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TRS Stand 20472 pair #381714050
details
property
value
status
complete
benchmark
2.42.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n097.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.80033493042 seconds
cpu usage
4.05811322
max memory
2.07450112E8
stage attributes
key
value
output-size
3567
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 52 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 10 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: flatten(nil) -> nil flatten(unit(x)) -> flatten(x) flatten(++(x, y)) -> ++(flatten(x), flatten(y)) flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y)) flatten(flatten(x)) -> flatten(x) rev(nil) -> nil rev(unit(x)) -> unit(x) rev(++(x, y)) -> ++(rev(y), rev(x)) rev(rev(x)) -> x ++(x, nil) -> x ++(nil, y) -> y ++(++(x, y), z) -> ++(x, ++(y, z)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(++(x_1, x_2)) = x_1 + x_2 POL(flatten(x_1)) = x_1 POL(nil) = 2 POL(rev(x_1)) = 2*x_1 POL(unit(x_1)) = 1 + 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: flatten(unit(x)) -> flatten(x) flatten(++(unit(x), y)) -> ++(flatten(x), flatten(y)) rev(nil) -> nil rev(unit(x)) -> unit(x) ++(x, nil) -> x ++(nil, y) -> y ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: flatten(nil) -> nil flatten(++(x, y)) -> ++(flatten(x), flatten(y)) flatten(flatten(x)) -> flatten(x) rev(++(x, y)) -> ++(rev(y), rev(x)) rev(rev(x)) -> x ++(++(x, y), z) -> ++(x, ++(y, z)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(++(x_1, x_2)) = 1 + x_1 + x_2 POL(flatten(x_1)) = 2*x_1 POL(nil) = 2 POL(rev(x_1)) = 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: flatten(nil) -> nil flatten(++(x, y)) -> ++(flatten(x), flatten(y)) rev(++(x, y)) -> ++(rev(y), rev(x))
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