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	n066.star.cs.uiowa.edu
space	Applicative_05

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	4.02363395691 seconds
cpu usage	12.03183288
max memory	7.16029952E8

stage attributes

key	value
output-size	6014
starexec-result	NO

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- NO proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be disproven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 42 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT,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)) popout

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job log

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actions

all output return to TRS Standard