4.56/1.76	YES
4.56/1.77	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.56/1.77	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.56/1.77	
4.56/1.77	
4.56/1.77	Outermost Termination of the given OTRS could be proven:
4.56/1.77	
4.56/1.77	(0) OTRS
4.56/1.77	(1) Raffelsieper-Zantema-Transformation [SOUND, 0 ms]
4.56/1.77	(2) QTRS
4.56/1.77	(3) QTRSRRRProof [EQUIVALENT, 42 ms]
4.56/1.77	(4) QTRS
4.56/1.77	(5) AAECC Innermost [EQUIVALENT, 0 ms]
4.56/1.77	(6) QTRS
4.56/1.77	(7) DependencyPairsProof [EQUIVALENT, 1 ms]
4.56/1.77	(8) QDP
4.56/1.77	(9) DependencyGraphProof [EQUIVALENT, 0 ms]
4.56/1.77	(10) AND
4.56/1.77	    (11) QDP
4.56/1.77	        (12) UsableRulesProof [EQUIVALENT, 0 ms]
4.56/1.77	        (13) QDP
4.56/1.77	        (14) QReductionProof [EQUIVALENT, 0 ms]
4.56/1.77	        (15) QDP
4.56/1.77	        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
4.56/1.77	        (17) YES
4.56/1.77	    (18) QDP
4.56/1.77	        (19) UsableRulesProof [EQUIVALENT, 0 ms]
4.56/1.77	        (20) QDP
4.56/1.77	        (21) QReductionProof [EQUIVALENT, 0 ms]
4.56/1.77	        (22) QDP
4.56/1.77	        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
4.56/1.77	        (24) YES
4.56/1.77	    (25) QDP
4.56/1.77	        (26) UsableRulesProof [EQUIVALENT, 0 ms]
4.56/1.77	        (27) QDP
4.56/1.77	        (28) QReductionProof [EQUIVALENT, 0 ms]
4.56/1.77	        (29) QDP
4.56/1.77	        (30) RFCMatchBoundsDPProof [EQUIVALENT, 15 ms]
4.56/1.77	        (31) YES
4.56/1.77	
4.56/1.77	
4.56/1.77	----------------------------------------
4.56/1.77	
4.56/1.77	(0)
4.56/1.77	Obligation:
4.56/1.77	Term rewrite system R:
4.56/1.77	The TRS R consists of the following rules:
4.56/1.77	
4.56/1.77	   f(f(g(x))) -> x
4.56/1.77	   g(b) -> f(g(b))
4.56/1.77	
4.56/1.77	
4.56/1.77	
4.56/1.77	Outermost Strategy.
4.56/1.77	
4.56/1.77	----------------------------------------
4.56/1.77	
4.56/1.77	(1) Raffelsieper-Zantema-Transformation (SOUND)
4.56/1.77	We applied the Raffelsieper-Zantema transformation  to transform the outermost TRS to a standard TRS.
4.56/1.77	----------------------------------------
4.56/1.77	
4.56/1.77	(2)
4.56/1.77	Obligation:
4.56/1.77	Q restricted rewrite system:
4.56/1.77	The TRS R consists of the following rules:
4.56/1.77	
4.56/1.77	   down(f(f(g(x)))) -> up(x)
4.56/1.77	   down(g(b)) -> up(f(g(b)))
4.56/1.77	   top(up(x)) -> top(down(x))
4.56/1.77	   down(f(g(y4))) -> f_flat(down(g(y4)))
4.56/1.77	   down(f(b)) -> f_flat(down(b))
4.56/1.77	   down(f(fresh_constant)) -> f_flat(down(fresh_constant))
4.56/1.77	   down(g(f(y6))) -> g_flat(down(f(y6)))
4.56/1.77	   down(g(g(y7))) -> g_flat(down(g(y7)))
4.56/1.77	   down(g(fresh_constant)) -> g_flat(down(fresh_constant))
4.56/1.77	   down(f(f(f(y9)))) -> f_flat(down(f(f(y9))))
4.56/1.77	   down(f(f(b))) -> f_flat(down(f(b)))
4.56/1.77	   down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant)))
4.56/1.77	   f_flat(up(x_1)) -> up(f(x_1))
4.56/1.77	   g_flat(up(x_1)) -> up(g(x_1))
4.56/1.77	
4.56/1.77	Q is empty.
4.56/1.77	
4.56/1.77	----------------------------------------
4.56/1.77	
4.56/1.77	(3) QTRSRRRProof (EQUIVALENT)
4.56/1.77	Used ordering:
4.56/1.77	Polynomial interpretation [POLO]:
4.56/1.77	
4.56/1.77	   POL(b) = 0
4.56/1.77	   POL(down(x_1)) = 2 + 2*x_1
4.56/1.77	   POL(f(x_1)) = x_1
4.56/1.77	   POL(f_flat(x_1)) = x_1
4.56/1.77	   POL(fresh_constant) = 0
4.56/1.77	   POL(g(x_1)) = 1 + 2*x_1
4.56/1.77	   POL(g_flat(x_1)) = 2*x_1
4.56/1.77	   POL(top(x_1)) = 2*x_1
4.56/1.77	   POL(up(x_1)) = 2 + 2*x_1
4.56/1.77	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
4.56/1.77	
4.56/1.77	   down(f(f(g(x)))) -> up(x)
4.56/1.77	
4.56/1.77	
4.56/1.77	
4.56/1.77	
4.56/1.77	----------------------------------------
4.56/1.77	
4.56/1.77	(4)
4.56/1.77	Obligation:
4.56/1.77	Q restricted rewrite system:
4.56/1.77	The TRS R consists of the following rules:
4.56/1.77	
4.56/1.77	   down(g(b)) -> up(f(g(b)))
4.56/1.77	   top(up(x)) -> top(down(x))
4.56/1.77	   down(f(g(y4))) -> f_flat(down(g(y4)))
4.56/1.77	   down(f(b)) -> f_flat(down(b))
4.56/1.77	   down(f(fresh_constant)) -> f_flat(down(fresh_constant))
4.56/1.77	   down(g(f(y6))) -> g_flat(down(f(y6)))
4.56/1.77	   down(g(g(y7))) -> g_flat(down(g(y7)))
4.56/1.77	   down(g(fresh_constant)) -> g_flat(down(fresh_constant))
4.56/1.77	   down(f(f(f(y9)))) -> f_flat(down(f(f(y9))))
4.56/1.77	   down(f(f(b))) -> f_flat(down(f(b)))
4.56/1.77	   down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant)))
4.56/1.77	   f_flat(up(x_1)) -> up(f(x_1))
4.56/1.77	   g_flat(up(x_1)) -> up(g(x_1))
4.56/1.77	
4.56/1.77	Q is empty.
