TRS Innermost pair #487524065

details

property	value
status	complete
benchmark	Ex25_Luc06_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.70545291901 seconds
cpu usage	3.890514429
max memory	2.80621056E8

stage attributes

key	value
output-size	8994
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) QTRS
(1) QTRS Reverse [SOUND, 0 ms]
(2) QTRS
(3) RFCMatchBoundsTRSProof [EQUIVALENT, 4 ms]
(4) YES


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

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

   active(f(f(X))) -> mark(c(f(g(f(X)))))
   active(c(X)) -> mark(d(X))
   active(h(X)) -> mark(c(d(X)))
   active(f(X)) -> f(active(X))
   active(h(X)) -> h(active(X))
   f(mark(X)) -> mark(f(X))
   h(mark(X)) -> mark(h(X))
   proper(f(X)) -> f(proper(X))
   proper(c(X)) -> c(proper(X))
   proper(g(X)) -> g(proper(X))
   proper(d(X)) -> d(proper(X))
   proper(h(X)) -> h(proper(X))
   f(ok(X)) -> ok(f(X))
   c(ok(X)) -> ok(c(X))
   g(ok(X)) -> ok(g(X))
   d(ok(X)) -> ok(d(X))
   h(ok(X)) -> ok(h(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))

The set Q consists of the following terms:

   active(c(x0))
   active(h(x0))
   active(f(x0))
   f(mark(x0))
   h(mark(x0))
   proper(f(x0))
   proper(c(x0))
   proper(g(x0))
   proper(d(x0))
   proper(h(x0))
   f(ok(x0))
   c(ok(x0))
   g(ok(x0))
   d(ok(x0))
   h(ok(x0))
   top(mark(x0))
   top(ok(x0))


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

(1) QTRS Reverse (SOUND)
We applied the QTRS Reverse Processor [REVERSE].
----------------------------------------

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

   f(f(active(X))) -> f(g(f(c(mark(X)))))
   c(active(X)) -> d(mark(X))
   h(active(X)) -> d(c(mark(X)))
   f(active(X)) -> active(f(X))
   h(active(X)) -> active(h(X))
   mark(f(X)) -> f(mark(X))
   mark(h(X)) -> h(mark(X))
   f(proper(X)) -> proper(f(X))
   c(proper(X)) -> proper(c(X))
   g(proper(X)) -> proper(g(X))
   d(proper(X)) -> proper(d(X))
   h(proper(X)) -> proper(h(X))
   ok(f(X)) -> f(ok(X))
   ok(c(X)) -> c(ok(X))
   ok(g(X)) -> g(ok(X))
   ok(d(X)) -> d(ok(X))
   ok(h(X)) -> h(ok(X))
   mark(top(X)) -> proper(top(X))
   ok(top(X)) -> active(top(X))

Q is empty.

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Innermost