TRS Standard pair #516963935

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	n061.star.cs.uiowa.edu
space	AProVE_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	5.15600895882 seconds
cpu usage	16.987145052
max memory	1.210990592E9

stage attributes

key	value
output-size	17140
starexec-result	YES

output

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


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YES
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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 proven:

(0) QTRS
(1) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 48 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 0 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, 12 ms]
        (33) QDP
        (34) UsableRulesProof [EQUIVALENT, 0 ms]
        (35) QDP
        (36) QDPOrderProof [EQUIVALENT, 6 ms]
        (37) QDP
        (38) PisEmptyProof [EQUIVALENT, 0 ms]
        (39) YES


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(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)))

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