TRS Standard pair #487073553

details

property	value
status	complete
benchmark	Ex3Lists.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	Applicative_05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.09953 seconds
cpu usage	4.31876
user time	4.12156
system time	0.197201
max virtual memory	1.8408912E7
max residence set size	260664.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) MNOCProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) UsableRulesProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) QReductionProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) QDP
        (19) UsableRulesProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (22) YES


----------------------------------------

(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   app(app(append, nil), l) -> l
   app(app(append, app(app(cons, h), t)), l) -> app(app(cons, h), app(app(append, t), l))
   app(app(map, f), nil) -> nil
   app(app(map, f), app(app(cons, h), t)) -> app(app(cons, app(f, h)), app(app(map, f), t))
   app(app(append, app(app(append, l1), l2)), l3) -> app(app(append, l1), app(app(append, l2), l3))
   app(app(map, f), app(app(append, l1), l2)) -> app(app(append, app(app(map, f), l1)), app(app(map, f), l2))

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(append, app(app(cons, h), t)), l) -> APP(app(cons, h), app(app(append, t), l))
   APP(app(append, app(app(cons, h), t)), l) -> APP(app(append, t), l)
   APP(app(append, app(app(cons, h), t)), l) -> APP(append, t)
   APP(app(map, f), app(app(cons, h), t)) -> APP(app(cons, app(f, h)), app(app(map, f), t))
   APP(app(map, f), app(app(cons, h), t)) -> APP(cons, app(f, h))
   APP(app(map, f), app(app(cons, h), t)) -> APP(f, h)
   APP(app(map, f), app(app(cons, h), t)) -> APP(app(map, f), t)
   APP(app(append, app(app(append, l1), l2)), l3) -> APP(app(append, l1), app(app(append, l2), l3))
   APP(app(append, app(app(append, l1), l2)), l3) -> APP(app(append, l2), l3)
   APP(app(append, app(app(append, l1), l2)), l3) -> APP(append, l2)
   APP(app(map, f), app(app(append, l1), l2)) -> APP(app(append, app(app(map, f), l1)), app(app(map, f), l2))
   APP(app(map, f), app(app(append, l1), l2)) -> APP(append, app(app(map, f), l1))
   APP(app(map, f), app(app(append, l1), l2)) -> APP(app(map, f), l1)
   APP(app(map, f), app(app(append, l1), l2)) -> APP(app(map, f), l2)

The TRS R consists of the following rules:

   app(app(append, nil), l) -> l
   app(app(append, app(app(cons, h), t)), l) -> app(app(cons, h), app(app(append, t), l))
   app(app(map, f), nil) -> nil
   app(app(map, f), app(app(cons, h), t)) -> app(app(cons, app(f, h)), app(app(map, f), t))
   app(app(append, app(app(append, l1), l2)), l3) -> app(app(append, l1), app(app(append, l2), l3))
   app(app(map, f), app(app(append, l1), l2)) -> app(app(append, app(app(map, f), l1)), app(app(map, f), l2))

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 2 SCCs with 7 less nodes.
----------------------------------------

(4)
Complex Obligation (AND)

----------------------------------------

(5)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

popout

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

job log

popout

actions all output return to TRS Standard