TRS Standard pair #487072098

details

property	value
status	complete
benchmark	Ex6_15_AEL02.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n070.star.cs.uiowa.edu
space	Strategy_removed_CSR_05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.37424 seconds
cpu usage	5.60959
user time	5.32285
system time	0.286736
max virtual memory	2.0076088E7
max residence set size	444188.0

stage attributes

key	value
starexec-result	NO

output

NO
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 disproven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 0 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) MNOCProof [EQUIVALENT, 14 ms]
        (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QReductionProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) MNOCProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) UsableRulesProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QReductionProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) QDP
        (24) UsableRulesProof [EQUIVALENT, 2 ms]
        (25) QDP
        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) QDP
        (29) MNOCProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) UsableRulesProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) QReductionProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (36) YES
    (37) QDP
        (38) MNOCProof [EQUIVALENT, 5 ms]
        (39) QDP
        (40) UsableRulesProof [EQUIVALENT, 0 ms]
        (41) QDP
        (42) QReductionProof [EQUIVALENT, 0 ms]
        (43) QDP
        (44) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (45) YES
    (46) QDP
        (47) MNOCProof [EQUIVALENT, 3 ms]
        (48) QDP
        (49) UsableRulesProof [EQUIVALENT, 0 ms]
        (50) QDP
        (51) QReductionProof [EQUIVALENT, 0 ms]
        (52) QDP
        (53) TransformationProof [EQUIVALENT, 0 ms]
        (54) QDP
        (55) TransformationProof [EQUIVALENT, 0 ms]
        (56) QDP
        (57) NonTerminationLoopProof [COMPLETE, 0 ms]
        (58) NO
    (59) QDP
        (60) MNOCProof [EQUIVALENT, 5 ms]
        (61) QDP
        (62) UsableRulesProof [EQUIVALENT, 0 ms]
        (63) QDP
        (64) QReductionProof [EQUIVALENT, 0 ms]
        (65) QDP
        (66) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (67) YES
    (68) QDP
        (69) MNOCProof [EQUIVALENT, 3 ms]
        (70) QDP
        (71) UsableRulesProof [EQUIVALENT, 0 ms]
        (72) QDP
        (73) QReductionProof [EQUIVALENT, 0 ms]
        (74) QDP
        (75) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (76) YES


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

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

   sel(s(X), cons(Y, Z)) -> sel(X, Z)
   sel(0, cons(X, Z)) -> X
   first(0, Z) -> nil
   first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
   from(X) -> cons(X, from(s(X)))
   sel1(s(X), cons(Y, Z)) -> sel1(X, Z)
   sel1(0, cons(X, Z)) -> quote(X)

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actions all output return to TRS Standard