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TRS Standard pair #516967390
details
property
value
status
complete
benchmark
TypeEx5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n119.star.cs.uiowa.edu
space
Applicative_05
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.62346386909 seconds
cpu usage
6.926723443
max memory
5.37632768E8
stage attributes
key
value
output-size
5559
starexec-result
NO
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- NO 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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be disproven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 37 ms] (2) QTRS (3) AAECC Innermost [EQUIVALENT, 0 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 0 ms] (6) QDP (7) UsableRulesProof [EQUIVALENT, 0 ms] (8) QDP (9) QReductionProof [EQUIVALENT, 0 ms] (10) QDP (11) ATransformationProof [EQUIVALENT, 0 ms] (12) QDP (13) TransformationProof [EQUIVALENT, 0 ms] (14) QDP (15) TransformationProof [EQUIVALENT, 0 ms] (16) QDP (17) NonTerminationLoopProof [COMPLETE, 0 ms] (18) NO ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: ap(ap(g, x), y) -> y ap(f, x) -> ap(f, app(g, x)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(ap(x_1, x_2)) = 1 + 2*x_1 + x_2 POL(app(x_1, x_2)) = x_1 + x_2 POL(f) = 0 POL(g) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: ap(ap(g, x), y) -> y ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: ap(f, x) -> ap(f, app(g, x)) Q is empty. ---------------------------------------- (3) AAECC Innermost (EQUIVALENT) We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is none The TRS R 2 is ap(f, x) -> ap(f, app(g, x)) The signature Sigma is {ap_2} ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: ap(f, x) -> ap(f, app(g, x)) The set Q consists of the following terms: ap(f, x0) ---------------------------------------- (5) DependencyPairsProof (EQUIVALENT)
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