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SRS Standard pair #516976330
details
property
value
status
complete
benchmark
random-222.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
Waldmann_19
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
11.647217989 seconds
cpu usage
40.138137568
max memory
1.75159296E9
stage attributes
key
value
output-size
6919
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 69 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 28 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) DependencyGraphProof [EQUIVALENT, 0 ms] (11) QDP (12) UsableRulesProof [EQUIVALENT, 0 ms] (13) QDP (14) QDPOrderProof [EQUIVALENT, 15 ms] (15) QDP (16) PisEmptyProof [EQUIVALENT, 0 ms] (17) YES (18) QDP (19) UsableRulesProof [EQUIVALENT, 0 ms] (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(b(a(a(x1)))) -> a(b(b(b(x1)))) b(b(a(a(x1)))) -> a(b(a(b(x1)))) b(a(a(b(x1)))) -> b(a(b(a(x1)))) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a(x_1)) = 1 + x_1 POL(b(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(b(a(a(x1)))) -> a(b(b(b(x1)))) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(b(a(a(x1)))) -> a(b(a(b(x1)))) b(a(a(b(x1)))) -> b(a(b(a(x1)))) Q is empty. ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: B(b(a(a(x1)))) -> B(a(b(x1))) B(b(a(a(x1)))) -> B(x1) B(a(a(b(x1)))) -> B(a(b(a(x1)))) B(a(a(b(x1)))) -> B(a(x1)) The TRS R consists of the following rules: b(b(a(a(x1)))) -> a(b(a(b(x1)))) b(a(a(b(x1)))) -> b(a(b(a(x1)))) Q is empty.
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