TRS Standard pair #516965520

details

property	value
status	complete
benchmark	z21.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n076.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	17.7248871326 seconds
cpu usage	47.50282762
max memory	1.543315456E9

stage attributes

key	value
output-size	15564
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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, 0 ms]
(2) QDP
(3) MRRProof [EQUIVALENT, 28 ms]
(4) QDP
(5) MRRProof [EQUIVALENT, 0 ms]
(6) QDP
(7) SemLabProof [SOUND, 459 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QDP
        (12) UsableRulesReductionPairsProof [EQUIVALENT, 8 ms]
        (13) QDP
        (14) DependencyGraphProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) QDPOrderProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) PisEmptyProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) DependencyGraphProof [EQUIVALENT, 0 ms]
        (24) QDP
        (25) QDPOrderProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) PisEmptyProof [EQUIVALENT, 0 ms]
        (28) YES


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

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

   f(f(a, b), x) -> f(a, f(a, x))
   f(f(b, a), x) -> f(b, f(b, x))
   f(x, f(y, z)) -> f(f(x, y), z)

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:

   F(f(a, b), x) -> F(a, f(a, x))
   F(f(a, b), x) -> F(a, x)
   F(f(b, a), x) -> F(b, f(b, x))
   F(f(b, a), x) -> F(b, x)
   F(x, f(y, z)) -> F(f(x, y), z)
   F(x, f(y, z)) -> F(x, y)

The TRS R consists of the following rules:

   f(f(a, b), x) -> f(a, f(a, x))
   f(f(b, a), x) -> f(b, f(b, x))
   f(x, f(y, z)) -> f(f(x, y), z)

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

(3) MRRProof (EQUIVALENT)
By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.

Strictly oriented dependency pairs:

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


Used ordering: Polynomial interpretation [POLO]:

   POL(F(x_1, x_2)) = 2*x_1 + 2*x_2
   POL(a) = 2
   POL(b) = 2
   POL(f(x_1, x_2)) = x_1 + x_2

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