15.23/4.93	YES
15.98/5.09	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
15.98/5.09	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
15.98/5.09	
15.98/5.09	
15.98/5.09	Termination w.r.t. Q of the given QTRS could be proven:
15.98/5.09	
15.98/5.09	(0) QTRS
15.98/5.09	(1) QTRS Reverse [EQUIVALENT, 0 ms]
15.98/5.09	(2) QTRS
15.98/5.09	(3) QTRSRoofMatchBoundsTAProof [EQUIVALENT, 930 ms]
15.98/5.09	(4) YES
15.98/5.09	
15.98/5.09	
15.98/5.09	----------------------------------------
15.98/5.09	
15.98/5.09	(0)
15.98/5.09	Obligation:
15.98/5.09	Q restricted rewrite system:
15.98/5.09	The TRS R consists of the following rules:
15.98/5.09	
15.98/5.09	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1))))))))))
15.98/5.09	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
15.98/5.09	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
15.98/5.09	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))
15.98/5.09	
15.98/5.09	Q is empty.
15.98/5.09	
15.98/5.09	----------------------------------------
15.98/5.09	
15.98/5.09	(1) QTRS Reverse (EQUIVALENT)
15.98/5.09	We applied the QTRS Reverse Processor [REVERSE].
15.98/5.09	----------------------------------------
15.98/5.09	
15.98/5.09	(2)
15.98/5.09	Obligation:
15.98/5.09	Q restricted rewrite system:
15.98/5.09	The TRS R consists of the following rules:
15.98/5.09	
15.98/5.09	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(1(1(2(1(x1))))))))))
15.98/5.09	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(1(1(2(1(x1)))))))))))))
15.98/5.09	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1))))))))))))))))
15.98/5.09	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1)))))))))))))))))))
15.98/5.09	
15.98/5.09	Q is empty.
15.98/5.09	
15.98/5.09	----------------------------------------
15.98/5.09	
15.98/5.09	(3) QTRSRoofMatchBoundsTAProof (EQUIVALENT)
15.98/5.09	The TRS R could be shown to be Match-Bounded [TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] by  3. Therefore it terminates.
15.98/5.09	
15.98/5.09	The compatible tree automaton used to show the Match-Boundedness is represented by: 
15.98/5.09	final states : [0, 1, 2]
15.98/5.09	transitions: 
15.98/5.09	10(0) -> 0
15.98/5.09	10(1) -> 0
15.98/5.09	10(2) -> 0
15.98/5.09	20(0) -> 1
15.98/5.09	20(1) -> 1
15.98/5.09	20(2) -> 1
15.98/5.09	00(0) -> 2
15.98/5.09	00(1) -> 2
15.98/5.09	00(2) -> 2
15.98/5.09	11(0) -> 10
15.98/5.09	21(10) -> 9
15.98/5.09	11(9) -> 8
15.98/5.09	11(8) -> 7
15.98/5.09	01(7) -> 6
15.98/5.09	11(6) -> 3
15.98/5.09	21(3) -> 5
15.98/5.09	01(5) -> 4
15.98/5.09	11(4) -> 3
15.98/5.09	21(3) -> 0
15.98/5.09	11(1) -> 10
15.98/5.09	11(2) -> 10
15.98/5.09	11(7) -> 10
15.98/5.09	11(5) -> 10
15.98/5.09	12(7) -> 18
15.98/5.09	22(18) -> 17
15.98/5.09	12(17) -> 16
15.98/5.09	12(16) -> 15
15.98/5.09	02(15) -> 14
15.98/5.09	12(14) -> 11
15.98/5.09	22(11) -> 13
15.98/5.09	02(13) -> 12
15.98/5.09	12(12) -> 11
15.98/5.09	22(11) -> 10
15.98/5.09	12(5) -> 18
15.98/5.09	12(15) -> 18
15.98/5.09	13(15) -> 26
15.98/5.09	23(26) -> 25
15.98/5.09	13(25) -> 24
15.98/5.09	13(24) -> 23
15.98/5.09	03(23) -> 22
15.98/5.09	13(22) -> 19
15.98/5.09	23(19) -> 21
15.98/5.09	03(21) -> 20
15.98/5.09	13(20) -> 19
15.98/5.09	23(19) -> 18
15.98/5.09	13(13) -> 26
15.98/5.09	5 -> 10
15.98/5.09	5 -> 8
15.98/5.09	13 -> 7
15.98/5.09	13 -> 18
15.98/5.09	21 -> 26
15.98/5.09	
15.98/5.09	----------------------------------------
15.98/5.09	
15.98/5.09	(4)
15.98/5.09	YES
16.29/5.22	EOF