TRS Standard pair #487068678

details

property	value
status	complete
benchmark	z27.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n073.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	20.011 seconds
cpu usage	31.6322
user time	29.7535
system time	1.87874
max virtual memory	1.8611916E7
max residence set size	4702864.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) DependencyPairsProof [EQUIVALENT, 0 ms]
(2) QDP
(3) QDPOrderProof [EQUIVALENT, 0 ms]
(4) QDP
(5) SemLabProof [SOUND, 188 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) PisEmptyProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) PisEmptyProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) QDP
        (20) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) PisEmptyProof [EQUIVALENT, 0 ms]
        (23) YES
    (24) QDP
        (25) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) PisEmptyProof [EQUIVALENT, 0 ms]
        (28) YES
    (29) QDP
        (30) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) PisEmptyProof [EQUIVALENT, 0 ms]
        (33) YES
    (34) QDP
        (35) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) PisEmptyProof [EQUIVALENT, 0 ms]
        (38) YES
    (39) QDP
        (40) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (41) QDP
        (42) PisEmptyProof [EQUIVALENT, 0 ms]
        (43) YES
    (44) QDP
        (45) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
        (46) QDP
        (47) PisEmptyProof [EQUIVALENT, 0 ms]
        (48) YES


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

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

   f(0, 1, x) -> f(g(x), g(x), x)
   f(g(x), y, z) -> g(f(x, y, z))
   f(x, g(y), z) -> g(f(x, y, z))
   f(x, y, g(z)) -> g(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(0, 1, x) -> F(g(x), g(x), x)
   F(g(x), y, z) -> F(x, y, z)
   F(x, g(y), z) -> F(x, y, z)
   F(x, y, g(z)) -> F(x, y, z)

The TRS R consists of the following rules:

   f(0, 1, x) -> f(g(x), g(x), x)
   f(g(x), y, z) -> g(f(x, y, z))
   f(x, g(y), z) -> g(f(x, y, z))
   f(x, y, g(z)) -> g(f(x, y, z))

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

(3) QDPOrderProof (EQUIVALENT)

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