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SRS Standard pair #487519367
details
property
value
status
complete
benchmark
z067.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n016.star.cs.uiowa.edu
space
Zantema_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
14.1802940369 seconds
cpu usage
50.264876537
max memory
5.376782336E9
stage attributes
key
value
output-size
8955
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRS Reverse [EQUIVALENT, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 14 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) DependencyPairsProof [EQUIVALENT, 22 ms] (8) QDP (9) MRRProof [EQUIVALENT, 25 ms] (10) QDP (11) MRRProof [EQUIVALENT, 0 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) AND (15) QDP (16) UsableRulesProof [EQUIVALENT, 0 ms] (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) QDPOrderProof [EQUIVALENT, 11 ms] (22) QDP (23) PisEmptyProof [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: P(x1) -> Q(Q(p(x1))) p(p(x1)) -> q(q(x1)) p(Q(Q(x1))) -> Q(Q(p(x1))) Q(p(q(x1))) -> q(p(Q(x1))) q(q(p(x1))) -> p(q(q(x1))) q(Q(x1)) -> x1 Q(q(x1)) -> x1 p(P(x1)) -> x1 P(p(x1)) -> 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: P(x1) -> p(Q(Q(x1))) p(p(x1)) -> q(q(x1)) Q(Q(p(x1))) -> p(Q(Q(x1))) q(p(Q(x1))) -> Q(p(q(x1))) p(q(q(x1))) -> q(q(p(x1))) Q(q(x1)) -> x1 q(Q(x1)) -> x1 P(p(x1)) -> x1 p(P(x1)) -> x1 Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(P(x_1)) = 2 + x_1 POL(Q(x_1)) = 1 + x_1 POL(p(x_1)) = x_1 POL(q(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: Q(q(x1)) -> x1 q(Q(x1)) -> x1 P(p(x1)) -> x1 p(P(x1)) -> x1
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