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TRS Standard pair #516965000
details
property
value
status
complete
benchmark
013.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n094.star.cs.uiowa.edu
space
AotoYamada_05
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.32018089294 seconds
cpu usage
6.146291139
max memory
4.75959296E8
stage attributes
key
value
output-size
11600
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 2 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) ATransformationProof [EQUIVALENT, 0 ms] (11) QDP (12) QReductionProof [EQUIVALENT, 0 ms] (13) QDP (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(append, nil), ys) -> ys app(app(append, app(app(cons, x), xs)), ys) -> app(app(cons, x), app(app(append, xs), ys)) app(app(flatwith, f), app(leaf, x)) -> app(app(cons, app(f, x)), nil) app(app(flatwith, f), app(node, xs)) -> app(app(flatwithsub, f), xs) app(app(flatwithsub, f), nil) -> nil app(app(flatwithsub, f), app(app(cons, x), xs)) -> app(app(append, app(app(flatwith, f), x)), app(app(flatwithsub, f), xs)) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(append, nil), ys) -> ys app(app(append, app(app(cons, x), xs)), ys) -> app(app(cons, x), app(app(append, xs), ys)) app(app(flatwith, f), app(leaf, x)) -> app(app(cons, app(f, x)), nil) app(app(flatwith, f), app(node, xs)) -> app(app(flatwithsub, f), xs) app(app(flatwithsub, f), nil) -> nil app(app(flatwithsub, f), app(app(cons, x), xs)) -> app(app(append, app(app(flatwith, f), x)), app(app(flatwithsub, f), xs)) The set Q consists of the following terms: app(app(append, nil), x0) app(app(append, app(app(cons, x0), x1)), x2) app(app(flatwith, x0), app(leaf, x1)) app(app(flatwith, x0), app(node, x1)) app(app(flatwithsub, x0), nil) app(app(flatwithsub, x0), app(app(cons, x1), x2)) ---------------------------------------- (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: APP(app(append, app(app(cons, x), xs)), ys) -> APP(app(cons, x), app(app(append, xs), ys)) APP(app(append, app(app(cons, x), xs)), ys) -> APP(app(append, xs), ys) APP(app(append, app(app(cons, x), xs)), ys) -> APP(append, xs) APP(app(flatwith, f), app(leaf, x)) -> APP(app(cons, app(f, x)), nil) APP(app(flatwith, f), app(leaf, x)) -> APP(cons, app(f, x)) APP(app(flatwith, f), app(leaf, x)) -> APP(f, x) APP(app(flatwith, f), app(node, xs)) -> APP(app(flatwithsub, f), xs) APP(app(flatwith, f), app(node, xs)) -> APP(flatwithsub, f) APP(app(flatwithsub, f), app(app(cons, x), xs)) -> APP(app(append, app(app(flatwith, f), x)), app(app(flatwithsub, f), xs))
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