TRS Standard pair #615302931

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	n053.star.cs.uiowa.edu
space	Applicative_05

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	3.46455097198 seconds
cpu usage	10.718139676
max memory	5.34929408E8

stage attributes

key	value
output-size	6021
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


Termination w.r.t. Q of the given QTRS could be disproven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 0 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

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Standard