SRS Stand 10685 pair #381719018

details

property	value
status	complete
benchmark	aprove05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n056.star.cs.uiowa.edu
space	Secret_06_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	8.27290415764 seconds
cpu usage	28.98864911
max memory	4.19295232E9

stage attributes

key	value
output-size	14850
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 69 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 71 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) MNOCProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QReductionProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPOrderProof [EQUIVALENT, 31 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, 0 ms]
        (29) QDP
        (30) QDPOrderProof [EQUIVALENT, 27 ms]
        (31) QDP
        (32) PisEmptyProof [EQUIVALENT, 0 ms]
        (33) YES


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

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

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

Q is empty.

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

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

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

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




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

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

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

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