TRS Standard pair #487069183

details

property	value
status	complete
benchmark	cade10.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	GTSSK07

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.28489 seconds
cpu usage	5.42391
user time	5.16861
system time	0.255296
max virtual memory	1.8477524E7
max residence set size	347844.0

stage attributes

key	value
starexec-result	YES

output

YES
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 proven:

(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, 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) NonInfProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) PisEmptyProof [EQUIVALENT, 0 ms]
        (29) YES


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

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

   f(true, x, y) -> f(gt(x, y), trunc(x), s(y))
   trunc(0) -> 0
   trunc(s(0)) -> 0
   trunc(s(s(x))) -> s(s(trunc(x)))
   gt(0, v) -> false
   gt(s(u), 0) -> true
   gt(s(u), s(v)) -> gt(u, v)

Q is empty.

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

(1) AAECC Innermost (EQUIVALENT)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 
   trunc(0) -> 0
   trunc(s(0)) -> 0
   trunc(s(s(x))) -> s(s(trunc(x)))
   gt(0, v) -> false
   gt(s(u), 0) -> true
   gt(s(u), s(v)) -> gt(u, v)

The TRS R 2 is 
   f(true, x, y) -> f(gt(x, y), trunc(x), s(y))

The signature Sigma is {f_3}
----------------------------------------

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

   f(true, x, y) -> f(gt(x, y), trunc(x), s(y))
   trunc(0) -> 0
   trunc(s(0)) -> 0
   trunc(s(s(x))) -> s(s(trunc(x)))
   gt(0, v) -> false
   gt(s(u), 0) -> true
   gt(s(u), s(v)) -> gt(u, v)

The set Q consists of the following terms:

   f(true, x0, x1)
   trunc(0)
   trunc(s(0))
   trunc(s(s(x0)))
   gt(0, x0)
   gt(s(x0), 0)
   gt(s(x0), s(x1))


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

(3) DependencyPairsProof (EQUIVALENT)

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