details

property	value
status	complete
benchmark	#3.13.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	Applicative_first_order_05

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	2.78616 seconds
cpu usage	6.83182
user time	6.5751
system time	0.256723
max virtual memory	1.8657296E7
max residence set size	444308.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.72
bare-result	YES

output

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app></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if_reach_14</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if_reach_14</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if_reach_15</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>x3</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if_reach_2</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if_reach_21</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if_reach_21</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if_reach_22</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if_reach_22</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if_reach_23</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if_reach_23</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if_reach_24</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if_reach_24</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if_reach_25</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>x3</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter3</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter2</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter21</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter21</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter22</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter22</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter23</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>filter23</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>filter24</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><switchInnermost><wcrProof><joinableCriticalPairsBFS>10</joinableCriticalPairsBFS></wcrProof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>eq2</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq2</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>union2</name></sharp><arg><funapp><name>edge3</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>union2</name></sharp><arg><var>i</var></arg><arg><var>h</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>if_reach_15</name></sharp><arg><funapp><name>eq2</name><arg><var>x</var></arg><arg><var>u</var></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>eq2</name></sharp><arg><var>x</var></arg><arg><var>u</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_reach_15</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>if_reach_25</name></sharp><arg><funapp><name>eq2</name><arg><var>y</var></arg><arg><var>v</var></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_reach_15</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>eq2</name></sharp><arg><var>y</var></arg><arg><var>v</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_reach_15</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>h</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_reach_25</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>or2</name></sharp><arg><funapp><name>reach4</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg><arg><var>h</var></arg></funapp></arg><arg><funapp><name>reach4</name><arg><var>v</var></arg><arg><var>y</var></arg><arg><funapp><name>union2</name><arg><var>i</var></arg><arg><var>h</var></arg></funapp></arg><arg><funapp><name>empty</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_reach_25</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg><arg><var>h</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_reach_25</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>reach4</name></sharp><arg><var>v</var></arg><arg><var>y</var></arg><arg><funapp><name>union2</name><arg><var>i</var></arg><arg><var>h</var></arg></funapp></arg><arg><funapp><name>empty</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_reach_25</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>union2</name></sharp><arg><var>i</var></arg><arg><var>h</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>filter3</name></sharp><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>filter24</name></sharp><arg><funapp><name>app</name><arg><var>f</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>filter3</name></sharp><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>filter24</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter3</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>filter24</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter3</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>eq1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>eq2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>or1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>or2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>union1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>union2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>reach3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>reach4</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>if_reach_14</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if_reach_15</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>x3</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>if_reach_24</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if_reach_25</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>x3</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>filter1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter3</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>filter23</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter24</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>filter1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter3</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>filter3</name></sharp><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>filter24</name></sharp><arg><funapp><name>app</name><arg><var>f</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>filter24</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter3</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>filter3</name></sharp><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>filter23</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter24</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>filter24</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter3</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>filter3</name></sharp><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>filter3</name></sharp><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>filter24</name></sharp><arg><funapp><name>app</name><arg><var>f</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>2</position></edge><edge><position>2</position><strict>true</strict><position>3</position></edge><edge><position>2</position><strict>true</strict><position>4</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>filter1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter3</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>filter23</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter24</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>1</position><strict>true</strict><position>2</position></edge><edge><position>1</position><strict>true</strict><position>3</position></edge><edge><position>2</position><strict>false</strict><position>4</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>filter24</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter3</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>1</position></edge><edge><position>4</position><strict>false</strict><position>2</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>filter24</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>f</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><sharp><name>filter3</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>1</position></edge><edge><position>4</position><strict>false</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>if_reach_14</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if_reach_15</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>x3</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>if_reach_24</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if_reach_25</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>x3</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>reach3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>reach4</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>if_reach_15</name></sharp><arg><funapp><name>eq2</name><arg><var>x</var></arg><arg><var>u</var></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_reach_15</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>if_reach_25</name></sharp><arg><funapp><name>eq2</name><arg><var>y</var></arg><arg><var>v</var></