TRS Inner 89993 pair #381733721

details

property	value
status	complete
benchmark	Ex5_Zan97_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n004.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.61286282539 seconds
cpu usage	3.602977461
max memory	2.30178816E8

stage attributes

key	value
output-size	6583
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) QTRS
(1) QTRSToCSRProof [SOUND, 0 ms]
(2) CSR
(3) CSRRRRProof [EQUIVALENT, 21 ms]
(4) CSR
(5) CSRRRRProof [EQUIVALENT, 0 ms]
(6) CSR
(7) CSRRRRProof [EQUIVALENT, 0 ms]
(8) CSR
(9) RisEmptyProof [EQUIVALENT, 0 ms]
(10) YES


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

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

   active(f(X)) -> mark(if(X, c, f(true)))
   active(if(true, X, Y)) -> mark(X)
   active(if(false, X, Y)) -> mark(Y)
   active(f(X)) -> f(active(X))
   active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
   active(if(X1, X2, X3)) -> if(X1, active(X2), X3)
   f(mark(X)) -> mark(f(X))
   if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
   if(X1, mark(X2), X3) -> mark(if(X1, X2, X3))
   proper(f(X)) -> f(proper(X))
   proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
   proper(c) -> ok(c)
   proper(true) -> ok(true)
   proper(false) -> ok(false)
   f(ok(X)) -> ok(f(X))
   if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))

The set Q consists of the following terms:

   active(f(x0))
   active(if(x0, x1, x2))
   f(mark(x0))
   if(mark(x0), x1, x2)
   if(x0, mark(x1), x2)
   proper(f(x0))
   proper(if(x0, x1, x2))
   proper(c)
   proper(true)
   proper(false)
   f(ok(x0))
   if(ok(x0), ok(x1), ok(x2))
   top(mark(x0))
   top(ok(x0))


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

   active(f(X)) -> mark(if(X, c, f(true)))
   active(if(true, X, Y)) -> mark(X)
   active(if(false, X, Y)) -> mark(Y)
   active(f(X)) -> f(active(X))
   active(if(X1, X2, X3)) -> if(active(X1), X2, X3)
   active(if(X1, X2, X3)) -> if(X1, active(X2), X3)
   f(mark(X)) -> mark(f(X))
   if(mark(X1), X2, X3) -> mark(if(X1, X2, X3))
   if(X1, mark(X2), X3) -> mark(if(X1, X2, X3))
   proper(f(X)) -> f(proper(X))
   proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3))
   proper(c) -> ok(c)
   proper(true) -> ok(true)
   proper(false) -> ok(false)
   f(ok(X)) -> ok(f(X))
   if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))

The set Q consists of the following terms:

   active(f(x0))
   active(if(x0, x1, x2))
   f(mark(x0))

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