TRS Standard pair #487067343

details

property	value
status	complete
benchmark	enger-nonloop-add.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n071.star.cs.uiowa.edu
space	EEG_IJCAR_12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	12.9925 seconds
cpu usage	35.0304
user time	34.1328
system time	0.897661
max virtual memory	1.8502032E7
max residence set size	2190616.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) AAECC Innermost [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QReductionProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QReductionProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) QDP
        (22) MNOCProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) NonLoopProof [COMPLETE, 893 ms]
        (25) NO


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

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

   add(true, x, xs) -> add(and(isNat(x), isList(xs)), x, Cons(x, xs))
   isList(Cons(x, xs)) -> isList(xs)
   isList(nil) -> true
   isNat(s(x)) -> isNat(x)
   isNat(0) -> true
   and(true, true) -> true
   and(false, x) -> false
   and(x, false) -> false

Q is empty.

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

(1) AAECC Innermost (EQUIVALENT)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 
   isList(Cons(x, xs)) -> isList(xs)
   isList(nil) -> true
   isNat(s(x)) -> isNat(x)
   isNat(0) -> true
   and(true, true) -> true
   and(false, x) -> false
   and(x, false) -> false

The TRS R 2 is 
   add(true, x, xs) -> add(and(isNat(x), isList(xs)), x, Cons(x, xs))

The signature Sigma is {add_3}
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   add(true, x, xs) -> add(and(isNat(x), isList(xs)), x, Cons(x, xs))
   isList(Cons(x, xs)) -> isList(xs)
   isList(nil) -> true
   isNat(s(x)) -> isNat(x)
   isNat(0) -> true
   and(true, true) -> true
   and(false, x) -> false
   and(x, false) -> false

The set Q consists of the following terms:

   add(true, x0, x1)
   isList(Cons(x0, x1))
   isList(nil)
   isNat(s(x0))
   isNat(0)
   and(true, true)
   and(false, x0)
   and(x0, false)


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

(3) DependencyPairsProof (EQUIVALENT)

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