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SRS Standard pair #516975736
details
property
value
status
complete
benchmark
aprove00.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n059.star.cs.uiowa.edu
space
Secret_06_SRS
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
11.0835740566 seconds
cpu usage
26.821982088
max memory
1.558278144E9
stage attributes
key
value
output-size
7901
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 15 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) MNOCProof [EQUIVALENT, 0 ms] (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) QReductionProof [EQUIVALENT, 0 ms] (16) QDP (17) QDPOrderProof [EQUIVALENT, 52 ms] (18) QDP (19) DependencyGraphProof [EQUIVALENT, 0 ms] (20) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1)))))))))) b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1)))))))))))) c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> 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: A(s(x1)) -> P(s(b(p(p(s(s(x1))))))) A(s(x1)) -> B(p(p(s(s(x1))))) A(s(x1)) -> P(p(s(s(x1)))) A(s(x1)) -> P(s(s(x1))) B(s(x1)) -> P(p(s(s(c(p(s(p(s(x1))))))))) B(s(x1)) -> P(s(s(c(p(s(p(s(x1)))))))) B(s(x1)) -> C(p(s(p(s(x1))))) B(s(x1)) -> P(s(p(s(x1)))) B(s(x1)) -> P(s(x1)) C(s(x1)) -> P(s(p(s(a(p(s(p(s(x1))))))))) C(s(x1)) -> P(s(a(p(s(p(s(x1))))))) C(s(x1)) -> A(p(s(p(s(x1))))) C(s(x1)) -> P(s(p(s(x1)))) C(s(x1)) -> P(s(x1)) P(p(s(x1))) -> P(x1) The TRS R consists of the following rules: a(s(x1)) -> s(s(s(p(s(b(p(p(s(s(x1)))))))))) b(s(x1)) -> s(s(s(p(p(s(s(c(p(s(p(s(x1)))))))))))) c(s(x1)) -> p(s(p(s(a(p(s(p(s(x1))))))))) p(p(s(x1))) -> p(x1) p(s(x1)) -> x1 Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 11 less nodes. ---------------------------------------- (4) Complex Obligation (AND) ---------------------------------------- (5)
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