SRS Standard pair #487092094

details

property	value
status	complete
benchmark	size-11-alpha-3-num-11.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Waldmann_07_size11

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.27513 seconds
cpu usage	9.92153
user time	9.47118
system time	0.45034
max virtual memory	2.1012324E7
max residence set size	1044936.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRS Reverse [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) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) QDPOrderProof [EQUIVALENT, 88 ms]
        (14) QDP
        (15) PisEmptyProof [EQUIVALENT, 0 ms]
        (16) YES


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

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

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

Q is empty.

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

(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
----------------------------------------

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

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

Q is empty.

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

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

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

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

The TRS R consists of the following rules:

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

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

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

(6)
Complex Obligation (AND)

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

(7)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   B(b(x1)) -> A(x1)
   A(x1) -> B(x1)

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