TRS Innermost pair #487093285

details

property	value
status	complete
benchmark	ExIntrod_GM01_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.76151 seconds
cpu usage	11.0542
user time	10.6222
system time	0.431947
max virtual memory	3.9371292E7
max residence set size	754008.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRSRRRProof [EQUIVALENT, 110 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 29 ms]
(4) QTRS
(5) QTRSRRRProof [EQUIVALENT, 23 ms]
(6) QTRS
(7) DependencyPairsProof [EQUIVALENT, 1 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QDP
        (12) UsableRulesProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) QReductionProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) QDP
        (19) UsableRulesProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QReductionProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPSizeChangeProof [EQUIVALENT, 2 ms]
        (24) YES
    (25) QDP
        (26) UsableRulesProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) QReductionProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (31) YES
    (32) QDP
        (33) UsableRulesProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) QReductionProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (38) YES
    (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) UsableRulesProof [EQUIVALENT, 0 ms]
        (48) QDP
        (49) QReductionProof [EQUIVALENT, 0 ms]
        (50) QDP
        (51) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (52) YES
    (53) QDP
        (54) MRRProof [EQUIVALENT, 40 ms]
        (55) QDP
        (56) MRRProof [EQUIVALENT, 61 ms]
        (57) QDP
        (58) MRRProof [EQUIVALENT, 46 ms]
        (59) QDP
        (60) QDPOrderProof [EQUIVALENT, 58 ms]
        (61) QDP
        (62) DependencyGraphProof [EQUIVALENT, 0 ms]
        (63) QDP
        (64) QDPOrderProof [EQUIVALENT, 27 ms]
        (65) QDP
        (66) QDPOrderProof [EQUIVALENT, 32 ms]
        (67) QDP
        (68) DependencyGraphProof [EQUIVALENT, 0 ms]
        (69) QDP
        (70) UsableRulesProof [EQUIVALENT, 0 ms]
        (71) QDP
        (72) QReductionProof [EQUIVALENT, 0 ms]
        (73) QDP
        (74) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (75) YES


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

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

   active(incr(nil)) -> mark(nil)
   active(incr(cons(X, L))) -> mark(cons(s(X), incr(L)))
   active(adx(nil)) -> mark(nil)
   active(adx(cons(X, L))) -> mark(incr(cons(X, adx(L))))
   active(nats) -> mark(adx(zeros))
   active(zeros) -> mark(cons(0, zeros))
   active(head(cons(X, L))) -> mark(X)
   active(tail(cons(X, L))) -> mark(L)

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actions all output return to TRS Innermost