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SRS Standard pair #487519499
details
property
value
status
complete
benchmark
z115.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n186.star.cs.uiowa.edu
space
Zantema_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.92553710938 seconds
cpu usage
8.30663627
max memory
1.097457664E9
stage attributes
key
value
output-size
3734
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 22 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 1 ms] (6) QDP (7) QDPOrderProof [EQUIVALENT, 7 ms] (8) QDP (9) DependencyGraphProof [EQUIVALENT, 0 ms] (10) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(x1)) -> d(c(x1)) a(b(x1)) -> c(c(c(x1))) b(b(x1)) -> a(c(c(x1))) c(c(x1)) -> b(x1) c(d(x1)) -> a(a(x1)) d(d(x1)) -> b(a(c(x1))) Q is empty. ---------------------------------------- (1) QTRS Reverse (EQUIVALENT) We applied the QTRS Reverse Processor [REVERSE]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(x1)) -> c(d(x1)) b(a(x1)) -> c(c(c(x1))) b(b(x1)) -> c(c(a(x1))) c(c(x1)) -> b(x1) d(c(x1)) -> a(a(x1)) d(d(x1)) -> c(a(b(x1))) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a(x_1)) = 15 + x_1 POL(b(x_1)) = 17 + x_1 POL(c(x_1)) = 9 + x_1 POL(d(x_1)) = 21 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: b(a(x1)) -> c(c(c(x1))) b(b(x1)) -> c(c(a(x1))) c(c(x1)) -> b(x1) d(d(x1)) -> c(a(b(x1))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(x1)) -> c(d(x1)) d(c(x1)) -> a(a(x1)) Q is empty. ---------------------------------------- (5) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ----------------------------------------
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