TRS Standard pair #487067298

details

property	value
status	complete
benchmark	enger-nonloop-toOne.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n173.star.cs.uiowa.edu
space	EEG_IJCAR_12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	11.9912 seconds
cpu usage	35.4872
user time	34.2374
system time	1.24978
max virtual memory	1.9191604E7
max residence set size	2917484.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1 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, 95 ms]
        (25) NO


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

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

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

The TRS R 2 is 
   f(tt, x) -> f(eq(toOne(x), s(0)), 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(toOne(x), s(0)), s(x))
   eq(s(x), s(y)) -> eq(x, y)
   eq(0, 0) -> tt
   toOne(s(s(x))) -> toOne(s(x))
   toOne(s(0)) -> s(0)

The set Q consists of the following terms:

   f(tt, x0)
   eq(s(x0), s(x1))
   eq(0, 0)
   toOne(s(s(x0)))
   toOne(s(0))


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

(3) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(4)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   F(tt, x) -> F(eq(toOne(x), s(0)), s(x))
   F(tt, x) -> EQ(toOne(x), s(0))
   F(tt, x) -> TOONE(x)
   EQ(s(x), s(y)) -> EQ(x, y)

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