31.90/8.93	YES
32.16/8.96	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
32.16/8.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
32.16/8.96	
32.16/8.96	
32.16/8.96	Termination w.r.t. Q of the given QTRS could be proven:
32.16/8.96	
32.16/8.96	(0) QTRS
32.16/8.96	(1) QTRS Reverse [EQUIVALENT, 0 ms]
32.16/8.96	(2) QTRS
32.16/8.96	(3) QTRSRoofMatchBoundsTAProof [EQUIVALENT, 1416 ms]
32.16/8.96	(4) YES
32.16/8.96	
32.16/8.96	
32.16/8.96	----------------------------------------
32.16/8.96	
32.16/8.96	(0)
32.16/8.96	Obligation:
32.16/8.96	Q restricted rewrite system:
32.16/8.96	The TRS R consists of the following rules:
32.16/8.96	
32.16/8.96	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(x1))))))))))
32.16/8.96	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x1)))))))))))))
32.16/8.96	   0(1(2(1(x1)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x1))))))))))))))))
32.16/8.96	   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)))))))))))))))))))
32.16/8.96	   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))))))))))))))))))))))
32.16/8.96	   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)))))))))))))))))))))))))
32.16/8.96	   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))))))))))))))))))))))))))))
32.16/8.96	   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)))))))))))))))))))))))))))))))
32.16/8.96	   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(0(1(2(x1))))))))))))))))))))))))))))))))))
32.16/8.96	   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(0(1(2(0(1(2(x1)))))))))))))))))))))))))))))))))))))
32.16/8.96	
32.16/8.96	Q is empty.
32.16/8.96	
32.16/8.96	----------------------------------------
32.16/8.96	
32.16/8.96	(1) QTRS Reverse (EQUIVALENT)
32.16/8.96	We applied the QTRS Reverse Processor [REVERSE].
32.16/8.96	----------------------------------------
32.16/8.96	
32.16/8.96	(2)
32.16/8.96	Obligation:
32.16/8.96	Q restricted rewrite system:
32.16/8.96	The TRS R consists of the following rules:
32.16/8.96	
32.16/8.96	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(1(1(2(1(x1))))))))))
32.16/8.96	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(1(1(2(1(x1)))))))))))))
32.16/8.96	   1(2(1(0(x1)))) -> 2(1(0(2(1(0(2(1(0(2(1(0(1(1(2(1(x1))))))))))))))))
32.16/8.96	   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)))))))))))))))))))
32.16/8.96	   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))))))))))))))))))))))
32.16/8.96	   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)))))))))))))))))))))))))
32.16/8.96	   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))))))))))))))))))))))))))))
32.16/8.96	   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)))))))))))))))))))))))))))))))
32.16/8.96	   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(2(1(0(1(1(2(1(x1))))))))))))))))))))))))))))))))))
32.16/8.96	   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(2(1(0(2(1(0(1(1(2(1(x1)))))))))))))))))))))))))))))))))))))
32.16/8.96	
32.16/8.96	Q is empty.
32.16/8.96	
32.16/8.96	----------------------------------------
32.16/8.96	
32.16/8.96	(3) QTRSRoofMatchBoundsTAProof (EQUIVALENT)
32.16/8.96	The TRS R could be shown to be Match-Bounded [TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] by  3. Therefore it terminates.
32.16/8.96	
32.16/8.96	The compatible tree automaton used to show the Match-Boundedness is represented by: 
32.16/8.96	final states : [0, 1, 2]
32.16/8.96	transitions: 
32.16/8.96	10(0) -> 0
32.16/8.96	10(1) -> 0
32.16/8.96	10(2) -> 0
32.16/8.96	20(0) -> 1
32.16/8.96	20(1) -> 1
32.16/8.96	20(2) -> 1
32.16/8.96	00(0) -> 2
32.16/8.96	00(1) -> 2
32.16/8.96	00(2) -> 2
32.16/8.96	11(0) -> 10
32.16/8.96	21(10) -> 9
32.16/8.96	11(9) -> 8
32.16/8.96	11(8) -> 7
32.16/8.96	01(7) -> 6
32.16/8.96	11(6) -> 3
32.16/8.96	21(3) -> 5
32.16/8.96	01(5) -> 4
32.16/8.96	11(4) -> 3
32.16/8.96	21(3) -> 0
32.16/8.96	11(1) -> 10
32.16/8.96	11(2) -> 10
32.16/8.96	11(7) -> 10
32.16/8.96	11(5) -> 10
32.16/8.96	12(7) -> 18
32.16/8.96	22(18) -> 17
32.16/8.96	12(17) -> 16
32.16/8.96	12(16) -> 15
32.16/8.96	02(15) -> 14
32.16/8.96	12(14) -> 11
32.16/8.96	22(11) -> 13
32.16/8.96	02(13) -> 12
32.16/8.96	12(12) -> 11
32.16/8.96	22(11) -> 10
32.16/8.96	12(5) -> 18
32.16/8.96	12(15) -> 18
32.16/8.96	13(15) -> 26
32.16/8.96	23(26) -> 25
32.16/8.96	13(25) -> 24
32.16/8.96	13(24) -> 23
32.16/8.96	03(23) -> 22
32.16/8.96	13(22) -> 19
32.16/8.96	23(19) -> 21
32.16/8.96	03(21) -> 20
32.16/8.96	13(20) -> 19
32.16/8.96	23(19) -> 18
32.16/8.96	13(13) -> 26
32.16/8.96	5 -> 10
32.16/8.96	5 -> 8
32.16/8.96	13 -> 7
32.16/8.96	13 -> 18
32.16/8.96	21 -> 26
32.16/8.96	
32.16/8.96	----------------------------------------
32.16/8.96	
32.16/8.96	(4)
32.16/8.96	YES
32.33/9.06	EOF