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SRS Standard pair #487520153
details
property
value
status
complete
benchmark
dup13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n124.star.cs.uiowa.edu
space
Trafo_06
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
60.4486739635 seconds
cpu usage
237.738785308
max memory
9.469476864E9
stage attributes
key
value
output-size
22592
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) RootLabelingProof [EQUIVALENT, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 42 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 35 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) QDP (9) QDPOrderProof [EQUIVALENT, 1458 ms] (10) QDP (11) QDPOrderProof [EQUIVALENT, 4027 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(a(a(a(x1)))) -> a(a(b(b(b(b(b(b(x1)))))))) b(b(a(a(x1)))) -> b(b(b(b(c(c(x1)))))) a(a(b(b(b(b(c(c(x1)))))))) -> a(a(a(a(a(a(b(b(x1)))))))) Q is empty. ---------------------------------------- (1) RootLabelingProof (EQUIVALENT) We used plain root labeling [ROOTLAB] with the following heuristic: LabelAll: All function symbols get labeled As Q is empty the root labeling was sound AND complete. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{a_1}(x1)))))))) a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(x1)))))))) a_{a_1}(a_{a_1}(a_{a_1}(a_{c_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))))) b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{a_1}(x1)))))) b_{b_1}(b_{a_1}(a_{a_1}(a_{b_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{b_1}(x1)))))) b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{c_1}(x1)))))) a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{a_1}(x1)))))))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{a_1}(x1)))))))) a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{b_1}(x1)))))))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(x1)))))))) a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{c_1}(x1)))))))) -> a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(b_{c_1}(x1)))))))) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a_{a_1}(x_1)) = x_1 POL(a_{b_1}(x_1)) = x_1 POL(a_{c_1}(x_1)) = 1 + x_1 POL(b_{a_1}(x_1)) = x_1 POL(b_{b_1}(x_1)) = x_1 POL(b_{c_1}(x_1)) = x_1 POL(c_{a_1}(x_1)) = x_1 POL(c_{b_1}(x_1)) = x_1 POL(c_{c_1}(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a_{a_1}(a_{a_1}(a_{a_1}(a_{c_1}(x1)))) -> a_{a_1}(a_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(x1)))))))) b_{b_1}(b_{a_1}(a_{a_1}(a_{c_1}(x1)))) -> b_{b_1}(b_{b_1}(b_{b_1}(b_{c_1}(c_{c_1}(c_{c_1}(x1)))))) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules:
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