SRS Stand 10685 pair #381717455

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	n025.star.cs.uiowa.edu
space	Secret_05_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.4997420311 seconds
cpu usage	22.569573109
max memory	3.681480704E9

stage attributes

key	value
output-size	17284
starexec-result	YES

output

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


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 9 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPOrderProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) PisEmptyProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) UsableRulesProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (16) YES
    (17) QDP
        (18) UsableRulesProof [EQUIVALENT, 0 ms]
        (19) QDP
        (20) MRRProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) MNOCProof [EQUIVALENT, 0 ms]
        (23) QDP
        (24) UsableRulesProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QDPOrderProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) PisEmptyProof [EQUIVALENT, 0 ms]
        (29) YES
    (30) QDP
        (31) UsableRulesProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) MRRProof [EQUIVALENT, 14 ms]
        (34) QDP
        (35) MNOCProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) UsableRulesProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) QDPOrderProof [EQUIVALENT, 145 ms]
        (40) QDP
        (41) DependencyGraphProof [EQUIVALENT, 0 ms]
        (42) 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)))))

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