TRS Innermost pair #516979279

details

property	value
status	complete
benchmark	Ex2_Luc03b_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n089.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.28977012634 seconds
cpu usage	6.000803441
max memory	4.76000256E8

stage attributes

key	value
output-size	8708
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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, 74 ms]
(4) CSR
(5) CSRRRRProof [EQUIVALENT, 11 ms]
(6) CSR
(7) RisEmptyProof [EQUIVALENT, 0 ms]
(8) YES


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

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

   active(fst(0, Z)) -> mark(nil)
   active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z)))
   active(from(X)) -> mark(cons(X, from(s(X))))
   active(add(0, X)) -> mark(X)
   active(add(s(X), Y)) -> mark(s(add(X, Y)))
   active(len(nil)) -> mark(0)
   active(len(cons(X, Z))) -> mark(s(len(Z)))
   active(cons(X1, X2)) -> cons(active(X1), X2)
   active(fst(X1, X2)) -> fst(active(X1), X2)
   active(fst(X1, X2)) -> fst(X1, active(X2))
   active(from(X)) -> from(active(X))
   active(add(X1, X2)) -> add(active(X1), X2)
   active(add(X1, X2)) -> add(X1, active(X2))
   active(len(X)) -> len(active(X))
   cons(mark(X1), X2) -> mark(cons(X1, X2))
   fst(mark(X1), X2) -> mark(fst(X1, X2))
   fst(X1, mark(X2)) -> mark(fst(X1, X2))
   from(mark(X)) -> mark(from(X))
   add(mark(X1), X2) -> mark(add(X1, X2))
   add(X1, mark(X2)) -> mark(add(X1, X2))
   len(mark(X)) -> mark(len(X))
   proper(0) -> ok(0)
   proper(s(X)) -> s(proper(X))
   proper(nil) -> ok(nil)
   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
   proper(fst(X1, X2)) -> fst(proper(X1), proper(X2))
   proper(from(X)) -> from(proper(X))
   proper(add(X1, X2)) -> add(proper(X1), proper(X2))
   proper(len(X)) -> len(proper(X))
   s(ok(X)) -> ok(s(X))
   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
   fst(ok(X1), ok(X2)) -> ok(fst(X1, X2))
   from(ok(X)) -> ok(from(X))
   add(ok(X1), ok(X2)) -> ok(add(X1, X2))
   len(ok(X)) -> ok(len(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))

The set Q consists of the following terms:

   active(from(x0))
   active(cons(x0, x1))
   active(fst(x0, x1))
   active(add(x0, x1))
   active(len(x0))
   cons(mark(x0), x1)
   fst(mark(x0), x1)
   fst(x0, mark(x1))
   from(mark(x0))
   add(mark(x0), x1)
   add(x0, mark(x1))
   len(mark(x0))
   proper(0)
   proper(s(x0))
   proper(nil)
   proper(cons(x0, x1))
   proper(fst(x0, x1))
   proper(from(x0))
   proper(add(x0, x1))
   proper(len(x0))
   s(ok(x0))
   cons(ok(x0), ok(x1))
   fst(ok(x0), ok(x1))
   from(ok(x0))
   add(ok(x0), ok(x1))
   len(ok(x0))
   top(mark(x0))
   top(ok(x0))

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