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TRS Stand 20472 pair #381712051
details
property
value
status
complete
benchmark
TakeDropWhile.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n105.star.cs.uiowa.edu
space
Applicative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.82683682442 seconds
cpu usage
4.188300565
max memory
2.11898368E8
stage attributes
key
value
output-size
5803
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) UsableRulesProof [EQUIVALENT, 0 ms] (6) QDP (7) QDPSizeChangeProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(app(if, true), x), y) -> x app(app(app(if, true), x), y) -> y app(app(takeWhile, p), nil) -> nil app(app(takeWhile, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(takeWhile, p), xs))), nil) app(app(dropWhile, p), nil) -> nil app(app(dropWhile, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(dropWhile, p), xs)), app(app(cons, x), xs)) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: APP(app(takeWhile, p), app(app(cons, x), xs)) -> APP(app(app(if, app(p, x)), app(app(cons, x), app(app(takeWhile, p), xs))), nil) APP(app(takeWhile, p), app(app(cons, x), xs)) -> APP(app(if, app(p, x)), app(app(cons, x), app(app(takeWhile, p), xs))) APP(app(takeWhile, p), app(app(cons, x), xs)) -> APP(if, app(p, x)) APP(app(takeWhile, p), app(app(cons, x), xs)) -> APP(p, x) APP(app(takeWhile, p), app(app(cons, x), xs)) -> APP(app(cons, x), app(app(takeWhile, p), xs)) APP(app(takeWhile, p), app(app(cons, x), xs)) -> APP(app(takeWhile, p), xs) APP(app(dropWhile, p), app(app(cons, x), xs)) -> APP(app(app(if, app(p, x)), app(app(dropWhile, p), xs)), app(app(cons, x), xs)) APP(app(dropWhile, p), app(app(cons, x), xs)) -> APP(app(if, app(p, x)), app(app(dropWhile, p), xs)) APP(app(dropWhile, p), app(app(cons, x), xs)) -> APP(if, app(p, x)) APP(app(dropWhile, p), app(app(cons, x), xs)) -> APP(p, x) APP(app(dropWhile, p), app(app(cons, x), xs)) -> APP(app(dropWhile, p), xs) The TRS R consists of the following rules: app(app(app(if, true), x), y) -> x app(app(app(if, true), x), y) -> y app(app(takeWhile, p), nil) -> nil app(app(takeWhile, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(takeWhile, p), xs))), nil) app(app(dropWhile, p), nil) -> nil app(app(dropWhile, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(dropWhile, p), xs)), app(app(cons, x), xs)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 7 less nodes. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: APP(app(takeWhile, p), app(app(cons, x), xs)) -> APP(app(takeWhile, p), xs) APP(app(takeWhile, p), app(app(cons, x), xs)) -> APP(p, x) APP(app(dropWhile, p), app(app(cons, x), xs)) -> APP(p, x) APP(app(dropWhile, p), app(app(cons, x), xs)) -> APP(app(dropWhile, p), xs) The TRS R consists of the following rules: app(app(app(if, true), x), y) -> x app(app(app(if, true), x), y) -> y app(app(takeWhile, p), nil) -> nil app(app(takeWhile, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(cons, x), app(app(takeWhile, p), xs))), nil) app(app(dropWhile, p), nil) -> nil app(app(dropWhile, p), app(app(cons, x), xs)) -> app(app(app(if, app(p, x)), app(app(dropWhile, p), xs)), app(app(cons, x), xs)) Q is empty.
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