TRS Outer 67415 pair #381918070

details

property	value
status	complete
benchmark	toyama_stop.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n037.star.cs.uiowa.edu
space	Zantema_08

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	50.4682271481 seconds
cpu usage	141.193045852
max memory	4.44178432E9

stage attributes

key	value
output-size	105062
starexec-result	YES

output

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


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YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 22 ms]
        (18) QDP
        (19) SplitQDPProof [EQUIVALENT, 0 ms]
        (20) AND
            (21) QDP
                (22) SemLabProof [SOUND, 0 ms]
                (23) QDP
                (24) DependencyGraphProof [EQUIVALENT, 0 ms]
                (25) QDP
                (26) QDPOrderProof [EQUIVALENT, 21 ms]
                (27) QDP
                (28) PisEmptyProof [SOUND, 0 ms]
                (29) TRUE
            (30) QDP
                (31) SemLabProof [SOUND, 2990 ms]
                (32) QDP
                (33) DependencyGraphProof [EQUIVALENT, 0 ms]
                (34) QDP
                (35) QDPOrderProof [EQUIVALENT, 0 ms]
                (36) QDP
                (37) PisEmptyProof [EQUIVALENT, 0 ms]
                (38) YES


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

   f(g(u, v), y, z) -> c
   f(0, 1, x) -> f(x, x, x)
   g(x, y) -> x
   g(x, y) -> y
   f(f(x, y, z), u, v) -> c
   f(0, u, v) -> c



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(f(g(u, v), y, z)) -> up(c)
   down(f(0, 1, x)) -> up(f(x, x, x))
   down(g(x, y)) -> up(x)
   down(g(x, y)) -> up(y)
   down(f(f(x, y, z), u, v)) -> up(c)
   down(f(0, u, v)) -> up(c)
   top(up(x)) -> top(down(x))
   down(f(c, y17, y18)) -> f_flat(down(c), block(y17), block(y18))
   down(f(c, y17, y18)) -> f_flat(block(c), down(y17), block(y18))
   down(f(c, y17, y18)) -> f_flat(block(c), block(y17), down(y18))
   down(f(1, y21, y22)) -> f_flat(down(1), block(y21), block(y22))
   down(f(1, y21, y22)) -> f_flat(block(1), down(y21), block(y22))
   down(f(1, y21, y22)) -> f_flat(block(1), block(y21), down(y22))
   down(f(fresh_constant, y23, y24)) -> f_flat(down(fresh_constant), block(y23), block(y24))
   down(f(fresh_constant, y23, y24)) -> f_flat(block(fresh_constant), down(y23), block(y24))
   down(f(fresh_constant, y23, y24)) -> f_flat(block(fresh_constant), block(y23), down(y24))
   f_flat(up(x_1), block(x_2), block(x_3)) -> up(f(x_1, x_2, x_3))

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actions all output return to TRS Outer 67415