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TRS Standard pair #516964795
details
property
value
status
complete
benchmark
31.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n088.star.cs.uiowa.edu
space
Applicative_first_order_05
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.78662800789 seconds
cpu usage
7.509587764
max memory
5.20957952E8
stage attributes
key
value
output-size
11138
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 50 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) QDPOrderProof [EQUIVALENT, 0 ms] (7) QDP (8) PisEmptyProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) UsableRulesProof [EQUIVALENT, 0 ms] (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(:, app(app(:, x), y)), z) -> app(app(:, x), app(app(:, y), z)) app(app(:, app(app(+, x), y)), z) -> app(app(+, app(app(:, x), z)), app(app(:, y), z)) app(app(:, z), app(app(+, x), app(f, y))) -> app(app(:, app(app(g, z), y)), app(app(+, x), a)) 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) 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(:, app(app(:, x), y)), z) -> APP(app(:, x), app(app(:, y), z)) APP(app(:, app(app(:, x), y)), z) -> APP(app(:, y), z) APP(app(:, app(app(:, x), y)), z) -> APP(:, y) APP(app(:, app(app(+, x), y)), z) -> APP(app(+, app(app(:, x), z)), app(app(:, y), z)) APP(app(:, app(app(+, x), y)), z) -> APP(+, app(app(:, x), z)) APP(app(:, app(app(+, x), y)), z) -> APP(app(:, x), z) APP(app(:, app(app(+, x), y)), z) -> APP(:, x) APP(app(:, app(app(+, x), y)), z) -> APP(app(:, y), z) APP(app(:, app(app(+, x), y)), z) -> APP(:, y) APP(app(:, z), app(app(+, x), app(f, y))) -> APP(app(:, app(app(g, z), y)), app(app(+, x), a)) APP(app(:, z), app(app(+, x), app(f, y))) -> APP(:, app(app(g, z), y)) APP(app(:, z), app(app(+, x), app(f, y))) -> APP(app(g, z), y) APP(app(:, z), app(app(+, x), app(f, y))) -> APP(g, z) APP(app(:, z), app(app(+, x), app(f, y))) -> APP(app(+, x), a) APP(app(map, f), app(app(cons, x), xs)) -> APP(app(cons, app(f, x)), app(app(map, f), xs)) APP(app(map, f), app(app(cons, x), xs)) -> APP(cons, app(f, x)) APP(app(map, f), app(app(cons, x), xs)) -> APP(f, x) APP(app(map, f), app(app(cons, x), xs)) -> APP(app(map, f), xs) APP(app(filter, f), app(app(cons, x), xs)) -> APP(app(app(app(filter2, app(f, x)), f), x), xs) APP(app(filter, f), app(app(cons, x), xs)) -> APP(app(app(filter2, app(f, x)), f), x) APP(app(filter, f), app(app(cons, x), xs)) -> APP(app(filter2, app(f, x)), f) APP(app(filter, f), app(app(cons, x), xs)) -> APP(filter2, app(f, x)) APP(app(filter, f), app(app(cons, x), xs)) -> APP(f, x) APP(app(app(app(filter2, true), f), x), xs) -> APP(app(cons, x), app(app(filter, f), xs)) APP(app(app(app(filter2, true), f), x), xs) -> APP(cons, x) APP(app(app(app(filter2, true), f), x), xs) -> APP(app(filter, f), xs) APP(app(app(app(filter2, true), f), x), xs) -> APP(filter, f) APP(app(app(app(filter2, false), f), x), xs) -> APP(app(filter, f), xs) APP(app(app(app(filter2, false), f), x), xs) -> APP(filter, f) The TRS R consists of the following rules: app(app(:, app(app(:, x), y)), z) -> app(app(:, x), app(app(:, y), z)) app(app(:, app(app(+, x), y)), z) -> app(app(+, app(app(:, x), z)), app(app(:, y), z)) app(app(:, z), app(app(+, x), app(f, y))) -> app(app(:, app(app(g, z), y)), app(app(+, x), a)) 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))
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