TRS Stand 20472 pair #381712438

details

property	value
status	complete
benchmark	4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n094.star.cs.uiowa.edu
space	Secret_07_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.99832320213 seconds
cpu usage	19.563354113
max memory	1.302441984E9

stage attributes

key	value
output-size	32269
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 23 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) MRRProof [EQUIVALENT, 29 ms]
        (9) QDP
        (10) MRRProof [EQUIVALENT, 17 ms]
        (11) QDP
        (12) DependencyGraphProof [EQUIVALENT, 0 ms]
        (13) AND
            (14) QDP
                (15) TransformationProof [EQUIVALENT, 0 ms]
                (16) QDP
                (17) DependencyGraphProof [EQUIVALENT, 0 ms]
                (18) TRUE
            (19) QDP
                (20) TransformationProof [EQUIVALENT, 0 ms]
                (21) QDP
                (22) TransformationProof [EQUIVALENT, 0 ms]
                (23) QDP
                (24) TransformationProof [EQUIVALENT, 0 ms]
                (25) QDP
                (26) TransformationProof [EQUIVALENT, 0 ms]
                (27) QDP
                (28) DependencyGraphProof [EQUIVALENT, 0 ms]
                (29) QDP
                (30) TransformationProof [EQUIVALENT, 0 ms]
                (31) QDP
                (32) DependencyGraphProof [EQUIVALENT, 0 ms]
                (33) QDP
                (34) TransformationProof [EQUIVALENT, 0 ms]
                (35) QDP
                (36) DependencyGraphProof [EQUIVALENT, 0 ms]
                (37) QDP
                (38) SplitQDPProof [EQUIVALENT, 0 ms]
                (39) AND
                    (40) QDP
                        (41) SemLabProof [SOUND, 0 ms]
                        (42) QDP
                        (43) DependencyGraphProof [EQUIVALENT, 0 ms]
                        (44) QDP
                        (45) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
                        (46) QDP
                        (47) MRRProof [EQUIVALENT, 5 ms]
                        (48) QDP
                        (49) PisEmptyProof [SOUND, 0 ms]
                        (50) TRUE
                    (51) QDP
                        (52) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
                        (53) QDP
                        (54) RFCMatchBoundsDPProof [EQUIVALENT, 0 ms]
                        (55) YES
    (56) QDP
        (57) TransformationProof [EQUIVALENT, 0 ms]
        (58) QDP
        (59) QDPOrderProof [EQUIVALENT, 415 ms]
        (60) QDP
        (61) PisEmptyProof [EQUIVALENT, 0 ms]
        (62) YES


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

   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))
   g(x, g(y, g(x, y))) -> g(a, g(x, g(y, b)))

Q is empty.

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(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
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(2)

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