Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Standard pair #487072388
details
property
value
status
complete
benchmark
12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n174.star.cs.uiowa.edu
space
Applicative_first_order_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.92415 seconds
cpu usage
4.64194
user time
4.45188
system time
0.19006
max virtual memory
1.8409712E7
max residence set size
288812.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 2 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) ATransformationProof [EQUIVALENT, 0 ms] (9) QDP (10) QDPSizeChangeProof [EQUIVALENT, 0 ms] (11) YES (12) QDP (13) UsableRulesProof [EQUIVALENT, 0 ms] (14) QDP (15) ATransformationProof [EQUIVALENT, 0 ms] (16) QDP (17) QDPSizeChangeProof [EQUIVALENT, 0 ms] (18) YES (19) QDP (20) QDPSizeChangeProof [EQUIVALENT, 0 ms] (21) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(not, app(not, x)) -> x app(not, app(app(or, x), y)) -> app(app(and, app(not, x)), app(not, y)) app(not, app(app(and, x), y)) -> app(app(or, app(not, x)), app(not, y)) app(app(and, x), app(app(or, y), z)) -> app(app(or, app(app(and, x), y)), app(app(and, x), z)) app(app(and, app(app(or, y), z)), x) -> app(app(or, app(app(and, x), y)), app(app(and, x), z)) 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(not, app(app(or, x), y)) -> APP(app(and, app(not, x)), app(not, y)) APP(not, app(app(or, x), y)) -> APP(and, app(not, x)) APP(not, app(app(or, x), y)) -> APP(not, x) APP(not, app(app(or, x), y)) -> APP(not, y) APP(not, app(app(and, x), y)) -> APP(app(or, app(not, x)), app(not, y)) APP(not, app(app(and, x), y)) -> APP(or, app(not, x)) APP(not, app(app(and, x), y)) -> APP(not, x) APP(not, app(app(and, x), y)) -> APP(not, y) APP(app(and, x), app(app(or, y), z)) -> APP(app(or, app(app(and, x), y)), app(app(and, x), z)) APP(app(and, x), app(app(or, y), z)) -> APP(or, app(app(and, x), y)) APP(app(and, x), app(app(or, y), z)) -> APP(app(and, x), y) APP(app(and, x), app(app(or, y), z)) -> APP(app(and, x), z) APP(app(and, app(app(or, y), z)), x) -> APP(app(or, app(app(and, x), y)), app(app(and, x), z)) APP(app(and, app(app(or, y), z)), x) -> APP(or, app(app(and, x), y)) APP(app(and, app(app(or, y), z)), x) -> APP(app(and, x), y) APP(app(and, app(app(or, y), z)), x) -> APP(and, x) APP(app(and, app(app(or, y), z)), x) -> APP(app(and, x), z) 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(not, app(not, x)) -> x app(not, app(app(or, x), y)) -> app(app(and, app(not, x)), app(not, y))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Standard