TRS Standard pair #516963965

details

property	value
status	complete
benchmark	JFP_Ex31.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n066.star.cs.uiowa.edu
space	AProVE_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	72.0958981514 seconds
cpu usage	153.983849955
max memory	3.322605568E9

stage attributes

key	value
output-size	58739
starexec-result	YES

output

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


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


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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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, 0 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) UsableRulesProof [EQUIVALENT, 0 ms]
        (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES
    (15) QDP
        (16) UsableRulesProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) UsableRulesReductionPairsProof [EQUIVALENT, 22 ms]
        (22) QDP
        (23) TransformationProof [EQUIVALENT, 0 ms]
        (24) QDP
        (25) DependencyGraphProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) TransformationProof [EQUIVALENT, 0 ms]
        (28) QDP
        (29) DependencyGraphProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) SemLabProof [SOUND, 15.8 s]
        (32) QDP
        (33) DependencyGraphProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) QDPOrderProof [EQUIVALENT, 29 ms]
        (36) QDP
        (37) QDPOrderProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) QDPOrderProof [EQUIVALENT, 2 ms]
        (40) QDP
        (41) QDPOrderProof [EQUIVALENT, 26 ms]
        (42) QDP
        (43) QDPOrderProof [EQUIVALENT, 29 ms]
        (44) QDP
        (45) QDPOrderProof [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:

   active(f(b, c, x)) -> mark(f(x, x, x))
   active(f(x, y, z)) -> f(x, y, active(z))
   active(d) -> m(b)
   f(x, y, mark(z)) -> mark(f(x, y, z))
   active(d) -> mark(c)
   proper(b) -> ok(b)
   proper(c) -> ok(c)
   proper(d) -> ok(d)
   proper(f(x, y, z)) -> f(proper(x), proper(y), proper(z))
   f(ok(x), ok(y), ok(z)) -> ok(f(x, y, z))
   top(mark(x)) -> top(proper(x))
   top(ok(x)) -> top(active(x))

Q is empty.

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

(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
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(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   ACTIVE(f(b, c, x)) -> F(x, x, x)
   ACTIVE(f(x, y, z)) -> F(x, y, active(z))
   ACTIVE(f(x, y, z)) -> ACTIVE(z)

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