Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Standard pair #516966480
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
n168.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.24401092529 seconds
cpu usage
5.922092597
max memory
4.71502848E8
stage attributes
key
value
output-size
3560
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 99 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 16 ms] (4) QTRS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))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Standard