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TRS Stand 20472 pair #381710627
details
property
value
status
complete
benchmark
010.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n026.star.cs.uiowa.edu
space
AotoYamada_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
17.2947649956 seconds
cpu usage
48.623292807
max memory
4.808245248E9
stage attributes
key
value
output-size
34463
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) ATransformationProof [EQUIVALENT, 0 ms] (13) QDP (14) QReductionProof [EQUIVALENT, 0 ms] (15) QDP (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] (17) YES (18) QDP (19) UsableRulesProof [EQUIVALENT, 1 ms] (20) QDP (21) QReductionProof [EQUIVALENT, 0 ms] (22) QDP (23) ATransformationProof [EQUIVALENT, 0 ms] (24) QDP (25) QReductionProof [EQUIVALENT, 0 ms] (26) QDP (27) QDPSizeChangeProof [EQUIVALENT, 0 ms] (28) YES (29) QDP (30) UsableRulesProof [EQUIVALENT, 1 ms] (31) QDP (32) QReductionProof [EQUIVALENT, 0 ms] (33) QDP (34) TransformationProof [EQUIVALENT, 0 ms] (35) QDP (36) TransformationProof [EQUIVALENT, 0 ms] (37) QDP (38) TransformationProof [EQUIVALENT, 0 ms] (39) QDP (40) QDPOrderProof [EQUIVALENT, 1213 ms] (41) QDP (42) UsableRulesProof [EQUIVALENT, 0 ms] (43) QDP (44) QDPSizeChangeProof [EQUIVALENT, 0 ms] (45) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(plus, 0), y) -> y app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y)) app(app(times, 0), y) -> 0 app(app(times, app(s, x)), y) -> app(app(plus, app(app(times, x), y)), y) app(app(app(curry, g), x), y) -> app(app(g, x), y) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) inc -> app(map, app(app(curry, plus), app(s, 0))) double -> app(map, app(app(curry, times), app(s, app(s, 0)))) 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(plus, 0), y) -> y app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y)) app(app(times, 0), y) -> 0 app(app(times, app(s, x)), y) -> app(app(plus, app(app(times, x), y)), y) app(app(app(curry, g), x), y) -> app(app(g, x), y) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) inc -> app(map, app(app(curry, plus), app(s, 0))) double -> app(map, app(app(curry, times), app(s, app(s, 0))))
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