TRS Standard pair #516965180

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	n010.star.cs.uiowa.edu
space	EEG_IJCAR_12

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	13.7659809589 seconds
cpu usage	41.167396115
max memory	1.330147328E9

stage attributes

key	value
output-size	13779
starexec-result	NO

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


NO
proof of /export/starexec/sandbox/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) 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, 1014 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)

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