRProof (EQUIVALENT) 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. Strictly oriented dependency pairs: B(a(a(x1))) -> B(c(x1)) B(a(a(x1))) -> C(x1) C(a(x1)) -> C(x1) B(c(a(x1))) -> B(c(x1)) B(c(a(x1))) -> C(x1) A(d(x1)) -> A(x1) A(a(x1)) -> B(a(x1))
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