TRS Standard pair #487069533

details

property	value
status	complete
benchmark	Ex1_Luc04b_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	AProVE
configuration	standard
runtime (wallclock)	3.49585 seconds
cpu usage	19.9196
user time	19.1135
system time	0.806048
max virtual memory	1.9093148E7
max residence set size	623744.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 125 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 25 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 9 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) QDP
        (20) UsableRulesProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (23) YES
    (24) QDP
        (25) UsableRulesProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (28) YES
    (29) QDP
        (30) UsableRulesProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (33) YES
    (34) QDP
        (35) MRRProof [EQUIVALENT, 6 ms]
        (36) QDP
        (37) MRRProof [EQUIVALENT, 40 ms]
        (38) QDP
        (39) QDPOrderProof [EQUIVALENT, 69 ms]
        (40) QDP
        (41) DependencyGraphProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) QDPOrderProof [EQUIVALENT, 66 ms]
        (44) QDP
        (45) QDPOrderProof [EQUIVALENT, 21 ms]
        (46) QDP
        (47) QDPOrderProof [EQUIVALENT, 0 ms]
        (48) QDP
        (49) UsableRulesProof [EQUIVALENT, 0 ms]
        (50) QDP
        (51) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (52) YES


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

   active(nats) -> mark(cons(0, incr(nats)))
   active(pairs) -> mark(cons(0, incr(odds)))
   active(odds) -> mark(incr(pairs))
   active(incr(cons(X, XS))) -> mark(cons(s(X), incr(XS)))
   active(head(cons(X, XS))) -> mark(X)
   active(tail(cons(X, XS))) -> mark(XS)
   mark(nats) -> active(nats)
   mark(cons(X1, X2)) -> active(cons(mark(X1), X2))
   mark(0) -> active(0)
   mark(incr(X)) -> active(incr(mark(X)))
   mark(pairs) -> active(pairs)
   mark(odds) -> active(odds)
   mark(s(X)) -> active(s(mark(X)))
   mark(head(X)) -> active(head(mark(X)))
   mark(tail(X)) -> active(tail(mark(X)))
   cons(mark(X1), X2) -> cons(X1, X2)
   cons(X1, mark(X2)) -> cons(X1, X2)
   cons(active(X1), X2) -> cons(X1, X2)
   cons(X1, active(X2)) -> cons(X1, X2)
   incr(mark(X)) -> incr(X)
   incr(active(X)) -> incr(X)
   s(mark(X)) -> s(X)
   s(active(X)) -> s(X)
   head(mark(X)) -> head(X)
   head(active(X)) -> head(X)
   tail(mark(X)) -> tail(X)
   tail(active(X)) -> tail(X)

Q is empty.

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