4.56/1.77	
4.56/1.77	----------------------------------------
4.56/1.77	
4.56/1.77	(5) AAECC Innermost (EQUIVALENT)
4.56/1.77	We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is 
4.56/1.77	   down(f(g(y4))) -> f_flat(down(g(y4)))
4.56/1.77	   down(f(b)) -> f_flat(down(b))
4.56/1.77	   down(f(fresh_constant)) -> f_flat(down(fresh_constant))
4.56/1.77	   down(g(f(y6))) -> g_flat(down(f(y6)))
4.56/1.77	   down(g(g(y7))) -> g_flat(down(g(y7)))
4.56/1.77	   down(g(fresh_constant)) -> g_flat(down(fresh_constant))
4.56/1.77	   down(f(f(f(y9)))) -> f_flat(down(f(f(y9))))
4.56/1.77	   down(f(f(b))) -> f_flat(down(f(b)))
4.56/1.77	   down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant)))
4.56/1.77	   f_flat(up(x_1)) -> up(f(x_1))
4.56/1.77	   g_flat(up(x_1)) -> up(g(x_1))
4.56/1.77	   down(g(b)) -> up(f(g(b)))
4.56/1.77	
4.56/1.77	The TRS R 2 is 
4.56/1.77	   top(up(x)) -> top(down(x))
4.56/1.77	
4.56/1.77	The signature Sigma is {top_1}
4.56/1.77	----------------------------------------
4.56/1.77	
4.56/1.77	(6)
4.56/1.77	Obligation:
4.56/1.77	Q restricted rewrite system:
4.56/1.77	The TRS R consists of the following rules:
4.56/1.77	
4.56/1.77	   down(g(b)) -> up(f(g(b)))
4.56/1.77	   top(up(x)) -> top(down(x))
4.56/1.77	   down(f(g(y4))) -> f_flat(down(g(y4)))
4.56/1.77	   down(f(b)) -> f_flat(down(b))
4.56/1.77	   down(f(fresh_constant)) -> f_flat(down(fresh_constant))
4.56/1.77	   down(g(f(y6))) -> g_flat(down(f(y6)))
4.56/1.77	   down(g(g(y7))) -> g_flat(down(g(y7)))
4.56/1.77	   down(g(fresh_constant)) -> g_flat(down(fresh_constant))
4.56/1.77	   down(f(f(f(y9)))) -> f_flat(down(f(f(y9))))
4.56/1.77	   down(f(f(b))) -> f_flat(down(f(b)))
4.56/1.77	   down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant)))
4.56/1.77	   f_flat(up(x_1)) -> up(f(x_1))
4.56/1.77	   g_flat(up(x_1)) -> up(g(x_1))
4.56/1.77	
4.56/1.77	The set Q consists of the following terms:
4.56/1.77	
4.56/1.77	   down(g(b))
4.56/1.77	   top(up(x0))
4.56/1.77	   down(f(g(x0)))
4.56/1.77	   down(f(b))
4.56/1.77	   down(f(fresh_constant))
4.56/1.77	   down(g(f(x0)))
4.56/1.77	   down(g(g(x0)))
4.56/1.77	   down(g(fresh_constant))
4.56/1.77	   down(f(f(f(x0))))
4.56/1.77	   down(f(f(b)))
4.56/1.77	   down(f(f(fresh_constant)))
4.56/1.77	   f_flat(up(x0))
4.56/1.77	   g_flat(up(x0))
4.56/1.77	
4.56/1.77	
4.56/1.77	----------------------------------------
4.56/1.77	
4.56/1.77	(7) DependencyPairsProof (EQUIVALENT)
4.56/1.77	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
4.56/1.77	----------------------------------------
4.56/1.77	
4.56/1.77	(8)
4.56/1.77	Obligation:
4.56/1.77	Q DP problem:
4.56/1.77	The TRS P consists of the following rules:
4.56/1.77	
4.56/1.77	   TOP(up(x)) -> TOP(down(x))
4.56/1.77	   TOP(up(x)) -> DOWN(x)
4.56/1.77	   DOWN(f(g(y4))) -> F_FLAT(down(g(y4)))
4.56/1.77	   DOWN(f(g(y4))) -> DOWN(g(y4))
4.56/1.77	   DOWN(f(b)) -> F_FLAT(down(b))
4.56/1.77	   DOWN(f(b)) -> DOWN(b)
4.56/1.77	   DOWN(f(fresh_constant)) -> F_FLAT(down(fresh_constant))
4.56/1.77	   DOWN(f(fresh_constant)) -> DOWN(fresh_constant)
4.56/1.77	   DOWN(g(f(y6))) -> G_FLAT(down(f(y6)))
4.56/1.77	   DOWN(g(f(y6))) -> DOWN(f(y6))
4.56/1.77	   DOWN(g(g(y7))) -> G_FLAT(down(g(y7)))
4.56/1.77	   DOWN(g(g(y7))) -> DOWN(g(y7))
4.56/1.77	   DOWN(g(fresh_constant)) -> G_FLAT(down(fresh_constant))
4.56/1.77	   DOWN(g(fresh_constant)) -> DOWN(fresh_constant)
4.56/1.77	   DOWN(f(f(f(y9)))) -> F_FLAT(down(f(f(y9))))
4.56/1.77	   DOWN(f(f(f(y9)))) -> DOWN(f(f(y9)))
4.56/1.77	   DOWN(f(f(b))) -> F_FLAT(down(f(b)))
4.56/1.77	   DOWN(f(f(b))) -> DOWN(f(b))
4.56/1.77	   DOWN(f(f(fresh_constant))) -> F_FLAT(down(f(fresh_constant)))
4.56/1.77	   DOWN(f(f(fresh_constant))) -> DOWN(f(fresh_constant))
4.56/1.77	
4.56/1.77	The TRS R consists of the following rules:
4.56/1.77	
4.56/1.77	   down(g(b)) -> up(f(g(b)))
4.56/1.77	   top(up(x)) -> top(down(x))
