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TRS Standard pair #516964820
details
property
value
status
complete
benchmark
#3.6.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
Applicative_first_order_05
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.9251229763 seconds
cpu usage
8.055629886
max memory
5.49326848E8
stage attributes
key
value
output-size
31439
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 25 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 76 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 (25) QDP (26) UsableRulesProof [EQUIVALENT, 0 ms] (27) QDP (28) ATransformationProof [EQUIVALENT, 0 ms] (29) QDP (30) QReductionProof [EQUIVALENT, 0 ms] (31) QDP (32) QDPOrderProof [EQUIVALENT, 64 ms] (33) QDP (34) PisEmptyProof [EQUIVALENT, 0 ms] (35) YES (36) QDP (37) QDPSizeChangeProof [EQUIVALENT, 0 ms] (38) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(le, 0), y) -> true app(app(le, app(s, x)), 0) -> false app(app(le, app(s, x)), app(s, y)) -> app(app(le, x), y) app(pred, app(s, x)) -> x app(app(minus, x), 0) -> x app(app(minus, x), app(s, y)) -> app(pred, app(app(minus, x), y)) app(app(gcd, 0), y) -> y app(app(gcd, app(s, x)), 0) -> app(s, x) app(app(gcd, app(s, x)), app(s, y)) -> app(app(app(if_gcd, app(app(le, y), x)), app(s, x)), app(s, y)) app(app(app(if_gcd, true), app(s, x)), app(s, y)) -> app(app(gcd, app(app(minus, x), y)), app(s, y)) app(app(app(if_gcd, false), app(s, x)), app(s, y)) -> app(app(gcd, app(app(minus, y), x)), app(s, x)) 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)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, 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(le, 0), y) -> true app(app(le, app(s, x)), 0) -> false app(app(le, app(s, x)), app(s, y)) -> app(app(le, x), y) app(pred, app(s, x)) -> x app(app(minus, x), 0) -> x app(app(minus, x), app(s, y)) -> app(pred, app(app(minus, x), y)) app(app(gcd, 0), y) -> y app(app(gcd, app(s, x)), 0) -> app(s, x)
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