TRS Standard pair #487068863

details

property	value
status	complete
benchmark	Liveness6.3.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n071.star.cs.uiowa.edu
space	AProVE_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.73036 seconds
cpu usage	11.5876
user time	11.086
system time	0.501675
max virtual memory	4.1956252E7
max residence set size	1312080.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 30 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 12 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) MRRProof [EQUIVALENT, 17 ms]
        (33) QDP
        (34) UsableRulesProof [EQUIVALENT, 0 ms]
        (35) QDP
        (36) QDPOrderProof [EQUIVALENT, 7 ms]
        (37) QDP
        (38) PisEmptyProof [EQUIVALENT, 0 ms]
        (39) YES


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

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

   rec(rec(x)) -> sent(rec(x))
   rec(sent(x)) -> sent(rec(x))
   rec(no(x)) -> sent(rec(x))
   rec(bot) -> up(sent(bot))
   rec(up(x)) -> up(rec(x))
   sent(up(x)) -> up(sent(x))
   no(up(x)) -> up(no(x))
   top(rec(up(x))) -> top(check(rec(x)))
   top(sent(up(x))) -> top(check(rec(x)))
   top(no(up(x))) -> top(check(rec(x)))
   check(up(x)) -> up(check(x))
   check(sent(x)) -> sent(check(x))
   check(rec(x)) -> rec(check(x))
   check(no(x)) -> no(check(x))
   check(no(x)) -> no(x)

Q is empty.

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

(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   rec(rec(x)) -> rec(sent(x))
   sent(rec(x)) -> rec(sent(x))
   no(rec(x)) -> rec(sent(x))
   bot'(rec(x)) -> bot'(sent(up(x)))
   up(rec(x)) -> rec(up(x))
   up(sent(x)) -> sent(up(x))
   up(no(x)) -> no(up(x))
   up(rec(top(x))) -> rec(check(top(x)))
   up(sent(top(x))) -> rec(check(top(x)))
   up(no(top(x))) -> rec(check(top(x)))
   up(check(x)) -> check(up(x))
   sent(check(x)) -> check(sent(x))
   rec(check(x)) -> check(rec(x))
   no(check(x)) -> check(no(x))
   no(check(x)) -> no(x)

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