4.56/1.77	   down(f(g(y4))) -> f_flat(down(g(y4)))
4.56/1.77	   down(f(b)) -> f_flat(down(b))
4.56/1.77	   down(f(fresh_constant)) -> f_flat(down(fresh_constant))
4.56/1.77	   down(g(f(y6))) -> g_flat(down(f(y6)))
4.56/1.77	   down(g(g(y7))) -> g_flat(down(g(y7)))
4.56/1.77	   down(g(fresh_constant)) -> g_flat(down(fresh_constant))
4.56/1.77	   down(f(f(f(y9)))) -> f_flat(down(f(f(y9))))
4.56/1.77	   down(f(f(b))) -> f_flat(down(f(b)))
4.56/1.77	   down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant)))
4.56/1.77	   f_flat(up(x_1)) -> up(f(x_1))
4.56/1.77	   g_flat(up(x_1)) -> up(g(x_1))
4.56/1.77	
4.56/1.77	The set Q consists of the following terms:
4.56/1.77	
4.56/1.77	   down(g(b))
4.56/1.77	   top(up(x0))
4.56/1.77	   down(f(g(x0)))
4.56/1.77	   down(f(b))
4.56/1.77	   down(f(fresh_constant))
4.56/1.77	   down(g(f(x0)))
4.56/1.77	   down(g(g(x0)))
4.56/1.77	   down(g(fresh_constant))
4.56/1.77	   down(f(f(f(x0))))
4.56/1.77	   down(f(f(b)))
4.56/1.77	   down(f(f(fresh_constant)))
4.56/1.77	   f_flat(up(x0))
4.56/1.77	   g_flat(up(x0))
4.56/1.77	
4.56/1.77	We have to consider all minimal (P,Q,R)-chains.
4.56/1.77	----------------------------------------
4.56/1.77	
4.56/1.77	(9) DependencyGraphProof (EQUIVALENT)
4.56/1.77	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 3 SCCs with 15 less nodes.
4.56/1.77	----------------------------------------
4.56/1.77	
4.56/1.77	(10)
4.56/1.77	Complex Obligation (AND)
4.56/1.77	
4.56/1.77	----------------------------------------
4.56/1.77	
4.56/1.77	(11)
4.56/1.77	Obligation:
4.56/1.77	Q DP problem:
4.56/1.77	The TRS P consists of the following rules:
4.56/1.77	
4.56/1.77	   DOWN(f(f(f(y9)))) -> DOWN(f(f(y9)))
4.56/1.77	
4.56/1.77	The TRS R consists of the following rules:
4.56/1.77	
4.56/1.77	   down(g(b)) -> up(f(g(b)))
4.56/1.77	   top(up(x)) -> top(down(x))
4.56/1.77	   down(f(g(y4))) -> f_flat(down(g(y4)))
4.56/1.77	   down(f(b)) -> f_flat(down(b))
4.56/1.77	   down(f(fresh_constant)) -> f_flat(down(fresh_constant))
4.56/1.77	   down(g(f(y6))) -> g_flat(down(f(y6)))
4.56/1.77	   down(g(g(y7))) -> g_flat(down(g(y7)))
4.56/1.77	   down(g(fresh_constant)) -> g_flat(down(fresh_constant))
4.56/1.77	   down(f(f(f(y9)))) -> f_flat(down(f(f(y9))))
4.56/1.77	   down(f(f(b))) -> f_flat(down(f(b)))
4.56/1.77	   down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant)))
4.56/1.77	   f_flat(up(x_1)) -> up(f(x_1))
4.56/1.78	   g_flat(up(x_1)) -> up(g(x_1))
4.56/1.78	
4.56/1.78	The set Q consists of the following terms:
4.56/1.78	
4.56/1.78	   down(g(b))
4.56/1.78	   top(up(x0))
4.56/1.78	   down(f(g(x0)))
4.56/1.78	   down(f(b))
4.56/1.78	   down(f(fresh_constant))
4.56/1.78	   down(g(f(x0)))
4.56/1.78	   down(g(g(x0)))
4.56/1.78	   down(g(fresh_constant))
4.56/1.78	   down(f(f(f(x0))))
4.56/1.78	   down(f(f(b)))
4.56/1.78	   down(f(f(fresh_constant)))
4.56/1.78	   f_flat(up(x0))
4.56/1.78	   g_flat(up(x0))
4.56/1.78	
4.56/1.78	We have to consider all minimal (P,Q,R)-chains.
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(12) UsableRulesProof (EQUIVALENT)
4.56/1.78	As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(13)
4.56/1.78	Obligation:
4.56/1.78	Q DP problem:
4.56/1.78	The TRS P consists of the following rules:
4.56/1.78	
4.56/1.78	   DOWN(f(f(f(y9)))) -> DOWN(f(f(y9)))
4.56/1.78	
4.56/1.78	R is empty.
4.56/1.78	The set Q consists of the following terms:
4.56/1.78	
4.56/1.78	   down(g(b))
4.56/1.78	   top(up(x0))
4.56/1.78	   down(f(g(x0)))
4.56/1.78	   down(f(b))
4.56/1.78	   down(f(fresh_constant))
4.56/1.78	   down(g(f(x0)))
4.56/1.78	   down(g(g(x0)))
4.56/1.78	   down(g(fresh_constant))
4.56/1.78	   down(f(f(f(x0))))
4.56/1.78	   down(f(f(b)))
4.56/1.78	   down(f(f(fresh_constant)))
4.56/1.78	   f_flat(up(x0))
4.56/1.78	   g_flat(up(x0))
4.56/1.78	
4.56/1.78	We have to consider all minimal (P,Q,R)-chains.
