TRS Inner 89993 pair #381734049

details

property	value
status	complete
benchmark	Ex4_7_56_Bor03_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n081.star.cs.uiowa.edu
space	Transformed_CSR_innermost_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.69309806824 seconds
cpu usage	3.610290551
max memory	2.21851648E8

stage attributes

key	value
output-size	10315
starexec-result	YES

output

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


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


YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) CSRInnermostProof [EQUIVALENT, 0 ms]
(4) CSR
(5) CSDependencyPairsProof [EQUIVALENT, 0 ms]
(6) QCSDP
(7) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QCSDP
        (10) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (11) QCSDP
        (12) PIsEmptyProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QCSDP
        (15) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (16) QCSDP
        (17) PIsEmptyProof [EQUIVALENT, 0 ms]
        (18) YES


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

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

   active(from(X)) -> mark(cons(X, from(s(X))))
   active(after(0, XS)) -> mark(XS)
   active(after(s(N), cons(X, XS))) -> mark(after(N, XS))
   active(from(X)) -> from(active(X))
   active(cons(X1, X2)) -> cons(active(X1), X2)
   active(s(X)) -> s(active(X))
   active(after(X1, X2)) -> after(active(X1), X2)
   active(after(X1, X2)) -> after(X1, active(X2))
   from(mark(X)) -> mark(from(X))
   cons(mark(X1), X2) -> mark(cons(X1, X2))
   s(mark(X)) -> mark(s(X))
   after(mark(X1), X2) -> mark(after(X1, X2))
   after(X1, mark(X2)) -> mark(after(X1, X2))
   proper(from(X)) -> from(proper(X))
   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
   proper(s(X)) -> s(proper(X))
   proper(after(X1, X2)) -> after(proper(X1), proper(X2))
   proper(0) -> ok(0)
   from(ok(X)) -> ok(from(X))
   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
   s(ok(X)) -> ok(s(X))
   after(ok(X1), ok(X2)) -> ok(after(X1, X2))
   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(s(x0))
   active(after(x0, x1))
   from(mark(x0))
   cons(mark(x0), x1)
   s(mark(x0))
   after(mark(x0), x1)
   after(x0, mark(x1))
   proper(from(x0))
   proper(cons(x0, x1))
   proper(s(x0))
   proper(after(x0, x1))
   proper(0)
   from(ok(x0))
   cons(ok(x0), ok(x1))
   s(ok(x0))
   after(ok(x0), ok(x1))
   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(from(X)) -> mark(cons(X, from(s(X))))
   active(after(0, XS)) -> mark(XS)
   active(after(s(N), cons(X, XS))) -> mark(after(N, XS))
   active(from(X)) -> from(active(X))

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