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TRS Stand 20472 pair #381711293
details
property
value
status
complete
benchmark
Ex3Lists.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n028.star.cs.uiowa.edu
space
Applicative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.79400014877 seconds
cpu usage
4.188222849
max memory
2.4410112E8
stage attributes
key
value
output-size
12554
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (9) QDP (10) MNOCProof [EQUIVALENT, 0 ms] (11) QDP (12) UsableRulesProof [EQUIVALENT, 0 ms] (13) QDP (14) QReductionProof [EQUIVALENT, 0 ms] (15) QDP (16) QDPSizeChangeProof [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: app(app(append, nil), l) -> l app(app(append, app(app(cons, h), t)), l) -> app(app(cons, h), app(app(append, t), l)) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, h), t)) -> app(app(cons, app(f, h)), app(app(map, f), t)) app(app(append, app(app(append, l1), l2)), l3) -> app(app(append, l1), app(app(append, l2), l3)) app(app(map, f), app(app(append, l1), l2)) -> app(app(append, app(app(map, f), l1)), app(app(map, f), l2)) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: APP(app(append, app(app(cons, h), t)), l) -> APP(app(cons, h), app(app(append, t), l)) APP(app(append, app(app(cons, h), t)), l) -> APP(app(append, t), l) APP(app(append, app(app(cons, h), t)), l) -> APP(append, t) APP(app(map, f), app(app(cons, h), t)) -> APP(app(cons, app(f, h)), app(app(map, f), t)) APP(app(map, f), app(app(cons, h), t)) -> APP(cons, app(f, h)) APP(app(map, f), app(app(cons, h), t)) -> APP(f, h) APP(app(map, f), app(app(cons, h), t)) -> APP(app(map, f), t) APP(app(append, app(app(append, l1), l2)), l3) -> APP(app(append, l1), app(app(append, l2), l3)) APP(app(append, app(app(append, l1), l2)), l3) -> APP(app(append, l2), l3) APP(app(append, app(app(append, l1), l2)), l3) -> APP(append, l2) APP(app(map, f), app(app(append, l1), l2)) -> APP(app(append, app(app(map, f), l1)), app(app(map, f), l2)) APP(app(map, f), app(app(append, l1), l2)) -> APP(append, app(app(map, f), l1)) APP(app(map, f), app(app(append, l1), l2)) -> APP(app(map, f), l1) APP(app(map, f), app(app(append, l1), l2)) -> APP(app(map, f), l2) The TRS R consists of the following rules: app(app(append, nil), l) -> l app(app(append, app(app(cons, h), t)), l) -> app(app(cons, h), app(app(append, t), l)) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, h), t)) -> app(app(cons, app(f, h)), app(app(map, f), t)) app(app(append, app(app(append, l1), l2)), l3) -> app(app(append, l1), app(app(append, l2), l3)) app(app(map, f), app(app(append, l1), l2)) -> app(app(append, app(app(map, f), l1)), app(app(map, f), l2)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 7 less nodes. ---------------------------------------- (4) Complex Obligation (AND)
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