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(14) QReductionProof (EQUIVALENT)
4.56/1.78	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
4.56/1.78	
4.56/1.78	   down(g(b))
4.56/1.78	   top(up(x0))
4.56/1.78	   down(f(g(x0)))
4.56/1.78	   down(f(b))
4.56/1.78	   down(f(fresh_constant))
4.56/1.78	   down(g(f(x0)))
4.56/1.78	   down(g(g(x0)))
4.56/1.78	   down(g(fresh_constant))
4.56/1.78	   down(f(f(f(x0))))
4.56/1.78	   down(f(f(b)))
4.56/1.78	   down(f(f(fresh_constant)))
4.56/1.78	   f_flat(up(x0))
4.56/1.78	   g_flat(up(x0))
4.56/1.78	
4.56/1.78	
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(15)
4.56/1.78	Obligation:
4.56/1.78	Q DP problem:
4.56/1.78	The TRS P consists of the following rules:
4.56/1.78	
4.56/1.78	   DOWN(f(f(f(y9)))) -> DOWN(f(f(y9)))
4.56/1.78	
4.56/1.78	R is empty.
4.56/1.78	Q is empty.
4.56/1.78	We have to consider all minimal (P,Q,R)-chains.
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(16) QDPSizeChangeProof (EQUIVALENT)
4.56/1.78	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
4.56/1.78	
4.56/1.78	From the DPs we obtained the following set of size-change graphs:
4.56/1.78	*DOWN(f(f(f(y9)))) -> DOWN(f(f(y9)))
4.56/1.78	The graph contains the following edges 1 > 1
4.56/1.78	
4.56/1.78	
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(17)
4.56/1.78	YES
4.56/1.78	
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(18)
4.56/1.78	Obligation:
4.56/1.78	Q DP problem:
4.56/1.78	The TRS P consists of the following rules:
4.56/1.78	
4.56/1.78	   DOWN(g(f(y6))) -> DOWN(f(y6))
4.56/1.78	   DOWN(f(g(y4))) -> DOWN(g(y4))
4.56/1.78	   DOWN(g(g(y7))) -> DOWN(g(y7))
4.56/1.78	
4.56/1.78	The TRS R consists of the following rules:
4.56/1.78	
4.56/1.78	   down(g(b)) -> up(f(g(b)))
4.56/1.78	   top(up(x)) -> top(down(x))
4.56/1.78	   down(f(g(y4))) -> f_flat(down(g(y4)))
4.56/1.78	   down(f(b)) -> f_flat(down(b))
4.56/1.78	   down(f(fresh_constant)) -> f_flat(down(fresh_constant))
4.56/1.78	   down(g(f(y6))) -> g_flat(down(f(y6)))
4.56/1.78	   down(g(g(y7))) -> g_flat(down(g(y7)))
4.56/1.78	   down(g(fresh_constant)) -> g_flat(down(fresh_constant))
4.56/1.78	   down(f(f(f(y9)))) -> f_flat(down(f(f(y9))))
4.56/1.78	   down(f(f(b))) -> f_flat(down(f(b)))
4.56/1.78	   down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant)))
4.56/1.78	   f_flat(up(x_1)) -> up(f(x_1))
4.56/1.78	   g_flat(up(x_1)) -> up(g(x_1))
4.56/1.78	
4.56/1.78	The set Q consists of the following terms:
4.56/1.78	
4.56/1.78	   down(g(b))
4.56/1.78	   top(up(x0))
4.56/1.78	   down(f(g(x0)))
4.56/1.78	   down(f(b))
4.56/1.78	   down(f(fresh_constant))
4.56/1.78	   down(g(f(x0)))
4.56/1.78	   down(g(g(x0)))
4.56/1.78	   down(g(fresh_constant))
4.56/1.78	   down(f(f(f(x0))))
4.56/1.78	   down(f(f(b)))
4.56/1.78	   down(f(f(fresh_constant)))
4.56/1.78	   f_flat(up(x0))
4.56/1.78	   g_flat(up(x0))
4.56/1.78	
4.56/1.78	We have to consider all minimal (P,Q,R)-chains.
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(19) UsableRulesProof (EQUIVALENT)
4.56/1.78	As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(20)
4.56/1.78	Obligation:
4.56/1.78	Q DP problem:
4.56/1.78	The TRS P consists of the following rules:
4.56/1.78	
4.56/1.78	   DOWN(g(f(y6))) -> DOWN(f(y6))
4.56/1.78	   DOWN(f(g(y4))) -> DOWN(g(y4))
4.56/1.78	   DOWN(g(g(y7))) -> DOWN(g(y7))
4.56/1.78	
4.56/1.78	R is empty.
4.56/1.78	The set Q consists of the following terms:
4.56/1.78	
4.56/1.78	   down(g(b))
4.56/1.78	   top(up(x0))
4.56/1.78	   down(f(g(x0)))
4.56/1.78	   down(f(b))
4.56/1.78	   down(f(fresh_constant))
4.56/1.78	   down(g(f(x0)))
4.56/1.78	   down(g(g(x0)))
4.56/1.78	   down(g(fresh_constant))
4.56/1.78	   down(f(f(f(x0))))
4.56/1.78	   down(f(f(b)))
4.56/1.78	   down(f(f(fresh_constant)))
4.56/1.78	   f_flat(up(x0))
4.56/1.78	   g_flat(up(x0))
4.56/1.78	
4.56/1.78	We have to consider all minimal (P,Q,R)-chains.
