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TRS Stand 20472 pair #381711125
details
property
value
status
complete
benchmark
thiemann39.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n192.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.21338605881 seconds
cpu usage
5.734066806
max memory
3.91749632E8
stage attributes
key
value
output-size
17434
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 59 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) QDPApplicativeOrderProof [EQUIVALENT, 31 ms] (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: a(a(divides, 0), a(s, y)) -> true a(a(divides, a(s, x)), a(s, y)) -> a(a(a(div2, x), a(s, y)), y) a(a(a(div2, x), y), 0) -> a(a(divides, x), y) a(a(a(div2, 0), y), a(s, z)) -> false a(a(a(div2, a(s, x)), y), a(s, z)) -> a(a(a(div2, x), y), z) a(a(filter, f), nil) -> nil a(a(filter, f), a(a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) a(a(a(if, true), x), xs) -> a(a(cons, x), xs) a(a(a(if, false), x), xs) -> xs a(a(not, f), x) -> a(not2, a(f, x)) a(not2, true) -> false a(not2, false) -> true a(sieve, nil) -> nil a(sieve, a(a(cons, x), xs)) -> a(a(cons, x), a(sieve, a(a(filter, a(not, a(divides, x))), 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: a(a(divides, 0), a(s, y)) -> true a(a(divides, a(s, x)), a(s, y)) -> a(a(a(div2, x), a(s, y)), y) a(a(a(div2, x), y), 0) -> a(a(divides, x), y) a(a(a(div2, 0), y), a(s, z)) -> false a(a(a(div2, a(s, x)), y), a(s, z)) -> a(a(a(div2, x), y), z) a(a(filter, f), nil) -> nil a(a(filter, f), a(a(cons, x), xs)) -> a(a(a(if, a(f, x)), x), a(a(filter, f), xs)) a(a(a(if, true), x), xs) -> a(a(cons, x), xs) a(a(a(if, false), x), xs) -> xs a(a(not, f), x) -> a(not2, a(f, x)) a(not2, true) -> false a(not2, false) -> true a(sieve, nil) -> nil a(sieve, a(a(cons, x), xs)) -> a(a(cons, x), a(sieve, a(a(filter, a(not, a(divides, x))), xs))) The set Q consists of the following terms: a(a(divides, 0), a(s, x0)) a(a(divides, a(s, x0)), a(s, x1)) a(a(a(div2, x0), x1), 0) a(a(a(div2, 0), x0), a(s, x1)) a(a(a(div2, a(s, x0)), x1), a(s, x2)) a(a(filter, x0), nil) a(a(filter, x0), a(a(cons, x1), x2)) a(a(a(if, true), x0), x1) a(a(a(if, false), x0), x1) a(a(not, x0), x1)
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