TRS Standard pair #516961295

details

property	value
status	complete
benchmark	Ex9_Luc04_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n173.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	124.440019846 seconds
cpu usage	327.672902372
max memory	6.106353664E9

stage attributes

key	value
output-size	91297
starexec-result	NO

output

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


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


NO
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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 disproven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 9 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) QDPOrderProof [EQUIVALENT, 79 ms]
        (12) QDP
        (13) QDPOrderProof [EQUIVALENT, 54 ms]
        (14) QDP
        (15) TransformationProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPOrderProof [EQUIVALENT, 1610 ms]
        (18) QDP
        (19) QDPOrderProof [EQUIVALENT, 2281 ms]
        (20) QDP
        (21) SplitQDPProof [EQUIVALENT, 0 ms]
        (22) AND
            (23) QDP
                (24) SemLabProof [SOUND, 0 ms]
                (25) QDP
                (26) QDPOrderProof [EQUIVALENT, 81 ms]
                (27) QDP
                (28) QDPOrderProof [EQUIVALENT, 92 ms]
                (29) QDP
                (30) QDPOrderProof [EQUIVALENT, 44 ms]
                (31) QDP
                (32) PisEmptyProof [SOUND, 0 ms]
                (33) TRUE
            (34) QDP
                (35) NonTerminationLoopProof [COMPLETE, 11.6 s]
                (36) NO


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

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

   active(f(a, b, X)) -> mark(f(X, X, X))
   active(c) -> mark(a)
   active(c) -> mark(b)
   mark(f(X1, X2, X3)) -> active(f(mark(X1), X2, mark(X3)))
   mark(a) -> active(a)
   mark(b) -> active(b)
   mark(c) -> active(c)
   f(mark(X1), X2, X3) -> f(X1, X2, X3)
   f(X1, mark(X2), X3) -> f(X1, X2, X3)
   f(X1, X2, mark(X3)) -> f(X1, X2, X3)
   f(active(X1), X2, X3) -> f(X1, X2, X3)
   f(X1, active(X2), X3) -> f(X1, X2, X3)
   f(X1, X2, active(X3)) -> f(X1, X2, X3)

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:

   ACTIVE(f(a, b, X)) -> MARK(f(X, X, X))
   ACTIVE(f(a, b, X)) -> F(X, X, X)
   ACTIVE(c) -> MARK(a)
   ACTIVE(c) -> MARK(b)
   MARK(f(X1, X2, X3)) -> ACTIVE(f(mark(X1), X2, mark(X3)))
   MARK(f(X1, X2, X3)) -> F(mark(X1), X2, mark(X3))
   MARK(f(X1, X2, X3)) -> MARK(X1)
   MARK(f(X1, X2, X3)) -> MARK(X3)
   MARK(a) -> ACTIVE(a)
   MARK(b) -> ACTIVE(b)
   MARK(c) -> ACTIVE(c)
   F(mark(X1), X2, X3) -> F(X1, X2, X3)
   F(X1, mark(X2), X3) -> F(X1, X2, X3)
   F(X1, X2, mark(X3)) -> F(X1, X2, X3)

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