SRS Standard pair #487089298

details

property	value
status	complete
benchmark	aprove1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	Secret_05_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.93154 seconds
cpu usage	16.3278
user time	15.6288
system time	0.69899
max virtual memory	6.2197468E7
max residence set size	1885280.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) DependencyPairsProof [EQUIVALENT, 26 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) UsableRulesProof [EQUIVALENT, 0 ms]
        (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES
    (15) QDP
        (16) UsableRulesProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) MRRProof [EQUIVALENT, 28 ms]
        (19) QDP
        (20) MNOCProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) QDPOrderProof [EQUIVALENT, 18 ms]
        (25) QDP
        (26) PisEmptyProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) QDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) QDP
        (31) MRRProof [EQUIVALENT, 36 ms]
        (32) QDP
        (33) MNOCProof [EQUIVALENT, 0 ms]
        (34) QDP
        (35) UsableRulesProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) QDPOrderProof [EQUIVALENT, 106 ms]
        (38) QDP
        (39) DependencyGraphProof [EQUIVALENT, 0 ms]
        (40) TRUE


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

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

   p(0(x1)) -> 0(s(s(p(x1))))
   p(s(x1)) -> x1
   p(p(s(x1))) -> p(x1)
   f(s(x1)) -> g(s(x1))
   g(x1) -> i(s(half(x1)))
   i(x1) -> f(p(x1))
   half(0(x1)) -> 0(s(s(half(x1))))
   half(s(s(x1))) -> s(half(p(p(s(s(x1))))))
   0(x1) -> x1
   rd(0(x1)) -> 0(0(0(0(0(0(rd(x1)))))))

Q is empty.

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

(1) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(2)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   P(0(x1)) -> 0^1(s(s(p(x1))))
   P(0(x1)) -> P(x1)
   P(p(s(x1))) -> P(x1)
   F(s(x1)) -> G(s(x1))
   G(x1) -> I(s(half(x1)))
   G(x1) -> HALF(x1)
   I(x1) -> F(p(x1))
   I(x1) -> P(x1)
   HALF(0(x1)) -> 0^1(s(s(half(x1))))
   HALF(0(x1)) -> HALF(x1)
   HALF(s(s(x1))) -> HALF(p(p(s(s(x1)))))
   HALF(s(s(x1))) -> P(p(s(s(x1))))
   HALF(s(s(x1))) -> P(s(s(x1)))
   RD(0(x1)) -> 0^1(0(0(0(0(0(rd(x1)))))))
   RD(0(x1)) -> 0^1(0(0(0(0(rd(x1))))))
   RD(0(x1)) -> 0^1(0(0(0(rd(x1)))))
   RD(0(x1)) -> 0^1(0(0(rd(x1))))
   RD(0(x1)) -> 0^1(0(rd(x1)))
   RD(0(x1)) -> 0^1(rd(x1))

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