TRS Standard pair #615300327

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	n153.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	1.73049688339 seconds
cpu usage	4.383087288
max memory	2.64962048E8

stage attributes

key	value
output-size	5946
starexec-result	"YES"

output

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


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished


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

(0) QTRS
(1) QTRSToCSRProof [EQUIVALENT, 0 ms]
(2) CSR
(3) CSRRRRProof [EQUIVALENT, 26 ms]
(4) CSR
(5) CSRRRRProof [EQUIVALENT, 0 ms]
(6) CSR
(7) CSRRRRProof [EQUIVALENT, 2 ms]
(8) CSR
(9) RisEmptyProof [EQUIVALENT, 0 ms]
(10) YES


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(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))

Q is empty.

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

(1) QTRSToCSRProof (EQUIVALENT)
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))

Q is empty.
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:

f: {1}
if: {1, 2}
c: empty set
true: empty set
false: empty set
The QTRS contained all rules created by the complete Giesl-Middeldorp transformation. Therefore, the inverse transformation is complete (and sound).
----------------------------------------

(2)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   f(X) -> if(X, c, f(true))
   if(true, X, Y) -> X
   if(false, X, Y) -> Y

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