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_reach_25</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg><arg><var>h</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_reach_25</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>reach4</name></sharp><arg><var>v</var></arg><arg><var>y</var></arg><arg><funapp><name>union2</name><arg><var>i</var></arg><arg><var>h</var></arg></funapp></arg><arg><funapp><name>empty</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_reach_15</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>h</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>union2</name><arg><funapp><name>empty</name></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><var>h</var></rhs></rule><rule><lhs><funapp><name>union2</name><arg><funapp><name>edge3</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><name>edge3</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>union2</name><arg><var>i</var></arg><arg><var>h</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>eq2</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>eq2</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq2</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq2</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>eq2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>eq2</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>eq2</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>eq2</name><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>eq2</name><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>union2</name><arg><funapp><name>empty</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>union2</name><arg><funapp><name>edge3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg><arg><var>x3</var></arg></funapp></innermostLhss><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>if_reach_15</name></sharp><arity>5</arity><polynomial><sum><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><variable>4</variable></polynomial><polynomial><variable>5</variable></polynomial></sum></polynomial></interpret><interpret><sharp><name>if_reach_25</name></sharp><arity>5</arity><polynomial><sum><polynomial><coefficient><integer>-2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><variable>4</variable></polynomial><polynomial><variable>5</variable></polynomial></sum></polynomial></interpret><interpret><name>eq2</name><arity>2</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><coefficient><integer>2</integer></coefficient></polynomial></interpret><interpret><name>s1</name><arity>1</arity><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><sharp><name>reach4</name></sharp><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><variable>3</variable></polynomial><polynomial><variable>4</variable></polynomial></sum></polynomial></interpret><interpret><name>union2</name><arity>2</arity><polynomial><sum><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></sum></polynomial></interpret><interpret><name>empty</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>edge3</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>if_reach_15</name></sharp><arg><funapp><name>eq2</name><arg><var>x</var></arg><arg><var>u</var></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_reach_25</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg><arg><var>h</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_reach_25</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>reach4</name></sharp><arg><var>v</var></arg><arg><var>y</var></arg><arg><funapp><name>union2</name><arg><var>i</var></arg><arg><var>h</var></arg></funapp></arg><arg><funapp><name>empty</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if_reach_15</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>h</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>union2</name><arg><funapp><name>empty</name></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><var>h</var></rhs></rule><rule><lhs><funapp><name>union2</name><arg><funapp><name>edge3</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><name>edge3</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>union2</name><arg><var>i</var></arg><arg><var>h</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>if_reach_25</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg><arg><var>h</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>if_reach_25</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>reach4</name></sharp><arg><var>v</var></arg><arg><var>y</var></arg><arg><funapp><name>union2</name><arg><var>i</var></arg><arg><var>h</var></arg></funapp></arg><arg><funapp><name>empty</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>if_reach_15</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>h</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>if_reach_15</name></sharp><arg><funapp><name>eq2</name><arg><var>x</var></arg><arg><var>u</var></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>eq2</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>eq2</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq2</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq2</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>eq2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>eq2</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>eq2</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>eq2</name><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>eq2</name><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>x1</var></arg></funapp></arg></funapp></innermostLhss><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>if_reach_15</name></sharp><arg><funapp><name>eq2</name><arg><var>x</var></arg><arg><var>u</var></arg></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>2</position></edge><edge><position>2</position><strict>false</strict><position>3</position></edge><edge><position>3</position><strict>false</strict><position>4</position></edge><edge><position>4</position><strict>false</strict><position>5</position></edge></sizeChangeGraph><sizeChangeGraph><rule><lhs><funapp><sharp><name>if_reach_15</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>h</var></arg></funapp></arg></funapp></rhs></rule><edge><position>2</position><strict>false</strict><position>1</position></edge><edge><position>3</position><strict>false</strict><position>2</position></edge><edge><position>4</position><strict>true</strict><position>3</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component></depGraphProc></dpProof></redPairUrProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>reach4</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>eq2</name></sharp><arg><var>x</var></arg><arg><var>u</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>if_reach_15</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>eq2</name></sharp><arg><var>y</var></arg><arg><var>v</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>eq1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>eq2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>if_reach_25</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>union2</name></sharp><arg><var>i</var></arg><arg><var>h</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>union1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>union2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>eq2</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq2</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>eq2</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq2</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>union2</name></sharp><arg><funapp><name>edge3</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>union2</name></sharp><arg><var>i</var></arg><arg><var>h</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>union2</name></sharp><arg><funapp><name>edge3</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>union2</name></sharp><arg><var>i</var></arg><arg><var>h</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>false</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>if_reach_25</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg><arg><var>y</var></arg><arg><funapp><name>edge3</name><arg><var>u</var></arg><arg><var>v</var></arg><arg><var>i</var></arg></funapp></arg><arg><var>h</var></arg></funapp></lhs><rhs><funapp><sharp><name>or2</name></sharp><arg><funapp><name>reach4</name><arg><var>x</var></arg><arg><var>y</var></arg><arg><var>i</var></arg><arg><var>h</var></arg></funapp></arg><arg><funapp><name>reach4</name><arg><var>v</var></arg><arg><var>y</var></arg><arg><funapp><name>union2</name><arg><var>i</var></arg><arg><var>h</var></arg></funapp></arg><arg><funapp><name>empty</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>or1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>or2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></switchInnermost></trsTerminationProof></uncurry></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (18 real / 0 unknown / 0 assumptions / 18 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem> popout

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