SRS Standard pair #487519925

details

property	value
status	complete
benchmark	z065.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n037.star.cs.uiowa.edu
space	Zantema_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.16442894936 seconds
cpu usage	13.12914492
max memory	1.713512448E9

stage attributes

key	value
output-size	9725
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) QTRS
(1) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) QTRSRRRProof [EQUIVALENT, 14 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 11 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 1 ms]
(8) AND
    (9) QDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) QDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) QDP
        (17) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (18) YES
    (19) QDP
        (20) UsableRulesProof [EQUIVALENT, 0 ms]
        (21) QDP
        (22) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (23) YES
    (24) QDP
        (25) UsableRulesProof [EQUIVALENT, 0 ms]
        (26) QDP
        (27) MRRProof [EQUIVALENT, 0 ms]
        (28) QDP
        (29) PisEmptyProof [EQUIVALENT, 0 ms]
        (30) YES


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

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

   0(*(x1)) -> *(1(x1))
   1(*(x1)) -> 0(#(x1))
   #(0(x1)) -> 0(#(x1))
   #(1(x1)) -> 1(#(x1))
   #($(x1)) -> *($(x1))
   #(#(x1)) -> #(x1)
   #(*(x1)) -> *(x1)

Q is empty.

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

(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
----------------------------------------

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

   *(0(x1)) -> 1(*(x1))
   *(1(x1)) -> #(0(x1))
   0(#(x1)) -> #(0(x1))
   1(#(x1)) -> #(1(x1))
   $(#(x1)) -> $(*(x1))
   #(#(x1)) -> #(x1)
   *(#(x1)) -> *(x1)

Q is empty.

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

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

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

   #(#(x1)) -> #(x1)
   *(#(x1)) -> *(x1)

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