TRS Outer 67415 pair #381917989

details

property	value
status	complete
benchmark	fg.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n033.star.cs.uiowa.edu
space	Zantema_08

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.4171500206 seconds
cpu usage	4.110264673
max memory	2.33816064E8

stage attributes

key	value
output-size	16963
starexec-result	YES

output

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


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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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) QTRSRRRProof [EQUIVALENT, 52 ms]
(4) QTRS
(5) AAECC Innermost [EQUIVALENT, 0 ms]
(6) QTRS
(7) DependencyPairsProof [EQUIVALENT, 0 ms]
(8) QDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) QDP
        (12) UsableRulesProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) QReductionProof [EQUIVALENT, 0 ms]
        (15) QDP
        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) QDP
        (19) UsableRulesProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QReductionProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) QDP
        (26) UsableRulesProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) QReductionProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) RFCMatchBoundsDPProof [EQUIVALENT, 0 ms]
        (31) YES


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

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

   f(g(x)) -> x
   g(b) -> f(g(b))



Outermost Strategy.

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(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(x))) -> up(x)
   down(g(b)) -> up(f(g(b)))
   top(up(x)) -> top(down(x))
   down(f(f(y3))) -> f_flat(down(f(y3)))
   down(f(b)) -> f_flat(down(b))
   down(f(fresh_constant)) -> f_flat(down(fresh_constant))
   down(g(f(y6))) -> g_flat(down(f(y6)))
   down(g(g(y7))) -> g_flat(down(g(y7)))
   down(g(fresh_constant)) -> g_flat(down(fresh_constant))
   f_flat(up(x_1)) -> up(f(x_1))
   g_flat(up(x_1)) -> up(g(x_1))

Q is empty.

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(3) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(b) = 0
   POL(down(x_1)) = 2 + 2*x_1
   POL(f(x_1)) = x_1
   POL(f_flat(x_1)) = x_1
   POL(fresh_constant) = 1
   POL(g(x_1)) = 1 + 2*x_1
   POL(g_flat(x_1)) = 2*x_1
   POL(top(x_1)) = x_1

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