TRS Stand 20472 pair #381715497

details

property	value
status	complete
benchmark	Ex2_Luc02a_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n109.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.53324198723 seconds
cpu usage	14.046762318
max memory	1.079005184E9

stage attributes

key	value
output-size	53540
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


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

(0) QTRS
(1) DependencyPairsProof [EQUIVALENT, 17 ms]
(2) QDP
(3) DependencyGraphProof [EQUIVALENT, 0 ms]
(4) AND
    (5) QDP
        (6) UsableRulesProof [EQUIVALENT, 0 ms]
        (7) QDP
        (8) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (9) YES
    (10) QDP
        (11) UsableRulesProof [EQUIVALENT, 0 ms]
        (12) QDP
        (13) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (14) YES
    (15) QDP
        (16) UsableRulesProof [EQUIVALENT, 0 ms]
        (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) UsableRulesProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) QDP
        (26) UsableRulesProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (29) YES
    (30) QDP
        (31) UsableRulesProof [EQUIVALENT, 0 ms]
        (32) QDP
        (33) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (34) YES
    (35) QDP
        (36) UsableRulesProof [EQUIVALENT, 0 ms]
        (37) QDP
        (38) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (39) YES
    (40) QDP
        (41) UsableRulesProof [EQUIVALENT, 0 ms]
        (42) QDP
        (43) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (44) YES
    (45) QDP
        (46) QDPOrderProof [EQUIVALENT, 389 ms]
        (47) QDP
        (48) QDPOrderProof [EQUIVALENT, 166 ms]
        (49) QDP
        (50) QDPOrderProof [EQUIVALENT, 346 ms]
        (51) QDP
        (52) DependencyGraphProof [EQUIVALENT, 0 ms]
        (53) QDP
        (54) UsableRulesProof [EQUIVALENT, 0 ms]
        (55) QDP
        (56) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (57) YES


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

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

   active(terms(N)) -> mark(cons(recip(sqr(N)), terms(s(N))))
   active(sqr(0)) -> mark(0)
   active(sqr(s(X))) -> mark(s(add(sqr(X), dbl(X))))
   active(dbl(0)) -> mark(0)
   active(dbl(s(X))) -> mark(s(s(dbl(X))))
   active(add(0, X)) -> mark(X)
   active(add(s(X), Y)) -> mark(s(add(X, Y)))
   active(first(0, X)) -> mark(nil)
   active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
   mark(terms(X)) -> active(terms(mark(X)))
   mark(cons(X1, X2)) -> active(cons(mark(X1), X2))
   mark(recip(X)) -> active(recip(mark(X)))
   mark(sqr(X)) -> active(sqr(mark(X)))
   mark(s(X)) -> active(s(mark(X)))
   mark(0) -> active(0)
   mark(add(X1, X2)) -> active(add(mark(X1), mark(X2)))
   mark(dbl(X)) -> active(dbl(mark(X)))
   mark(first(X1, X2)) -> active(first(mark(X1), mark(X2)))
   mark(nil) -> active(nil)
   terms(mark(X)) -> terms(X)

popout

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

job log

popout

actions all output return to TRS Stand 20472