11.04/3.60	YES
11.40/3.71	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
11.40/3.71	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.40/3.71	
11.40/3.71	
11.40/3.71	Termination w.r.t. Q of the given QTRS could be proven:
11.40/3.71	
11.40/3.71	(0) QTRS
11.40/3.71	(1) QTRS Reverse [EQUIVALENT, 0 ms]
11.40/3.71	(2) QTRS
11.40/3.71	(3) QTRSRoofMatchBoundsTAProof [EQUIVALENT, 1065 ms]
11.40/3.71	(4) YES
11.40/3.71	
11.40/3.71	
11.40/3.71	----------------------------------------
11.40/3.71	
11.40/3.71	(0)
11.40/3.71	Obligation:
11.40/3.71	Q restricted rewrite system:
11.40/3.71	The TRS R consists of the following rules:
11.40/3.71	
11.40/3.71	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1))))))))))
11.40/3.71	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
11.40/3.71	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
11.40/3.71	   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)))))))))))))))))))
11.40/3.71	   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))))))))))))))))))))))
11.40/3.71	   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)))))))))))))))))))))))))
11.40/3.71	   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))))))))))))))))))))))))))))
11.40/3.71	   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(0(1(2(x1)))))))))))))))))))))))))))))))
11.40/3.71	
11.40/3.71	Q is empty.
11.40/3.71	
11.40/3.71	----------------------------------------
11.40/3.71	
11.40/3.71	(1) QTRS Reverse (EQUIVALENT)
11.40/3.71	We applied the QTRS Reverse Processor [REVERSE].
11.40/3.71	----------------------------------------
11.40/3.71	
11.40/3.71	(2)
11.40/3.71	Obligation:
11.40/3.71	Q restricted rewrite system:
11.40/3.71	The TRS R consists of the following rules:
11.40/3.71	
11.40/3.71	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(1(1(2(1(x1))))))))))
11.40/3.71	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(1(1(2(1(x1)))))))))))))
11.40/3.71	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1))))))))))))))))
11.40/3.71	   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)))))))))))))))))))
11.40/3.71	   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))))))))))))))))))))))
11.40/3.71	   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)))))))))))))))))))))))))
11.40/3.71	   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))))))))))))))))))))))))))))
11.40/3.71	   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(2(1(0(1(1(2(1(x1)))))))))))))))))))))))))))))))
11.40/3.71	
11.40/3.71	Q is empty.
11.40/3.71	
11.40/3.71	----------------------------------------
11.40/3.71	
11.40/3.71	(3) QTRSRoofMatchBoundsTAProof (EQUIVALENT)
11.40/3.71	The TRS R could be shown to be Match-Bounded [TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] by  3. Therefore it terminates.
11.40/3.71	
11.40/3.71	The compatible tree automaton used to show the Match-Boundedness is represented by: 
11.40/3.71	final states : [0, 1, 2]
11.40/3.71	transitions: 
11.40/3.71	10(0) -> 0
11.40/3.71	10(1) -> 0
11.40/3.71	10(2) -> 0
11.40/3.71	20(0) -> 1
11.40/3.71	20(1) -> 1
11.40/3.71	20(2) -> 1
11.40/3.71	00(0) -> 2
11.40/3.71	00(1) -> 2
11.40/3.71	00(2) -> 2
11.40/3.71	11(0) -> 10
11.40/3.71	21(10) -> 9
11.40/3.71	11(9) -> 8
11.40/3.71	11(8) -> 7
11.40/3.71	01(7) -> 6
11.40/3.71	11(6) -> 3
11.40/3.71	21(3) -> 5
11.40/3.71	01(5) -> 4
11.40/3.71	11(4) -> 3
11.40/3.71	21(3) -> 0
11.40/3.71	11(1) -> 10
11.40/3.71	11(2) -> 10
11.40/3.71	11(7) -> 10
11.40/3.71	11(5) -> 10
11.40/3.71	12(7) -> 18
11.40/3.71	22(18) -> 17
11.40/3.71	12(17) -> 16
11.40/3.71	12(16) -> 15
11.40/3.71	02(15) -> 14
11.40/3.71	12(14) -> 11
11.40/3.71	22(11) -> 13
11.40/3.71	02(13) -> 12
11.40/3.71	12(12) -> 11
11.40/3.71	22(11) -> 10
11.40/3.71	12(5) -> 18
11.40/3.71	12(15) -> 18
11.40/3.71	13(15) -> 26
11.40/3.71	23(26) -> 25
11.40/3.71	13(25) -> 24
11.40/3.71	13(24) -> 23
11.40/3.71	03(23) -> 22
11.40/3.71	13(22) -> 19
11.40/3.71	23(19) -> 21
11.40/3.71	03(21) -> 20
11.40/3.71	13(20) -> 19
11.40/3.71	23(19) -> 18
11.40/3.71	13(13) -> 26
11.40/3.71	5 -> 10
11.40/3.71	5 -> 8
11.40/3.71	13 -> 7
11.40/3.71	13 -> 18
11.40/3.71	21 -> 26
11.40/3.71	
11.40/3.71	----------------------------------------
11.40/3.71	
11.40/3.71	(4)
11.40/3.71	YES
11.75/3.79	EOF