details

property	value
status	complete
benchmark	TypeEx3.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n186.star.cs.uiowa.edu
space	Applicative_05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.43396 seconds
cpu usage	9.81962
user time	9.44082
system time	0.3788
max virtual memory	3.6587904E7
max residence set size	575656.0

stage attributes

key	value
starexec-result	NO

output

NO 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be disproven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 18 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) TransformationProof [EQUIVALENT, 0 ms] (6) QDP (7) NonTerminationLoopProof [COMPLETE, 0 ms] (8) NO ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(f, 0), n) -> app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n) 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)) 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(f, 0), n) -> APP(app(hd, app(app(map, f), app(app(cons, 0), nil))), n) APP(app(f, 0), n) -> APP(hd, app(app(map, f), app(app(cons, 0), nil))) APP(app(f, 0), n) -> APP(app(map, f), app(app(cons, 0), nil)) APP(app(f, 0), n) -> APP(map, f) APP(app(f, 0), n) -> APP(app(cons, 0), nil) APP(app(f, 0), n) -> APP(cons, 0) 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) The TRS R consists of the following rules: app(app(f, 0), n) -> app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n) 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)) 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 4 less nodes. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: APP(app(f, 0), n) -> APP(app(map, f), app(app(cons, 0), nil)) APP(app(f, 0), n) -> APP(app(hd, app(app(map, f), app(app(cons, 0), nil))), n) APP(app(f, 0), n) -> APP(app(cons, 0), nil) 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(f, x) APP(app(map, f), app(app(cons, x), xs)) -> APP(app(map, f), xs) The TRS R consists of the following rules: app(app(f, 0), n) -> app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n) 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)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule APP(app(f, 0), n) -> APP(app(hd, app(app(map, f), app(app(cons, 0), nil))), n) at position [0,1] we obtained the following new rules [LPAR04]: (APP(app(0, 0), y1) -> APP(app(hd, app(app(hd, app(app(map, map), app(app(cons, 0), nil))), app(app(cons, 0), nil))), y1),APP(app(0, 0), y1) -> APP(app(hd, app(app(hd, app(app(map, map), app(app(cons, 0), nil))), app(app(cons, 0), nil))), y1)) (APP(app(x0, 0), y1) -> APP(app(hd, app(app(cons, app(x0, 0)), app(app(map, x0), nil))), y1),APP(app(x0, 0), y1) -> APP(app(hd, app(app(cons, app(x0, 0)), app(app(map, x0), nil))), y1)) (APP(app(y0, 0), y1) -> APP(app(hd, app(app(map, y0), app(app(hd, app(app(map, cons), app(app(cons, 0), nil))), nil))), y1),APP(app(y0, 0), y1) -> APP(app(hd, app(app(map, y0), app(app(hd, app(app(map, cons), app(app(cons, 0), nil))), nil))), y1)) ---------------------------------------- (6) popout

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job log

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actions

all output return to TRS Standard