TRS Standard pair #487072208

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	n073.star.cs.uiowa.edu
space	Secret_07_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	11.065 seconds
cpu usage	29.5881
user time	27.981
system time	1.60708
max virtual memory	1.8836248E7
max residence set size	3878852.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 16 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) MRRProof [EQUIVALENT, 21 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, 1 ms]
        (23) AND
            (24) QDP
                (25) SemLabProof [SOUND, 0 ms]
                (26) QDP
                (27) DependencyGraphProof [EQUIVALENT, 0 ms]
                (28) QDP
                (29) UsableRulesReductionPairsProof [EQUIVALENT, 4 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)

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))

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