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TRS Stand 20472 pair #381713051
details
property
value
status
complete
benchmark
BTreeMember.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n056.star.cs.uiowa.edu
space
Applicative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.83971905708 seconds
cpu usage
4.460800863
max memory
2.65273344E8
stage attributes
key
value
output-size
12849
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 15 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 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) ATransformationProof [EQUIVALENT, 0 ms] (20) QDP (21) QReductionProof [EQUIVALENT, 0 ms] (22) QDP (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(lt, app(s, x)), app(s, y)) -> app(app(lt, x), y) app(app(lt, 0), app(s, y)) -> true app(app(lt, y), 0) -> false app(app(eq, x), x) -> true app(app(eq, app(s, x)), 0) -> false app(app(eq, 0), app(s, x)) -> false app(app(member, w), null) -> false app(app(member, w), app(app(app(fork, x), y), z)) -> app(app(app(if, app(app(lt, w), y)), app(app(member, w), x)), app(app(app(if, app(app(eq, w), y)), true), app(app(member, w), z))) 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(lt, app(s, x)), app(s, y)) -> app(app(lt, x), y) app(app(lt, 0), app(s, y)) -> true app(app(lt, y), 0) -> false app(app(eq, x), x) -> true app(app(eq, app(s, x)), 0) -> false app(app(eq, 0), app(s, x)) -> false app(app(member, w), null) -> false app(app(member, w), app(app(app(fork, x), y), z)) -> app(app(app(if, app(app(lt, w), y)), app(app(member, w), x)), app(app(app(if, app(app(eq, w), y)), true), app(app(member, w), z))) The set Q consists of the following terms: app(app(lt, app(s, x0)), app(s, x1)) app(app(lt, 0), app(s, x0)) app(app(lt, x0), 0) app(app(eq, x0), x0) app(app(eq, app(s, x0)), 0) app(app(eq, 0), app(s, x0)) app(app(member, x0), null) app(app(member, x0), app(app(app(fork, x1), 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:
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