TRS Stand 20472 pair #381711309

details

property	value
status	complete
benchmark	while.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n101.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.5447537899 seconds
cpu usage	4.73221774
max memory	2.61341184E8

stage attributes

key	value
output-size	9508
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) QTRS
(1) AAECC Innermost [EQUIVALENT, 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) QReductionProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QReductionProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) NonInfProof [EQUIVALENT, 52 ms]
        (20) QDP
        (21) PisEmptyProof [EQUIVALENT, 0 ms]
        (22) YES


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

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

   f(t, x, y) -> f(g(x, y), x, s(y))
   g(s(x), 0) -> t
   g(s(x), s(y)) -> g(x, y)

Q is empty.

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

(1) AAECC Innermost (EQUIVALENT)
We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 
   g(s(x), 0) -> t
   g(s(x), s(y)) -> g(x, y)

The TRS R 2 is 
   f(t, x, y) -> f(g(x, y), x, s(y))

The signature Sigma is {f_3}
----------------------------------------

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

   f(t, x, y) -> f(g(x, y), x, s(y))
   g(s(x), 0) -> t
   g(s(x), s(y)) -> g(x, y)

The set Q consists of the following terms:

   f(t, x0, x1)
   g(s(x0), 0)
   g(s(x0), s(x1))


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

(3) DependencyPairsProof (EQUIVALENT)
Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
----------------------------------------

(4)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   F(t, x, y) -> F(g(x, y), x, s(y))
   F(t, x, y) -> G(x, y)
   G(s(x), s(y)) -> G(x, y)

The TRS R consists of the following rules:

   f(t, x, y) -> f(g(x, y), x, s(y))
   g(s(x), 0) -> t
   g(s(x), s(y)) -> g(x, y)

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