TRS Standard pair #615304086

details

property	value
status	complete
benchmark	emmes-nonloop-ex4_1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n014.star.cs.uiowa.edu
space	EEG_IJCAR_12

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	11.9326930046 seconds
cpu usage	26.636706939
max memory	1.329516544E9

stage attributes

key	value
output-size	12294
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


Termination w.r.t. Q of the given QTRS could be disproven:

(0) QTRS
(1) AAECC Innermost [EQUIVALENT, 9 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, 149 ms]
        (25) NO


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

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

   f(true, x) -> f(eq(0, minus(x, x)), plus1(x))
   plus1(x) -> s(x)
   minus(x, 0) -> x
   minus(0, y) -> 0
   minus(s(x), s(y)) -> minus(x, y)
   eq(0, 0) -> true
   eq(s(x), 0) -> false
   eq(0, s(y)) -> false
   eq(s(x), s(y)) -> eq(x, y)

Q is empty.

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

(1) AAECC Innermost (EQUIVALENT)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 
   plus1(x) -> s(x)
   minus(x, 0) -> x
   minus(0, y) -> 0
   minus(s(x), s(y)) -> minus(x, y)
   eq(0, 0) -> true
   eq(s(x), 0) -> false
   eq(0, s(y)) -> false
   eq(s(x), s(y)) -> eq(x, y)

The TRS R 2 is 
   f(true, x) -> f(eq(0, minus(x, x)), plus1(x))

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

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

   f(true, x) -> f(eq(0, minus(x, x)), plus1(x))
   plus1(x) -> s(x)
   minus(x, 0) -> x
   minus(0, y) -> 0
   minus(s(x), s(y)) -> minus(x, y)
   eq(0, 0) -> true
   eq(s(x), 0) -> false
   eq(0, s(y)) -> false
   eq(s(x), s(y)) -> eq(x, y)

The set Q consists of the following terms:

   f(true, x0)
   plus1(x0)
   minus(x0, 0)
   minus(0, x0)

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