TRS Standard pair #516963305

details

property	value
status	complete
benchmark	Ex4_Zan97_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n048.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.44096803665 seconds
cpu usage	6.134371938
max memory	4.81263616E8

stage attributes

key	value
output-size	11942
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

(0) QTRS
(1) QTRSToCSRProof [EQUIVALENT, 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
    (19) QCSDP
        (20) QCSDPSubtermProof [EQUIVALENT, 0 ms]
        (21) QCSDP
        (22) PIsEmptyProof [EQUIVALENT, 0 ms]
        (23) YES


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

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

   active(f(X)) -> mark(cons(X, f(g(X))))
   active(g(0)) -> mark(s(0))
   active(g(s(X))) -> mark(s(s(g(X))))
   active(sel(0, cons(X, Y))) -> mark(X)
   active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
   active(f(X)) -> f(active(X))
   active(cons(X1, X2)) -> cons(active(X1), X2)
   active(g(X)) -> g(active(X))
   active(s(X)) -> s(active(X))
   active(sel(X1, X2)) -> sel(active(X1), X2)
   active(sel(X1, X2)) -> sel(X1, active(X2))
   f(mark(X)) -> mark(f(X))
   cons(mark(X1), X2) -> mark(cons(X1, X2))
   g(mark(X)) -> mark(g(X))
   s(mark(X)) -> mark(s(X))
   sel(mark(X1), X2) -> mark(sel(X1, X2))
   sel(X1, mark(X2)) -> mark(sel(X1, X2))
   proper(f(X)) -> f(proper(X))
   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
   proper(g(X)) -> g(proper(X))
   proper(0) -> ok(0)
   proper(s(X)) -> s(proper(X))
   proper(sel(X1, X2)) -> sel(proper(X1), proper(X2))
   f(ok(X)) -> ok(f(X))
   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
   g(ok(X)) -> ok(g(X))
   s(ok(X)) -> ok(s(X))
   sel(ok(X1), ok(X2)) -> ok(sel(X1, X2))
   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(cons(X, f(g(X))))
   active(g(0)) -> mark(s(0))
   active(g(s(X))) -> mark(s(s(g(X))))
   active(sel(0, cons(X, Y))) -> mark(X)
   active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z))
   active(f(X)) -> f(active(X))
   active(cons(X1, X2)) -> cons(active(X1), X2)
   active(g(X)) -> g(active(X))
   active(s(X)) -> s(active(X))
   active(sel(X1, X2)) -> sel(active(X1), X2)
   active(sel(X1, X2)) -> sel(X1, active(X2))
   f(mark(X)) -> mark(f(X))
   cons(mark(X1), X2) -> mark(cons(X1, X2))
   g(mark(X)) -> mark(g(X))
   s(mark(X)) -> mark(s(X))

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