TRS Standard pair #487066613

details

property	value
status	complete
benchmark	ex4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n186.star.cs.uiowa.edu
space	AProVE_10

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	13.1329 seconds
cpu usage	36.4544
user time	35.5108
system time	0.94363
max virtual memory	3.684186E7
max residence set size	2334968.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1 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, 1211 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
   if(true, x, y) -> x
   if(false, x, y) -> y
   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
   if(true, x, y) -> x
   if(false, x, y) -> y
   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
   if(true, x, y) -> x
   if(false, x, y) -> y
   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)
   if(true, x0, x1)
   if(false, x0, x1)

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