TRS Inner 89993 pair #381733865

details

property	value
status	complete
benchmark	Ex14_AEGL02_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n014.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.13062000275 seconds
cpu usage	5.232765291
max memory	3.65469696E8

stage attributes

key	value
output-size	10768
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 30 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QReductionProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) QDPQMonotonicMRRProof [EQUIVALENT, 40 ms]
        (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QReductionProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES


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

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

   a__from(X) -> cons(mark(X), from(s(X)))
   a__length(nil) -> 0
   a__length(cons(X, Y)) -> s(a__length1(Y))
   a__length1(X) -> a__length(X)
   mark(from(X)) -> a__from(mark(X))
   mark(length(X)) -> a__length(X)
   mark(length1(X)) -> a__length1(X)
   mark(cons(X1, X2)) -> cons(mark(X1), X2)
   mark(s(X)) -> s(mark(X))
   mark(nil) -> nil
   mark(0) -> 0
   a__from(X) -> from(X)
   a__length(X) -> length(X)
   a__length1(X) -> length1(X)

The set Q consists of the following terms:

   a__from(x0)
   a__length1(x0)
   mark(from(x0))
   mark(length(x0))
   mark(length1(x0))
   mark(cons(x0, x1))
   mark(s(x0))
   mark(nil)
   mark(0)
   a__length(x0)


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

(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:

   A__FROM(X) -> MARK(X)
   A__LENGTH(cons(X, Y)) -> A__LENGTH1(Y)
   A__LENGTH1(X) -> A__LENGTH(X)
   MARK(from(X)) -> A__FROM(mark(X))
   MARK(from(X)) -> MARK(X)
   MARK(length(X)) -> A__LENGTH(X)
   MARK(length1(X)) -> A__LENGTH1(X)
   MARK(cons(X1, X2)) -> MARK(X1)
   MARK(s(X)) -> MARK(X)

The TRS R consists of the following rules:

   a__from(X) -> cons(mark(X), from(s(X)))
   a__length(nil) -> 0
   a__length(cons(X, Y)) -> s(a__length1(Y))
   a__length1(X) -> a__length(X)
   mark(from(X)) -> a__from(mark(X))

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