TRS Standard pair #487066628

details

property	value
status	complete
benchmark	halfdouble.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n072.star.cs.uiowa.edu
space	AProVE_10

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	13.0778 seconds
cpu usage	27.2103
user time	25.4728
system time	1.73749
max virtual memory	1.8554492E7
max residence set size	4341432.0

stage attributes

key	value
starexec-result	NO

output

NO
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 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, 1 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) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QReductionProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) QDP
        (29) MNOCProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) NonLoopProof [COMPLETE, 768 ms]
        (32) NO


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

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

   f(tt, x) -> f(eq(x, half(double(x))), s(x))
   eq(s(x), s(y)) -> eq(x, y)
   eq(0, 0) -> tt
   double(s(x)) -> s(s(double(x)))
   double(0) -> 0
   half(s(s(x))) -> s(half(x))
   half(0) -> 0

Q is empty.

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

(1) AAECC Innermost (EQUIVALENT)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 
   eq(s(x), s(y)) -> eq(x, y)
   eq(0, 0) -> tt
   double(s(x)) -> s(s(double(x)))
   double(0) -> 0
   half(s(s(x))) -> s(half(x))
   half(0) -> 0

The TRS R 2 is 
   f(tt, x) -> f(eq(x, half(double(x))), s(x))

The signature Sigma is {f_2}
----------------------------------------

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

   f(tt, x) -> f(eq(x, half(double(x))), s(x))
   eq(s(x), s(y)) -> eq(x, y)
   eq(0, 0) -> tt
   double(s(x)) -> s(s(double(x)))
   double(0) -> 0
   half(s(s(x))) -> s(half(x))
   half(0) -> 0

The set Q consists of the following terms:

   f(tt, x0)
   eq(s(x0), s(x1))
   eq(0, 0)
   double(s(x0))
   double(0)
   half(s(s(x0)))
   half(0)

popout

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

job log

popout

actions all output return to TRS Standard