TRS Stand 20472 pair #381714254

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	n114.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	14.2475459576 seconds
cpu usage	28.136487004
max memory	4.225421312E9

stage attributes

key	value
output-size	39253
starexec-result	YES

output

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


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YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 203 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))

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