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(21) QReductionProof (EQUIVALENT)
4.56/1.78	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
4.56/1.78	
4.56/1.78	   down(g(b))
4.56/1.78	   top(up(x0))
4.56/1.78	   down(f(g(x0)))
4.56/1.78	   down(f(b))
4.56/1.78	   down(f(fresh_constant))
4.56/1.78	   down(g(f(x0)))
4.56/1.78	   down(g(g(x0)))
4.56/1.78	   down(g(fresh_constant))
4.56/1.78	   down(f(f(f(x0))))
4.56/1.78	   down(f(f(b)))
4.56/1.78	   down(f(f(fresh_constant)))
4.56/1.78	   f_flat(up(x0))
4.56/1.78	   g_flat(up(x0))
4.56/1.78	
4.56/1.78	
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(22)
4.56/1.78	Obligation:
4.56/1.78	Q DP problem:
4.56/1.78	The TRS P consists of the following rules:
4.56/1.78	
4.56/1.78	   DOWN(g(f(y6))) -> DOWN(f(y6))
4.56/1.78	   DOWN(f(g(y4))) -> DOWN(g(y4))
4.56/1.78	   DOWN(g(g(y7))) -> DOWN(g(y7))
4.56/1.78	
4.56/1.78	R is empty.
4.56/1.78	Q is empty.
4.56/1.78	We have to consider all minimal (P,Q,R)-chains.
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(23) QDPSizeChangeProof (EQUIVALENT)
4.56/1.78	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
4.56/1.78	
4.56/1.78	From the DPs we obtained the following set of size-change graphs:
4.56/1.78	*DOWN(f(g(y4))) -> DOWN(g(y4))
4.56/1.78	The graph contains the following edges 1 > 1
4.56/1.78	
4.56/1.78	
4.56/1.78	*DOWN(g(g(y7))) -> DOWN(g(y7))
4.56/1.78	The graph contains the following edges 1 > 1
4.56/1.78	
4.56/1.78	
4.56/1.78	*DOWN(g(f(y6))) -> DOWN(f(y6))
4.56/1.78	The graph contains the following edges 1 > 1
4.56/1.78	
4.56/1.78	
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(24)
4.56/1.78	YES
4.56/1.78	
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(25)
4.56/1.78	Obligation:
4.56/1.78	Q DP problem:
4.56/1.78	The TRS P consists of the following rules:
4.56/1.78	
4.56/1.78	   TOP(up(x)) -> TOP(down(x))
4.56/1.78	
4.56/1.78	The TRS R consists of the following rules:
4.56/1.78	
4.56/1.78	   down(g(b)) -> up(f(g(b)))
4.56/1.78	   top(up(x)) -> top(down(x))
4.56/1.78	   down(f(g(y4))) -> f_flat(down(g(y4)))
4.56/1.78	   down(f(b)) -> f_flat(down(b))
4.56/1.78	   down(f(fresh_constant)) -> f_flat(down(fresh_constant))
4.56/1.78	   down(g(f(y6))) -> g_flat(down(f(y6)))
4.56/1.78	   down(g(g(y7))) -> g_flat(down(g(y7)))
4.56/1.78	   down(g(fresh_constant)) -> g_flat(down(fresh_constant))
4.56/1.78	   down(f(f(f(y9)))) -> f_flat(down(f(f(y9))))
4.56/1.78	   down(f(f(b))) -> f_flat(down(f(b)))
4.56/1.78	   down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant)))
4.56/1.78	   f_flat(up(x_1)) -> up(f(x_1))
4.56/1.78	   g_flat(up(x_1)) -> up(g(x_1))
4.56/1.78	
4.56/1.78	The set Q consists of the following terms:
4.56/1.78	
4.56/1.78	   down(g(b))
4.56/1.78	   top(up(x0))
4.56/1.78	   down(f(g(x0)))
4.56/1.78	   down(f(b))
4.56/1.78	   down(f(fresh_constant))
4.56/1.78	   down(g(f(x0)))
4.56/1.78	   down(g(g(x0)))
4.56/1.78	   down(g(fresh_constant))
4.56/1.78	   down(f(f(f(x0))))
4.56/1.78	   down(f(f(b)))
4.56/1.78	   down(f(f(fresh_constant)))
4.56/1.78	   f_flat(up(x0))
4.56/1.78	   g_flat(up(x0))
4.56/1.78	
4.56/1.78	We have to consider all minimal (P,Q,R)-chains.
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(26) UsableRulesProof (EQUIVALENT)
4.56/1.78	As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(27)
4.56/1.78	Obligation:
4.56/1.78	Q DP problem:
4.56/1.78	The TRS P consists of the following rules:
4.56/1.78	
4.56/1.78	   TOP(up(x)) -> TOP(down(x))
4.56/1.78	
4.56/1.78	The TRS R consists of the following rules:
4.56/1.78	
4.56/1.78	   down(g(b)) -> up(f(g(b)))
4.56/1.78	   down(f(g(y4))) -> f_flat(down(g(y4)))
4.56/1.78	   down(f(b)) -> f_flat(down(b))
4.56/1.78	   down(f(fresh_constant)) -> f_flat(down(fresh_constant))
4.56/1.78	   down(g(f(y6))) -> g_flat(down(f(y6)))
4.56/1.78	   down(g(g(y7))) -> g_flat(down(g(y7)))
4.56/1.78	   down(g(fresh_constant)) -> g_flat(down(fresh_constant))
4.56/1.78	   down(f(f(f(y9)))) -> f_flat(down(f(f(y9))))
4.56/1.78	   down(f(f(b))) -> f_flat(down(f(b)))
4.56/1.78	   down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant)))
4.56/1.78	   f_flat(up(x_1)) -> up(f(x_1))
4.56/1.78	   g_flat(up(x_1)) -> up(g(x_1))
4.56/1.78	
4.56/1.78	The set Q consists of the following terms:
4.56/1.78	
4.56/1.78	   down(g(b))
4.56/1.78	   top(up(x0))
4.56/1.78	   down(f(g(x0)))
4.56/1.78	   down(f(b))
4.56/1.78	   down(f(fresh_constant))
4.56/1.78	   down(g(f(x0)))
4.56/1.78	   down(g(g(x0)))
4.56/1.78	   down(g(fresh_constant))
4.56/1.78	   down(f(f(f(x0))))
4.56/1.78	   down(f(f(b)))
4.56/1.78	   down(f(f(fresh_constant)))
4.56/1.78	   f_flat(up(x0))
4.56/1.78	   g_flat(up(x0))
4.56/1.78	
4.56/1.78	We have to consider all minimal (P,Q,R)-chains.
