TRS Innermost pair #516979143

details

property	value
status	complete
benchmark	Ex24_GM04_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n065.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.1756670475 seconds
cpu usage	5.588750332
max memory	4.82504704E8

stage attributes

key	value
output-size	4897
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

(0) QTRS
(1) QTRSToCSRProof [SOUND, 0 ms]
(2) CSR
(3) CSRRRRProof [EQUIVALENT, 28 ms]
(4) CSR
(5) CSDependencyPairsProof [EQUIVALENT, 0 ms]
(6) QCSDP
(7) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(8) TRUE


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

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

   active(f(X, g(X), Y)) -> mark(f(Y, Y, Y))
   active(g(b)) -> mark(c)
   active(b) -> mark(c)
   active(g(X)) -> g(active(X))
   g(mark(X)) -> mark(g(X))
   proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3))
   proper(g(X)) -> g(proper(X))
   proper(b) -> ok(b)
   proper(c) -> ok(c)
   f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3))
   g(ok(X)) -> ok(g(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))

The set Q consists of the following terms:

   active(f(x0, g(x0), x1))
   active(b)
   active(g(x0))
   g(mark(x0))
   proper(f(x0, x1, x2))
   proper(g(x0))
   proper(b)
   proper(c)
   f(ok(x0), ok(x1), ok(x2))
   g(ok(x0))
   top(mark(x0))
   top(ok(x0))


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

(1) QTRSToCSRProof (SOUND)
The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:

   active(f(X, g(X), Y)) -> mark(f(Y, Y, Y))
   active(g(b)) -> mark(c)
   active(b) -> mark(c)
   active(g(X)) -> g(active(X))
   g(mark(X)) -> mark(g(X))
   proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3))
   proper(g(X)) -> g(proper(X))
   proper(b) -> ok(b)
   proper(c) -> ok(c)
   f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3))
   g(ok(X)) -> ok(g(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))

The set Q consists of the following terms:

   active(f(x0, g(x0), x1))
   active(b)
   active(g(x0))
   g(mark(x0))
   proper(f(x0, x1, x2))
   proper(g(x0))
   proper(b)
   proper(c)
   f(ok(x0), ok(x1), ok(x2))
   g(ok(x0))
   top(mark(x0))
   top(ok(x0))

Special symbols used for the transformation (see [GM04]):
top: top_1, active: active_1, mark: mark_1, ok: ok_1, proper: proper_1
The replacement map contains the following entries:

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job log

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actions all output return to TRS Innermost