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TRS Standard pair #516967310
details
property
value
status
complete
benchmark
Ex9Maps.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
Applicative_05
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
7.19733381271 seconds
cpu usage
21.930871563
max memory
1.241079808E9
stage attributes
key
value
output-size
210729
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 21 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) QDP (7) TransformationProof [EQUIVALENT, 0 ms] (8) QDP (9) TransformationProof [EQUIVALENT, 0 ms] (10) QDP (11) TransformationProof [EQUIVALENT, 0 ms] (12) QDP (13) TransformationProof [EQUIVALENT, 25 ms] (14) QDP (15) TransformationProof [EQUIVALENT, 64 ms] (16) QDP (17) TransformationProof [EQUIVALENT, 0 ms] (18) QDP (19) UsableRulesProof [EQUIVALENT, 0 ms] (20) QDP (21) TransformationProof [EQUIVALENT, 202 ms] (22) QDP (23) TransformationProof [EQUIVALENT, 404 ms] (24) QDP (25) MRRProof [EQUIVALENT, 373 ms] (26) QDP (27) PisEmptyProof [EQUIVALENT, 0 ms] (28) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(map_1, f), app(app(cons, h), t)) -> app(app(cons, app(f, h)), app(app(map_1, f), t)) app(app(app(map_2, f), c), app(app(cons, h), t)) -> app(app(cons, app(app(f, h), c)), app(app(app(map_2, f), c), t)) app(app(app(app(map_3, f), g), c), app(app(cons, h), t)) -> app(app(cons, app(app(app(f, g), h), c)), app(app(app(app(map_3, f), g), c), t)) 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(map_1, f), app(app(cons, h), t)) -> app(app(cons, app(f, h)), app(app(map_1, f), t)) app(app(app(map_2, f), c), app(app(cons, h), t)) -> app(app(cons, app(app(f, h), c)), app(app(app(map_2, f), c), t)) app(app(app(app(map_3, f), g), c), app(app(cons, h), t)) -> app(app(cons, app(app(app(f, g), h), c)), app(app(app(app(map_3, f), g), c), t)) The set Q consists of the following terms: app(app(map_1, x0), app(app(cons, x1), x2)) app(app(app(map_2, x0), x1), app(app(cons, x2), x3)) app(app(app(app(map_3, x0), g), x1), app(app(cons, x2), x3)) ---------------------------------------- (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(map_1, f), app(app(cons, h), t)) -> APP(app(cons, app(f, h)), app(app(map_1, f), t)) APP(app(map_1, f), app(app(cons, h), t)) -> APP(cons, app(f, h)) APP(app(map_1, f), app(app(cons, h), t)) -> APP(f, h) APP(app(map_1, f), app(app(cons, h), t)) -> APP(app(map_1, f), t) APP(app(app(map_2, f), c), app(app(cons, h), t)) -> APP(app(cons, app(app(f, h), c)), app(app(app(map_2, f), c), t)) APP(app(app(map_2, f), c), app(app(cons, h), t)) -> APP(cons, app(app(f, h), c)) APP(app(app(map_2, f), c), app(app(cons, h), t)) -> APP(app(f, h), c) APP(app(app(map_2, f), c), app(app(cons, h), t)) -> APP(f, h) APP(app(app(map_2, f), c), app(app(cons, h), t)) -> APP(app(app(map_2, f), c), t) APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) -> APP(app(cons, app(app(app(f, g), h), c)), app(app(app(app(map_3, f), g), c), t))
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