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(28) QReductionProof (EQUIVALENT)
4.56/1.78	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
4.56/1.78	
4.56/1.78	   top(up(x0))
4.56/1.78	
4.56/1.78	
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(29)
4.56/1.78	Obligation:
4.56/1.78	Q DP problem:
4.56/1.78	The TRS P consists of the following rules:
4.56/1.78	
4.56/1.78	   TOP(up(x)) -> TOP(down(x))
4.56/1.78	
4.56/1.78	The TRS R consists of the following rules:
4.56/1.78	
4.56/1.78	   down(g(b)) -> up(f(g(b)))
4.56/1.78	   down(f(g(y4))) -> f_flat(down(g(y4)))
4.56/1.78	   down(f(b)) -> f_flat(down(b))
4.56/1.78	   down(f(fresh_constant)) -> f_flat(down(fresh_constant))
4.56/1.78	   down(g(f(y6))) -> g_flat(down(f(y6)))
4.56/1.78	   down(g(g(y7))) -> g_flat(down(g(y7)))
4.56/1.78	   down(g(fresh_constant)) -> g_flat(down(fresh_constant))
4.56/1.78	   down(f(f(f(y9)))) -> f_flat(down(f(f(y9))))
4.56/1.78	   down(f(f(b))) -> f_flat(down(f(b)))
4.56/1.78	   down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant)))
4.56/1.78	   f_flat(up(x_1)) -> up(f(x_1))
4.56/1.78	   g_flat(up(x_1)) -> up(g(x_1))
4.56/1.78	
4.56/1.78	The set Q consists of the following terms:
4.56/1.78	
4.56/1.78	   down(g(b))
4.56/1.78	   down(f(g(x0)))
4.56/1.78	   down(f(b))
4.56/1.78	   down(f(fresh_constant))
4.56/1.78	   down(g(f(x0)))
4.56/1.78	   down(g(g(x0)))
4.56/1.78	   down(g(fresh_constant))
4.56/1.78	   down(f(f(f(x0))))
4.56/1.78	   down(f(f(b)))
4.56/1.78	   down(f(f(fresh_constant)))
4.56/1.78	   f_flat(up(x0))
4.56/1.78	   g_flat(up(x0))
4.56/1.78	
4.56/1.78	We have to consider all minimal (P,Q,R)-chains.
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(30) RFCMatchBoundsDPProof (EQUIVALENT)
4.56/1.78	Finiteness of the DP problem can be shown by a matchbound of 9. 
4.56/1.78	As the DP problem is minimal we only have to initialize the certificate graph by the rules of P:
4.56/1.78	
4.56/1.78	   TOP(up(x)) -> TOP(down(x))
4.56/1.78	
4.56/1.78	To find matches we regarded all rules of R and P:
4.56/1.78	
4.56/1.78	   down(g(b)) -> up(f(g(b)))
4.56/1.78	   down(f(g(y4))) -> f_flat(down(g(y4)))
4.56/1.78	   down(f(b)) -> f_flat(down(b))
4.56/1.78	   down(f(fresh_constant)) -> f_flat(down(fresh_constant))
4.56/1.78	   down(g(f(y6))) -> g_flat(down(f(y6)))
4.56/1.78	   down(g(g(y7))) -> g_flat(down(g(y7)))
4.56/1.78	   down(g(fresh_constant)) -> g_flat(down(fresh_constant))
4.56/1.78	   down(f(f(f(y9)))) -> f_flat(down(f(f(y9))))
4.56/1.78	   down(f(f(b))) -> f_flat(down(f(b)))
4.56/1.78	   down(f(f(fresh_constant))) -> f_flat(down(f(fresh_constant)))
4.56/1.78	   f_flat(up(x_1)) -> up(f(x_1))
4.56/1.78	   g_flat(up(x_1)) -> up(g(x_1))
4.56/1.78	   TOP(up(x)) -> TOP(down(x))
4.56/1.78	
4.56/1.78	The certificate found is represented by the following graph.
4.56/1.78	The certificate consists of the following enumerated nodes:
4.56/1.78	462, 463, 464, 465, 466, 467, 469, 470, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 487, 488, 489, 490, 514, 515, 516, 517, 518, 519, 520, 522, 523, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 538, 539, 540, 541, 542, 543, 544, 545, 546, 549, 550, 551, 553, 555, 556, 557, 558, 559, 560, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 603, 604, 655, 656, 657
4.56/1.78	
4.56/1.78	Node 462 is start node and node 463 is final node.
