SRS Standard pair #487084666

details

property	value
status	complete
benchmark	size-12-alpha-3-num-61.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Waldmann_07_size12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	11.5131 seconds
cpu usage	21.6936
user time	20.8639
system time	0.829677
max virtual memory	3.9643316E7
max residence set size	2350892.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) DependencyPairsProof [EQUIVALENT, 3 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) QDP
(5) QDPOrderProof [EQUIVALENT, 123 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) QDPOrderProof [EQUIVALENT, 41 ms]
        (11) QDP
        (12) PisEmptyProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES


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

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

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

The TRS R consists of the following rules:

   a(x1) -> x1
   a(a(x1)) -> a(b(c(x1)))
   b(x1) -> x1
   c(b(x1)) -> b(a(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 1 SCC with 2 less nodes.
----------------------------------------

(4)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

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

The TRS R consists of the following rules:

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

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

(5) QDPOrderProof (EQUIVALENT)
We use the reduction pair processor [LPAR04,JAR06].

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