16.21/5.17	YES
16.96/5.38	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
16.96/5.38	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
16.96/5.38	
16.96/5.38	
16.96/5.38	Termination w.r.t. Q of the given QTRS could be proven:
16.96/5.38	
16.96/5.38	(0) QTRS
16.96/5.38	(1) QTRS Reverse [EQUIVALENT, 0 ms]
16.96/5.38	(2) QTRS
16.96/5.38	(3) QTRSRoofMatchBoundsTAProof [EQUIVALENT, 1055 ms]
16.96/5.38	(4) YES
16.96/5.38	
16.96/5.38	
16.96/5.38	----------------------------------------
16.96/5.38	
16.96/5.38	(0)
16.96/5.38	Obligation:
16.96/5.38	Q restricted rewrite system:
16.96/5.38	The TRS R consists of the following rules:
16.96/5.38	
16.96/5.38	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1))))))))))
16.96/5.38	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
16.96/5.38	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
16.96/5.38	   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)))))))))))))))))))
16.96/5.38	   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))))))))))))))))))))))
16.96/5.38	
16.96/5.38	Q is empty.
16.96/5.38	
16.96/5.38	----------------------------------------
16.96/5.38	
16.96/5.38	(1) QTRS Reverse (EQUIVALENT)
16.96/5.38	We applied the QTRS Reverse Processor [REVERSE].
16.96/5.38	----------------------------------------
16.96/5.38	
16.96/5.38	(2)
16.96/5.38	Obligation:
16.96/5.38	Q restricted rewrite system:
16.96/5.38	The TRS R consists of the following rules:
16.96/5.38	
16.96/5.38	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(1(1(2(1(x1))))))))))
16.96/5.38	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(1(1(2(1(x1)))))))))))))
16.96/5.38	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1))))))))))))))))
16.96/5.38	   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)))))))))))))))))))
16.96/5.38	   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))))))))))))))))))))))
16.96/5.38	
16.96/5.38	Q is empty.
16.96/5.38	
16.96/5.38	----------------------------------------
16.96/5.38	
16.96/5.38	(3) QTRSRoofMatchBoundsTAProof (EQUIVALENT)
16.96/5.38	The TRS R could be shown to be Match-Bounded [TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] by  3. Therefore it terminates.
16.96/5.38	
16.96/5.38	The compatible tree automaton used to show the Match-Boundedness is represented by: 
16.96/5.38	final states : [0, 1, 2]
16.96/5.38	transitions: 
16.96/5.38	10(0) -> 0
16.96/5.38	10(1) -> 0
16.96/5.38	10(2) -> 0
16.96/5.38	20(0) -> 1
16.96/5.38	20(1) -> 1
16.96/5.38	20(2) -> 1
16.96/5.38	00(0) -> 2
16.96/5.38	00(1) -> 2
16.96/5.38	00(2) -> 2
16.96/5.38	11(0) -> 10
16.96/5.38	21(10) -> 9
16.96/5.38	11(9) -> 8
16.96/5.38	11(8) -> 7
16.96/5.38	01(7) -> 6
16.96/5.38	11(6) -> 3
16.96/5.38	21(3) -> 5
16.96/5.38	01(5) -> 4
16.96/5.38	11(4) -> 3
16.96/5.38	21(3) -> 0
16.96/5.38	11(1) -> 10
16.96/5.38	11(2) -> 10
16.96/5.38	11(7) -> 10
16.96/5.38	11(5) -> 10
16.96/5.38	12(7) -> 18
16.96/5.39	22(18) -> 17
16.96/5.39	12(17) -> 16
16.96/5.39	12(16) -> 15
16.96/5.39	02(15) -> 14
16.96/5.39	12(14) -> 11
16.96/5.39	22(11) -> 13
16.96/5.39	02(13) -> 12
16.96/5.39	12(12) -> 11
16.96/5.39	22(11) -> 10
16.96/5.39	12(5) -> 18
16.96/5.39	12(15) -> 18
16.96/5.39	13(15) -> 26
16.96/5.39	23(26) -> 25
16.96/5.39	13(25) -> 24
16.96/5.39	13(24) -> 23
16.96/5.39	03(23) -> 22
16.96/5.39	13(22) -> 19
16.96/5.39	23(19) -> 21
16.96/5.39	03(21) -> 20
16.96/5.39	13(20) -> 19
16.96/5.39	23(19) -> 18
16.96/5.39	13(13) -> 26
16.96/5.39	5 -> 10
16.96/5.39	5 -> 8
16.96/5.39	13 -> 7
16.96/5.39	13 -> 18
16.96/5.39	21 -> 26
16.96/5.39	
16.96/5.39	----------------------------------------
16.96/5.39	
16.96/5.39	(4)
16.96/5.39	YES
17.14/5.43	EOF