SRS Standard pair #487089352

details

property	value
status	complete
benchmark	aprove3.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	Secret_05_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.90431 seconds
cpu usage	12.5353
user time	11.9415
system time	0.593783
max virtual memory	2.1011324E7
max residence set size	1594852.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) Overlay + Local Confluence [EQUIVALENT, 0 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) QReductionProof [EQUIVALENT, 2 ms]
        (13) QDP
        (14) QDPOrderProof [EQUIVALENT, 73 ms]
        (15) QDP
        (16) QDPOrderProof [EQUIVALENT, 78 ms]
        (17) QDP
        (18) DependencyGraphProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) UsableRulesProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) QReductionProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QDPOrderProof [EQUIVALENT, 12 ms]
        (25) QDP
        (26) PisEmptyProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) QDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) QReductionProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) QDPOrderProof [EQUIVALENT, 225 ms]
        (34) QDP
        (35) UsableRulesProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) QReductionProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (40) YES


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

   p(0(x1)) -> s(s(0(s(s(p(x1))))))
   p(s(0(x1))) -> 0(x1)
   p(s(s(x1))) -> s(p(s(x1)))
   f(s(x1)) -> g(q(i(x1)))
   g(x1) -> f(p(p(x1)))
   q(i(x1)) -> q(s(x1))
   q(s(x1)) -> s(s(x1))
   i(x1) -> s(x1)

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:

   0(p(x1)) -> p(s(s(0(s(s(x1))))))
   0(s(p(x1))) -> 0(x1)
   s(s(p(x1))) -> s(p(s(x1)))
   s(f(x1)) -> i(q(g(x1)))
   g(x1) -> p(p(f(x1)))
   i(q(x1)) -> s(q(x1))
   s(q(x1)) -> s(s(x1))
   i(x1) -> s(x1)

Q is empty.

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(3) Overlay + Local Confluence (EQUIVALENT)
The TRS is overlay and locally confluent. By [NOC] we can switch to innermost.
----------------------------------------

(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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job log

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