SRS Stand 10685 pair #381718609

details

property	value
status	complete
benchmark	aprove06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n100.star.cs.uiowa.edu
space	Secret_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.81360912323 seconds
cpu usage	18.481847225
max memory	2.769092608E9

stage attributes

key	value
output-size	20242
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) QTRSRRRProof [EQUIVALENT, 67 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 44 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 4 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 1 ms]
        (11) YES
    (12) QDP
        (13) MNOCProof [EQUIVALENT, 2 ms]
        (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QReductionProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPOrderProof [EQUIVALENT, 27 ms]
        (20) QDP
        (21) PisEmptyProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) QDP
        (24) MNOCProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) UsableRulesProof [EQUIVALENT, 0 ms]
        (27) QDP
        (28) QReductionProof [EQUIVALENT, 1 ms]
        (29) QDP
        (30) QDPOrderProof [EQUIVALENT, 11 ms]
        (31) QDP
        (32) PisEmptyProof [EQUIVALENT, 0 ms]
        (33) YES
    (34) QDP
        (35) MNOCProof [EQUIVALENT, 0 ms]
        (36) QDP
        (37) UsableRulesProof [EQUIVALENT, 0 ms]
        (38) QDP
        (39) QReductionProof [EQUIVALENT, 0 ms]
        (40) QDP
        (41) QDPOrderProof [EQUIVALENT, 14 ms]
        (42) QDP
        (43) PisEmptyProof [EQUIVALENT, 0 ms]
        (44) YES


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

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

   tower(0(x1)) -> s(0(p(s(p(s(x1))))))
   tower(s(x1)) -> p(s(p(s(twoto(p(s(p(s(tower(p(s(p(s(x1))))))))))))))
   twoto(0(x1)) -> s(0(x1))
   twoto(s(x1)) -> p(p(s(p(p(p(s(s(p(s(s(p(s(s(p(s(twice(p(s(p(s(p(p(p(s(s(s(twoto(p(s(p(s(x1))))))))))))))))))))))))))))))))
   twice(0(x1)) -> 0(x1)
   twice(s(x1)) -> p(p(p(s(s(s(s(s(twice(p(p(p(s(s(s(x1)))))))))))))))
   p(p(s(x1))) -> p(x1)
   p(s(x1)) -> x1
   p(0(x1)) -> 0(s(s(s(s(s(s(s(s(x1)))))))))

Q is empty.

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

(1) QTRSRRRProof (EQUIVALENT)
Used ordering:
Polynomial interpretation [POLO]:

   POL(0(x_1)) = x_1
   POL(p(x_1)) = x_1
   POL(s(x_1)) = x_1
   POL(tower(x_1)) = 1 + x_1
   POL(twice(x_1)) = x_1
   POL(twoto(x_1)) = x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   tower(0(x1)) -> s(0(p(s(p(s(x1))))))




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

popout

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

job log

popout

actions all output return to SRS Stand 10685