TRS Outer 67415 pair #381918107

details

property	value
status	complete
benchmark	Ex1_GL02a_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n027.star.cs.uiowa.edu
space	Strategy_outermost_added_08

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	27.8313639164 seconds
cpu usage	108.50859045
max memory	6.214631424E9

stage attributes

key	value
output-size	42436
starexec-result	YES

output

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


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


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Outermost Termination of the given OTRS could be proven:

(0) OTRS
(1) Raffelsieper-Zantema-Transformation [SOUND, 0 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 0 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) TransformationProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) DependencyGraphProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPOrderProof [EQUIVALENT, 28 ms]
        (18) QDP
        (19) DependencyGraphProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QDPOrderProof [EQUIVALENT, 25 ms]
        (22) QDP
        (23) QDPOrderProof [EQUIVALENT, 5887 ms]
        (24) QDP
        (25) PisEmptyProof [EQUIVALENT, 0 ms]
        (26) YES


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

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

   eq(n__0, n__0) -> true
   eq(n__s(X), n__s(Y)) -> eq(activate(X), activate(Y))
   eq(X, Y) -> false
   inf(X) -> cons(X, n__inf(s(X)))
   take(0, X) -> nil
   take(s(X), cons(Y, L)) -> cons(activate(Y), n__take(activate(X), activate(L)))
   length(nil) -> 0
   length(cons(X, L)) -> s(n__length(activate(L)))
   0 -> n__0
   s(X) -> n__s(X)
   inf(X) -> n__inf(X)
   take(X1, X2) -> n__take(X1, X2)
   length(X) -> n__length(X)
   activate(n__0) -> 0
   activate(n__s(X)) -> s(X)
   activate(n__inf(X)) -> inf(X)
   activate(n__take(X1, X2)) -> take(X1, X2)
   activate(n__length(X)) -> length(X)
   activate(X) -> X



Outermost Strategy.

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

(1) Raffelsieper-Zantema-Transformation (SOUND)
We applied the Raffelsieper-Zantema transformation  to transform the outermost TRS to a standard TRS.
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   down(eq(n__0, n__0)) -> up(true)
   down(eq(n__s(X), n__s(Y))) -> up(eq(activate(X), activate(Y)))
   down(eq(X, Y)) -> up(false)
   down(inf(X)) -> up(cons(X, n__inf(s(X))))
   down(take(0, X)) -> up(nil)
   down(take(s(X), cons(Y, L))) -> up(cons(activate(Y), n__take(activate(X), activate(L))))
   down(length(nil)) -> up(0)
   down(length(cons(X, L))) -> up(s(n__length(activate(L))))
   down(0) -> up(n__0)
   down(s(X)) -> up(n__s(X))
   down(inf(X)) -> up(n__inf(X))
   down(take(X1, X2)) -> up(n__take(X1, X2))
   down(length(X)) -> up(n__length(X))
   down(activate(n__0)) -> up(0)
   down(activate(n__s(X))) -> up(s(X))
   down(activate(n__inf(X))) -> up(inf(X))

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Outer 67415