TRS Standard pair #487067373

details

property	value
status	complete
benchmark	emmes-nonloop-ex7_7.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	EEG_IJCAR_12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	26.7119 seconds
cpu usage	95.6713
user time	93.5316
system time	2.13963
max virtual memory	3.7551996E7
max residence set size	4057484.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 9 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) 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, 12.1 s]
        (32) NO


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

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

   f(true, xs) -> f(eq(s(length(xs)), length(cons(a, xs))), append(cons(b, nil), xs))
   length(nil) -> 0
   length(cons(x, xs)) -> s(length(xs))
   eq(0, 0) -> true
   eq(s(x), 0) -> false
   eq(0, s(y)) -> false
   eq(s(x), s(y)) -> eq(x, y)
   append(nil, ys) -> ys
   append(cons(x, xs), ys) -> cons(x, append(xs, ys))

Q is empty.

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

(1) AAECC Innermost (EQUIVALENT)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 
   length(nil) -> 0
   length(cons(x, xs)) -> s(length(xs))
   eq(0, 0) -> true
   eq(s(x), 0) -> false
   eq(0, s(y)) -> false
   eq(s(x), s(y)) -> eq(x, y)
   append(nil, ys) -> ys
   append(cons(x, xs), ys) -> cons(x, append(xs, ys))

The TRS R 2 is 
   f(true, xs) -> f(eq(s(length(xs)), length(cons(a, xs))), append(cons(b, nil), xs))

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

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

   f(true, xs) -> f(eq(s(length(xs)), length(cons(a, xs))), append(cons(b, nil), xs))
   length(nil) -> 0
   length(cons(x, xs)) -> s(length(xs))
   eq(0, 0) -> true
   eq(s(x), 0) -> false
   eq(0, s(y)) -> false
   eq(s(x), s(y)) -> eq(x, y)
   append(nil, ys) -> ys
   append(cons(x, xs), ys) -> cons(x, append(xs, ys))

The set Q consists of the following terms:

   f(true, x0)
   length(nil)
   length(cons(x0, x1))

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