SRS Standard pair #516969088

details

property	value
status	complete
benchmark	jw3.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	Waldmann_06_SRS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	5.68288993835 seconds
cpu usage	19.259205103
max memory	1.299521536E9

stage attributes

key	value
output-size	8880
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 10 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) QDPOrderProof [EQUIVALENT, 76 ms]
        (7) QDP
        (8) DependencyGraphProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) QDPOrderProof [EQUIVALENT, 23 ms]
        (14) QDP
        (15) QDPOrderProof [EQUIVALENT, 350 ms]
        (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES


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

   a(b(b(x1))) -> P(a(b(x1)))
   a(P(x1)) -> P(a(x(x1)))
   a(x(x1)) -> x(a(x1))
   b(P(x1)) -> b(Q(x1))
   Q(x(x1)) -> a(Q(x1))
   Q(a(x1)) -> b(b(a(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(b(b(x1))) -> A(b(x1))
   A(P(x1)) -> A(x(x1))
   A(x(x1)) -> A(x1)
   B(P(x1)) -> B(Q(x1))
   B(P(x1)) -> Q^1(x1)
   Q^1(x(x1)) -> A(Q(x1))
   Q^1(x(x1)) -> Q^1(x1)
   Q^1(a(x1)) -> B(b(a(x1)))
   Q^1(a(x1)) -> B(a(x1))

The TRS R consists of the following rules:

   a(b(b(x1))) -> P(a(b(x1)))
   a(P(x1)) -> P(a(x(x1)))
   a(x(x1)) -> x(a(x1))
   b(P(x1)) -> b(Q(x1))
   Q(x(x1)) -> a(Q(x1))
   Q(a(x1)) -> b(b(a(x1)))

Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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(3) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node.
----------------------------------------

(4)
Complex Obligation (AND)

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

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

   A(P(x1)) -> A(x(x1))
   A(x(x1)) -> A(x1)

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