TRS Standard pair #516967490

details

property	value
status	complete
benchmark	1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n082.star.cs.uiowa.edu
space	Secret_07_TRS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	11.7750148773 seconds
cpu usage	33.221126389
max memory	1.535209472E9

stage attributes

key	value
output-size	23238
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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, 30 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) MRRProof [EQUIVALENT, 19 ms]
        (9) QDP
        (10) TransformationProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) DependencyGraphProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) TransformationProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) TransformationProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) DependencyGraphProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) SplitQDPProof [EQUIVALENT, 0 ms]
        (23) AND
            (24) QDP
                (25) SemLabProof [SOUND, 0 ms]
                (26) QDP
                (27) DependencyGraphProof [EQUIVALENT, 0 ms]
                (28) QDP
                (29) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
                (30) QDP
                (31) MRRProof [EQUIVALENT, 0 ms]
                (32) QDP
                (33) PisEmptyProof [SOUND, 0 ms]
                (34) TRUE
            (35) QDP
                (36) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
                (37) QDP
                (38) RFCMatchBoundsDPProof [EQUIVALENT, 0 ms]
                (39) YES
    (40) QDP
        (41) TransformationProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) QDPOrderProof [EQUIVALENT, 232 ms]
        (44) QDP
        (45) PisEmptyProof [EQUIVALENT, 0 ms]
        (46) YES


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

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

   g(x, x) -> g(a, b)
   g(c, g(c, x)) -> g(e, g(d, x))
   g(d, g(d, x)) -> g(c, g(e, x))
   g(e, g(e, x)) -> g(d, g(c, x))
   f(g(x, y)) -> g(y, g(f(f(x)), a))

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:

   G(x, x) -> G(a, b)
   G(c, g(c, x)) -> G(e, g(d, x))
   G(c, g(c, x)) -> G(d, x)
   G(d, g(d, x)) -> G(c, g(e, x))
   G(d, g(d, x)) -> G(e, x)
   G(e, g(e, x)) -> G(d, g(c, x))
   G(e, g(e, x)) -> G(c, x)
   F(g(x, y)) -> G(y, g(f(f(x)), a))
   F(g(x, y)) -> G(f(f(x)), a)
   F(g(x, y)) -> F(f(x))
   F(g(x, y)) -> F(x)

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