4.56/1.78	
4.56/1.78	Those nodes are connected through the following edges:
4.56/1.78	
4.56/1.78	* 462 to 464 labelled TOP_1(0)* 462 to 477 labelled TOP_1(1)* 462 to 490 labelled TOP_1(2)* 462 to 549 labelled TOP_1(3)* 463 to 463 labelled #_1(0)* 464 to 463 labelled down_1(0)* 464 to 465 labelled up_1(1)* 464 to 469 labelled f_flat_1(1), g_flat_1(1)* 464 to 472 labelled g_flat_1(1)* 464 to 474 labelled f_flat_1(1)* 464 to 480 labelled up_1(2)* 465 to 466 labelled f_1(1)* 466 to 467 labelled g_1(1)* 467 to 463 labelled b(1)* 469 to 470 labelled down_1(1)* 469 to 465 labelled up_1(1)* 469 to 472 labelled g_flat_1(1)* 469 to 469 labelled g_flat_1(1)* 469 to 480 labelled up_1(2)* 470 to 463 labelled g_1(1), b(1), fresh_constant(1)* 472 to 473 labelled down_1(1)* 472 to 469 labelled f_flat_1(1)* 472 to 474 labelled f_flat_1(1)* 472 to 480 labelled up_1(2)* 473 to 463 labelled f_1(1)* 474 to 475 labelled down_1(1)* 474 to 478 labelled f_flat_1(2)* 474 to 474 labelled f_flat_1(1)* 475 to 476 labelled f_1(1)* 476 to 463 labelled f_1(1), b(1), fresh_constant(1)* 477 to 465 labelled down_1(1)* 477 to 481 labelled f_flat_1(2), g_flat_1(2)* 477 to 480 labelled down_1(1)* 477 to 487 labelled up_1(3)* 477 to 488 labelled g_flat_1(2)* 478 to 479 labelled down_1(2)* 479 to 463 labelled b(2), fresh_constant(2)* 480 to 465 labelled f_1(2), g_1(2)* 480 to 480 labelled f_1(2), g_1(2)* 480 to 466 labelled f_1(2)* 481 to 482 labelled down_1(2)* 481 to 483 labelled up_1(2)* 481 to 488 labelled g_flat_1(2)* 481 to 514 labelled g_flat_1(3)* 481 to 516 labelled f_flat_1(3), g_flat_1(3)* 481 to 481 labelled f_flat_1(2)* 481 to 518 labelled f_flat_1(3)* 481 to 487 labelled up_1(3)* 481 to 527 labelled up_1(4)* 482 to 467 labelled g_1(2)* 482 to 465 labelled g_1(2)* 482 to 480 labelled f_1(2), g_1(2)* 483 to 484 labelled f_1(2)* 484 to 485 labelled g_1(2)* 485 to 463 labelled b(2)* 487 to 483 labelled f_1(3), g_1(3)* 487 to 487 labelled f_1(3), g_1(3), f_1(5)* 487 to 527 labelled f_1(3), g_1(3), f_1(5)* 488 to 489 labelled down_1(2)* 488 to 481 labelled f_flat_1(2)* 488 to 487 labelled up_1(3)* 489 to 466 labelled f_1(2)* 489 to 465 labelled f_1(2)* 490 to 487 labelled down_1(2)* 490 to 522 labelled g_flat_1(3), f_flat_1(3)* 490 to 528 labelled f_flat_1(3), g_flat_1(3)* 490 to 533 labelled f_flat_1(3)* 490 to 546 labelled up_1(4)* 514 to 515 labelled down_1(3)* 514 to 481 labelled f_flat_1(2)* 514 to 516 labelled f_flat_1(3)* 514 to 518 labelled f_flat_1(3)* 514 to 487 labelled up_1(3)* 514 to 527 labelled up_1(4)* 515 to 465 labelled f_1(3)* 515 to 480 labelled f_1(3)* 515 to 466 labelled f_1(3)* 516 to 517 labelled down_1(3)* 516 to 488 labelled g_flat_1(2)* 516 to 514 labelled g_flat_1(3)* 516 to 516 labelled g_flat_1(3)* 516 to 487 labelled up_1(3)* 516 to 527 labelled up_1(4)* 517 to 465 labelled g_1(3)* 517 to 480 labelled g_1(3)* 518 to 519 labelled down_1(3)* 518 to 481 labelled f_flat_1(2)* 518 to 518 labelled f_flat_1(3)* 518 to 487 labelled up_1(3)* 518 to 527 labelled up_1(4)* 519 to 520 labelled f_1(3)* 520 to 465 labelled f_1(3)* 520 to 480 labelled f_1(3)* 520 to 466 labelled f_1(3)* 522 to 523 labelled down_1(3)* 522 to 525 labelled f_flat_1(3)* 522 to 538 labelled up_1(4)* 522 to 541 labelled f_flat_1(4), g_flat_1(4)* 522 to 533 labelled f_flat_1(3)* 522 to 543 labelled f_flat_1(4)* 522 to 539 labelled f_flat_1(4), g_flat_1(4)* 522 to 553 labelled up_1(5)* 523 to 484 labelled f_1(3)* 523 to 483 labelled f_1(3)* 523 to 487 labelled f_1(3)* 523 to 527 labelled f_1(3), g_1(3)* 525 to 526 labelled down_1(3)* 525 to 530 labelled up_1(3)* 526 to 485 labelled g_1(3)* 527 to 487 labelled g_1(4), f_1(4)* 527 to 527 labelled g_1(4), f_1(4)* 528 to 529 labelled down_1(3)* 528 to 522 labelled g_flat_1(3)* 528 to 539 labelled g_flat_1(4)* 528 to 541 labelled g_flat_1(4)* 528 to 546 labelled up_1(4)* 528 to 553 labelled up_1(5)* 529 to 483 labelled g_1(3)* 529 to 487 labelled g_1(3)* 530 to 531 labelled f_1(3)* 530 to 590 labelled f_1(4)* 530 to 589 labelled f_1(4)* 530 to 591 labelled f_1(4)* 531 to 532 labelled g_1(3)* 532 to 463 labelled b(3)* 533 to 534 labelled down_1(3)* 534 to 535 labelled f_1(3)* 535 to 484 labelled f_1(3)* 538 to 530 labelled f_1(4)* 539 to 540 labelled down_1(4)* 539 to 541 labelled f_flat_1(4)* 539 to 533 labelled f_flat_1(3)* 539 to 543 labelled f_flat_1(4)* 539 to 539 labelled f_flat_1(4)* 539 to 550 labelled f_flat_1(5)* 539 to 553 labelled up_1(5)* 539 to 589 labelled up_1(6)* 540 to 483 labelled f_1(4)* 540 to 487 labelled f_1(4)* 540 to 527 labelled f_1(4)* 541 to 542 labelled down_1(4)* 