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TRS Standard pair #487073433
details
property
value
status
complete
benchmark
012.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n189.star.cs.uiowa.edu
space
AotoYamada_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.75458 seconds
cpu usage
4.00308
user time
3.82936
system time
0.173721
max virtual memory
1.8343376E7
max residence set size
245896.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 25 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) QDP (7) UsableRulesProof [EQUIVALENT, 0 ms] (8) QDP (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(and, true), true) -> true app(app(and, x), false) -> false app(app(and, false), y) -> false app(app(or, true), y) -> true app(app(or, x), true) -> true app(app(or, false), false) -> false app(app(forall, p), nil) -> true app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) app(app(forsome, p), nil) -> false app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(and, true), true) -> true app(app(and, x), false) -> false app(app(and, false), y) -> false app(app(or, true), y) -> true app(app(or, x), true) -> true app(app(or, false), false) -> false app(app(forall, p), nil) -> true app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) app(app(forsome, p), nil) -> false app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) The set Q consists of the following terms: app(app(and, true), true) app(app(and, x0), false) app(app(and, false), x0) app(app(or, true), x0) app(app(or, x0), true) app(app(or, false), false) app(app(forall, x0), nil) app(app(forall, x0), app(app(cons, x1), x2)) app(app(forsome, x0), nil) app(app(forsome, x0), app(app(cons, x1), x2)) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: APP(app(forall, p), app(app(cons, x), xs)) -> APP(app(and, app(p, x)), app(app(forall, p), xs)) APP(app(forall, p), app(app(cons, x), xs)) -> APP(and, app(p, x)) APP(app(forall, p), app(app(cons, x), xs)) -> APP(p, x) APP(app(forall, p), app(app(cons, x), xs)) -> APP(app(forall, p), xs) APP(app(forsome, p), app(app(cons, x), xs)) -> APP(app(or, app(p, x)), app(app(forsome, p), xs)) APP(app(forsome, p), app(app(cons, x), xs)) -> APP(or, app(p, x)) APP(app(forsome, p), app(app(cons, x), xs)) -> APP(p, x) APP(app(forsome, p), app(app(cons, x), xs)) -> APP(app(forsome, p), xs) The TRS R consists of the following rules: app(app(and, true), true) -> true app(app(and, x), false) -> false
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