SRS Standard pair #487085140

details

property	value
status	complete
benchmark	size-12-alpha-3-num-52.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.92294 seconds
cpu usage	12.4791
user time	11.924
system time	0.555099
max virtual memory	3.8970764E7
max residence set size	1710564.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) DependencyPairsProof [EQUIVALENT, 8 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 1 ms]
        (7) QDP
        (8) MNOCProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) MRRProof [EQUIVALENT, 2 ms]
        (11) QDP
        (12) PisEmptyProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) QDPOrderProof [EQUIVALENT, 79 ms]
        (16) QDP
        (17) UsableRulesProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 1 ms]
        (20) YES


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

   a(x1) -> x1
   a(a(x1)) -> a(b(x1))
   b(x1) -> x1
   c(b(x1)) -> b(a(c(c(x1))))

Q is empty.

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

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

(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   A(a(x1)) -> A(b(x1))
   A(a(x1)) -> B(x1)
   C(b(x1)) -> B(a(c(c(x1))))
   C(b(x1)) -> A(c(c(x1)))
   C(b(x1)) -> C(c(x1))
   C(b(x1)) -> C(x1)

The TRS R consists of the following rules:

   a(x1) -> x1
   a(a(x1)) -> a(b(x1))
   b(x1) -> x1
   c(b(x1)) -> b(a(c(c(x1))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(3) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 3 less nodes.
----------------------------------------

(4)
Complex Obligation (AND)

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

(5)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   A(a(x1)) -> A(b(x1))

The TRS R consists of the following rules:

   a(x1) -> x1
   a(a(x1)) -> a(b(x1))
   b(x1) -> x1
   c(b(x1)) -> b(a(c(c(x1))))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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