TRS Standard pair #615297506

details

property	value
status	complete
benchmark	jw08.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n002.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	1.83488297462 seconds
cpu usage	4.699241036
max memory	2.67558912E8

stage attributes

key	value
output-size	4071
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


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

(0) QTRS
(1) Overlay + Local Confluence [EQUIVALENT, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 4 ms]
(6) QDP
(7) UsableRulesProof [EQUIVALENT, 0 ms]
(8) QDP
(9) QDPOrderProof [EQUIVALENT, 0 ms]
(10) QDP
(11) PisEmptyProof [EQUIVALENT, 0 ms]
(12) YES


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

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

   f(a, f(x, a)) -> f(a, f(a, f(f(a, a), x)))

Q is empty.

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

(1) Overlay + Local Confluence (EQUIVALENT)
The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.
----------------------------------------

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

   f(a, f(x, a)) -> f(a, f(a, f(f(a, a), x)))

The set Q consists of the following terms:

   f(a, f(x0, a))


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

(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:

   F(a, f(x, a)) -> F(a, f(a, f(f(a, a), x)))
   F(a, f(x, a)) -> F(a, f(f(a, a), x))
   F(a, f(x, a)) -> F(f(a, a), x)
   F(a, f(x, a)) -> F(a, a)

The TRS R consists of the following rules:

   f(a, f(x, a)) -> f(a, f(a, f(f(a, a), x)))

The set Q consists of the following terms:

   f(a, f(x0, a))

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

(5) DependencyGraphProof (EQUIVALENT)
The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.
----------------------------------------

(6)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   F(a, f(x, a)) -> F(a, f(f(a, a), x))

The TRS R consists of the following rules:

   f(a, f(x, a)) -> f(a, f(a, f(f(a, a), x)))

The set Q consists of the following terms:

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