29.01/8.31	YES
29.20/8.34	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
29.20/8.34	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
29.20/8.34	
29.20/8.34	
29.20/8.34	Termination w.r.t. Q of the given QTRS could be proven:
29.20/8.34	
29.20/8.34	(0) QTRS
29.20/8.34	(1) QTRS Reverse [EQUIVALENT, 0 ms]
29.20/8.34	(2) QTRS
29.20/8.34	(3) QTRSRoofMatchBoundsTAProof [EQUIVALENT, 1377 ms]
29.20/8.34	(4) YES
29.20/8.34	
29.20/8.34	
29.20/8.34	----------------------------------------
29.20/8.34	
29.20/8.34	(0)
29.20/8.34	Obligation:
29.20/8.34	Q restricted rewrite system:
29.20/8.34	The TRS R consists of the following rules:
29.20/8.34	
29.20/8.34	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1))))))))))
29.20/8.34	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
29.20/8.34	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
29.20/8.34	   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)))))))))))))))))))
29.20/8.34	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))
29.20/8.34	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1)))))))))))))))))))))))))
29.20/8.34	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))))))))))))))
29.20/8.34	
29.20/8.34	Q is empty.
29.20/8.34	
29.20/8.34	----------------------------------------
29.20/8.34	
29.20/8.34	(1) QTRS Reverse (EQUIVALENT)
29.20/8.34	We applied the QTRS Reverse Processor [REVERSE].
29.20/8.34	----------------------------------------
29.20/8.34	
29.20/8.34	(2)
29.20/8.34	Obligation:
29.20/8.34	Q restricted rewrite system:
29.20/8.34	The TRS R consists of the following rules:
29.20/8.34	
29.20/8.34	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(1(1(2(1(x1))))))))))
29.20/8.34	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(1(1(2(1(x1)))))))))))))
29.20/8.34	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1))))))))))))))))
29.20/8.34	   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)))))))))))))))))))
29.20/8.34	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1))))))))))))))))))))))
29.20/8.34	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1)))))))))))))))))))))))))
29.20/8.34	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1))))))))))))))))))))))))))))
29.20/8.34	
29.20/8.34	Q is empty.
29.20/8.34	
29.20/8.34	----------------------------------------
29.20/8.34	
29.20/8.34	(3) QTRSRoofMatchBoundsTAProof (EQUIVALENT)
29.20/8.34	The TRS R could be shown to be Match-Bounded [TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] by  3. Therefore it terminates.
29.20/8.34	
29.20/8.34	The compatible tree automaton used to show the Match-Boundedness is represented by: 
29.20/8.34	final states : [0, 1, 2]
29.20/8.34	transitions: 
29.20/8.34	10(0) -> 0
29.20/8.34	10(1) -> 0
29.20/8.34	10(2) -> 0
29.20/8.34	20(0) -> 1
29.20/8.34	20(1) -> 1
29.20/8.34	20(2) -> 1
29.20/8.34	00(0) -> 2
29.20/8.34	00(1) -> 2
29.20/8.34	00(2) -> 2
29.20/8.34	11(0) -> 10
29.20/8.34	21(10) -> 9
29.20/8.34	11(9) -> 8
29.20/8.34	11(8) -> 7
29.20/8.34	01(7) -> 6
29.20/8.34	11(6) -> 3
29.20/8.34	21(3) -> 5
29.20/8.34	01(5) -> 4
29.20/8.34	11(4) -> 3
29.20/8.34	21(3) -> 0
29.20/8.34	11(1) -> 10
29.20/8.34	11(2) -> 10
29.20/8.34	11(7) -> 10
29.20/8.34	11(5) -> 10
29.20/8.34	12(7) -> 18
29.20/8.34	22(18) -> 17
29.20/8.34	12(17) -> 16
29.20/8.34	12(16) -> 15
29.20/8.34	02(15) -> 14
29.20/8.34	12(14) -> 11
29.20/8.34	22(11) -> 13
29.20/8.34	02(13) -> 12
29.20/8.34	12(12) -> 11
29.20/8.34	22(11) -> 10
29.20/8.34	12(5) -> 18
29.20/8.34	12(15) -> 18
29.20/8.34	13(15) -> 26
29.20/8.34	23(26) -> 25
29.20/8.34	13(25) -> 24
29.20/8.34	13(24) -> 23
29.20/8.34	03(23) -> 22
29.20/8.34	13(22) -> 19
29.20/8.34	23(19) -> 21
29.20/8.34	03(21) -> 20
29.20/8.34	13(20) -> 19
29.20/8.34	23(19) -> 18
29.20/8.34	13(13) -> 26
29.20/8.34	5 -> 10
29.20/8.34	5 -> 8
29.20/8.34	13 -> 7
29.20/8.34	13 -> 18
29.20/8.34	21 -> 26
29.20/8.34	
29.20/8.34	----------------------------------------
29.20/8.34	
29.20/8.34	(4)
29.20/8.34	YES
29.33/8.42	EOF