TRS Standard pair #487069163

details

property	value
status	complete
benchmark	cade06.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	GTSSK07

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.58394 seconds
cpu usage	6.20524
user time	5.9285
system time	0.276738
max virtual memory	1.8477524E7
max residence set size	372592.0

stage attributes

key	value
starexec-result	YES

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

(0) QTRS
(1) AAECC Innermost [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 25 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, 120 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, z) -> f(gt(x, plus(y, z)), x, s(y), z)
   f(true, x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z))
   plus(n, 0) -> n
   plus(n, s(m)) -> s(plus(n, m))
   gt(0, v) -> false
   gt(s(u), 0) -> true
   gt(s(u), s(v)) -> gt(u, v)

Q is empty.

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

The signature Sigma is {f_4}
----------------------------------------

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

   f(true, x, y, z) -> f(gt(x, plus(y, z)), x, s(y), z)
   f(true, x, y, z) -> f(gt(x, plus(y, z)), x, y, s(z))
   plus(n, 0) -> n
   plus(n, s(m)) -> s(plus(n, m))
   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, x2)
   plus(x0, 0)
   plus(x0, s(x1))
   gt(0, x0)
   gt(s(x0), 0)
   gt(s(x0), s(x1))


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

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