2.99/1.56	YES
3.41/1.60	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.41/1.60	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.41/1.60	
3.41/1.60	
3.41/1.60	Termination w.r.t. Q of the given QTRS could be proven:
3.41/1.60	
3.41/1.60	(0) QTRS
3.41/1.60	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.41/1.60	(2) QTRS
3.41/1.60	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 27 ms]
3.41/1.60	(4) YES
3.41/1.60	
3.41/1.60	
3.41/1.60	----------------------------------------
3.41/1.60	
3.41/1.60	(0)
3.41/1.60	Obligation:
3.41/1.60	Q restricted rewrite system:
3.41/1.60	The TRS R consists of the following rules:
3.41/1.60	
3.41/1.60	   a(a(x1)) -> a(b(a(x1)))
3.41/1.60	   b(a(b(x1))) -> a(c(a(x1)))
3.41/1.60	
3.41/1.60	Q is empty.
3.41/1.60	
3.41/1.60	----------------------------------------
3.41/1.60	
3.41/1.60	(1) QTRS Reverse (EQUIVALENT)
3.41/1.60	We applied the QTRS Reverse Processor [REVERSE].
3.41/1.60	----------------------------------------
3.41/1.60	
3.41/1.60	(2)
3.41/1.60	Obligation:
3.41/1.60	Q restricted rewrite system:
3.41/1.60	The TRS R consists of the following rules:
3.41/1.60	
3.41/1.60	   a(a(x1)) -> a(b(a(x1)))
3.41/1.60	   b(a(b(x1))) -> a(c(a(x1)))
3.41/1.60	
3.41/1.60	Q is empty.
3.41/1.60	
3.41/1.60	----------------------------------------
3.41/1.60	
3.41/1.60	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
3.41/1.60	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 5. This implies Q-termination of R.
3.41/1.60	The following rules were used to construct the certificate:
3.41/1.60	
3.41/1.60	   a(a(x1)) -> a(b(a(x1)))
3.41/1.60	   b(a(b(x1))) -> a(c(a(x1)))
3.41/1.60	
3.41/1.60	The certificate found is represented by the following graph.
3.41/1.60	The certificate consists of the following enumerated nodes:
3.41/1.60	17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46
3.41/1.60	
3.41/1.60	Node 17 is start node and node 18 is final node.
3.41/1.60	
3.41/1.60	Those nodes are connected through the following edges:
3.41/1.60	
3.41/1.60	* 17 to 19 labelled a_1(0)* 17 to 21 labelled a_1(0)* 17 to 27 labelled a_1(1)* 18 to 18 labelled #_1(0)* 19 to 20 labelled b_1(0)* 19 to 25 labelled a_1(1)* 20 to 18 labelled a_1(0)* 20 to 23 labelled a_1(1)* 20 to 29 labelled a_1(2)* 20 to 33 labelled a_1(3)* 21 to 22 labelled c_1(0)* 22 to 18 labelled a_1(0)* 22 to 23 labelled a_1(1)* 22 to 29 labelled a_1(2)* 22 to 33 labelled a_1(3)* 23 to 24 labelled b_1(1)* 23 to 25 labelled a_1(1)* 23 to 31 labelled a_1(2)* 24 to 18 labelled a_1(1)* 24 to 23 labelled a_1(1)* 24 to 29 labelled a_1(2)* 24 to 33 labelled a_1(3)* 25 to 26 labelled c_1(1)* 26 to 18 labelled a_1(1)* 26 to 23 labelled a_1(1)* 26 to 24 labelled a_1(1)* 26 to 29 labelled a_1(2)* 26 to 30 labelled a_1(1)* 26 to 33 labelled a_1(3)* 26 to 34 labelled a_1(1)* 27 to 28 labelled b_1(1)* 28 to 25 labelled a_1(1)* 29 to 30 labelled b_1(2)* 29 to 25 labelled a_1(1)* 29 to 31 labelled a_1(2)* 29 to 37 labelled a_1(3)* 30 to 25 labelled a_1(2)* 30 to 18 labelled a_1(2)* 30 to 23 labelled a_1(2), a_1(1)* 30 to 29 labelled a_1(2)* 30 to 31 labelled a_1(2)* 30 to 33 labelled a_1(3), a_1(2)* 30 to 37 labelled a_1(2)* 31 to 32 labelled c_1(2)* 32 to 24 labelled a_1(2)* 32 to 29 labelled a_1(2)* 32 to 35 labelled a_1(3)* 32 to 30 labelled a_1(2)* 32 to 33 labelled a_1(3)* 32 to 39 labelled a_1(4)* 32 to 34 labelled a_1(2)* 33 to 34 labelled b_1(3)* 34 to 31 labelled a_1(3)* 34 to 37 labelled a_1(3)* 35 to 36 labelled b_1(3)* 35 to 37 labelled a_1(3)* 35 to 25 labelled a_1(1)* 35 to 31 labelled a_1(2)* 35 to 43 labelled a_1(4)* 36 to 29 labelled a_1(3), a_1(2)* 36 to 33 labelled a_1(3)* 36 to 25 labelled a_1(3)* 36 to 18 labelled a_1(3)* 36 to 23 labelled a_1(3), a_1(1)* 36 to 39 labelled a_1(4)* 37 to 38 labelled c_1(3)* 38 to 30 labelled a_1(3)* 38 to 34 labelled a_1(3)* 38 to 35 labelled a_1(3)* 38 to 29 labelled a_1(2)* 38 to 33 labelled a_1(3)* 38 to 41 labelled a_1(4)* 38 to 39 labelled a_1(4)* 38 to 45 labelled a_1(5)* 39 to 40 labelled b_1(4)* 40 to 37 labelled a_1(4)* 40 to 43 labelled a_1(4)* 41 to 42 labelled b_1(4)* 41 to 43 labelled a_1(4)* 42 to 33 labelled a_1(4)* 42 to 31 labelled a_1(4)* 43 to 44 labelled c_1(4)* 44 to 34 labelled a_1(4)* 44 to 41 labelled a_1(4)* 44 to 39 labelled a_1(4)* 44 to 40 labelled a_1(4)* 44 to 45 labelled a_1(5)* 45 to 46 labelled b_1(5)* 46 to 43 labelled a_1(5)* 46 to 37 labelled a_1(5)
3.41/1.60	
3.41/1.60	
3.41/1.60	----------------------------------------
3.41/1.60	
3.41/1.60	(4)
3.41/1.60	YES
3.44/1.62	EOF