TRS Standard pair #487067313

details

property	value
status	complete
benchmark	velroyen-nonloop-ConvLower_c.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	EEG_IJCAR_12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	12.6661 seconds
cpu usage	37.4488
user time	35.9379
system time	1.51083
max virtual memory	3.6980644E7
max residence set size	3472676.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 10 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) 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, 283 ms]
        (32) NO


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

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

   while(true, s(s(s(i)))) -> while(gt(s(s(s(i))), s(0)), f(s(s(s(i)))))
   f(i) -> if(neq(i, s(s(0))), i)
   gt(s(x), s(y)) -> gt(x, y)
   gt(s(x), 0) -> true
   gt(0, 0) -> false
   gt(0, s(y)) -> false
   if(true, i) -> plus(i, s(0))
   if(false, i) -> i
   neq(s(x), s(y)) -> neq(x, y)
   neq(0, 0) -> false
   neq(0, s(y)) -> true
   neq(s(x), 0) -> true
   plus(s(x), y) -> plus(x, s(y))
   plus(0, y) -> y

Q is empty.

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

(1) AAECC Innermost (EQUIVALENT)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 
   f(i) -> if(neq(i, s(s(0))), i)
   gt(s(x), s(y)) -> gt(x, y)
   gt(s(x), 0) -> true
   gt(0, 0) -> false
   gt(0, s(y)) -> false
   if(true, i) -> plus(i, s(0))
   if(false, i) -> i
   neq(s(x), s(y)) -> neq(x, y)
   neq(0, 0) -> false
   neq(0, s(y)) -> true
   neq(s(x), 0) -> true
   plus(s(x), y) -> plus(x, s(y))
   plus(0, y) -> y

The TRS R 2 is 
   while(true, s(s(s(i)))) -> while(gt(s(s(s(i))), s(0)), f(s(s(s(i)))))

The signature Sigma is {while_2}
----------------------------------------

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

   while(true, s(s(s(i)))) -> while(gt(s(s(s(i))), s(0)), f(s(s(s(i)))))
   f(i) -> if(neq(i, s(s(0))), i)
   gt(s(x), s(y)) -> gt(x, y)
   gt(s(x), 0) -> true
   gt(0, 0) -> false

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