541 to 522 labelled g_flat_1(3)* 541 to 539 labelled g_flat_1(4)* 541 to 541 labelled g_flat_1(4)* 541 to 546 labelled up_1(4)* 541 to 550 labelled g_flat_1(5)* 541 to 553 labelled up_1(5)* 541 to 590 labelled up_1(6)* 542 to 483 labelled g_1(4)* 542 to 487 labelled g_1(4)* 542 to 527 labelled g_1(4)* 543 to 544 labelled down_1(4)* 543 to 533 labelled f_flat_1(3)* 543 to 543 labelled f_flat_1(4)* 543 to 539 labelled f_flat_1(4)* 543 to 550 labelled f_flat_1(5)* 543 to 553 labelled up_1(5)* 543 to 589 labelled up_1(6)* 544 to 545 labelled f_1(4)* 545 to 483 labelled f_1(4)* 545 to 487 labelled f_1(4)* 546 to 538 labelled g_1(4), f_1(4)* 546 to 546 labelled f_1(4), g_1(4)* 546 to 553 labelled g_1(4), f_1(4)* 549 to 546 labelled down_1(3)* 549 to 557 labelled g_flat_1(4), f_flat_1(4)* 549 to 559 labelled f_flat_1(4), g_flat_1(4)* 549 to 579 labelled f_flat_1(4)* 550 to 551 labelled down_1(5)* 550 to 539 labelled g_flat_1(4), f_flat_1(4)* 550 to 541 labelled g_flat_1(4), f_flat_1(4)* 550 to 555 labelled g_flat_1(6)* 550 to 550 labelled g_flat_1(5), f_flat_1(5)* 550 to 533 labelled f_flat_1(3)* 550 to 543 labelled f_flat_1(4)* 550 to 576 labelled f_flat_1(6)* 550 to 553 labelled up_1(5)* 550 to 590 labelled up_1(6)* 550 to 589 labelled up_1(6)* 550 to 591 labelled up_1(7)* 551 to 487 labelled g_1(5), f_1(5)* 551 to 527 labelled g_1(5), f_1(5)* 553 to 546 labelled f_1(5), g_1(5)* 553 to 553 labelled f_1(5), g_1(5), f_1(7), f_1(8)* 553 to 590 labelled f_1(5), g_1(5), f_1(7), f_1(8)* 553 to 589 labelled f_1(5), g_1(5), f_1(8)* 553 to 591 labelled f_1(8)* 555 to 556 labelled down_1(6)* 555 to 541 labelled f_flat_1(4)* 555 to 550 labelled f_flat_1(5)* 555 to 533 labelled f_flat_1(3)* 555 to 543 labelled f_flat_1(4)* 555 to 539 labelled f_flat_1(4)* 555 to 576 labelled f_flat_1(6)* 555 to 553 labelled up_1(5)* 555 to 589 labelled up_1(6)* 555 to 591 labelled up_1(7)* 556 to 487 labelled f_1(6)* 556 to 527 labelled f_1(6)* 557 to 558 labelled down_1(4)* 557 to 584 labelled f_flat_1(5), g_flat_1(5)* 557 to 579 labelled f_flat_1(4)* 557 to 586 labelled f_flat_1(5)* 557 to 582 labelled f_flat_1(5), g_flat_1(5)* 558 to 530 labelled f_1(4)* 558 to 538 labelled f_1(4)* 558 to 546 labelled f_1(4)* 558 to 553 labelled g_1(4), f_1(4)* 558 to 590 labelled f_1(4), g_1(4)* 558 to 589 labelled f_1(4), g_1(4)* 558 to 591 labelled f_1(4)* 559 to 560 labelled down_1(4)* 559 to 582 labelled g_flat_1(5)* 559 to 584 labelled g_flat_1(5)* 560 to 538 labelled g_1(4)* 560 to 546 labelled g_1(4)* 576 to 577 labelled down_1(6)* 576 to 543 labelled f_flat_1(4)* 576 to 539 labelled f_flat_1(4)* 576 to 576 labelled f_flat_1(6)* 576 to 550 labelled f_flat_1(5)* 576 to 553 labelled up_1(5)* 576 to 589 labelled up_1(6)* 576 to 591 labelled up_1(7)* 577 to 578 labelled f_1(6)* 578 to 487 labelled f_1(6)* 578 to 527 labelled f_1(6)* 579 to 580 labelled down_1(4)* 580 to 581 labelled f_1(4)* 581 to 531 labelled f_1(4)* 582 to 583 labelled down_1(5)* 582 to 584 labelled f_flat_1(5)* 582 to 579 labelled f_flat_1(4)* 582 to 586 labelled f_flat_1(5)* 582 to 582 labelled f_flat_1(5)* 582 to 594 labelled f_flat_1(6)* 582 to 596 labelled f_flat_1(6)* 582 to 592 labelled f_flat_1(6)* 583 to 530 labelled f_1(5)* 583 to 538 labelled f_1(5)* 583 to 546 labelled f_1(5)* 583 to 553 labelled f_1(5)* 584 to 585 labelled down_1(5)* 584 to 582 labelled g_flat_1(5)* 584 to 584 labelled g_flat_1(5)* 584 to 592 labelled g_flat_1(6), f_flat_1(6)* 584 to 594 labelled g_flat_1(6), f_flat_1(6)* 584 to 596 labelled f_flat_1(6)* 585 to 538 labelled g_1(5)* 585 to 546 labelled g_1(5)* 585 to 553 labelled g_1(5)* 585 to 590 labelled f_1(5), g_1(5)* 585 to 589 labelled f_1(5), g_1(5)* 585 to 591 labelled g_1(5), f_1(5)* 586 to 587 labelled down_1(5)* 586 to 579 labelled f_flat_1(4)* 586 to 586 labelled f_flat_1(5)* 586 to 582 labelled f_flat_1(5)* 586 to 584 labelled f_flat_1(5)* 587 to 588 labelled f_1(5)* 588 to 530 labelled f_1(5)* 588 to 538 labelled f_1(5)* 588 to 546 labelled f_1(5)* 589 to 553 labelled f_1(6)* 589 to 590 labelled f_1(6)* 589 to 589 labelled f_1(6)* 589 to 591 labelled f_1(6)* 590 to 553 labelled g_1(6)* 590 to 590 labelled g_1(6)* 590 to 589 labelled g_1(6)* 590 to 591 labelled g_1(6), f_1(5)* 591 to 589 labelled g_1(7), f_1(7)* 591 to 591 labelled g_1(7), f_1(7)* 592 to 593 labelled down_1(6)* 592 to 584 labelled f_flat_1(5)* 592 to 594 labelled f_flat_1(6)* 592 to 586 labelled f_flat_1(5)* 592 to 582 labelled f_flat_1(5)* 592 to 596 labelled f_flat_1(6)* 592 to 592 labelled f_flat_1(6)* 592 to 599 labelled f_flat_1(7)* 593 to 546 labelled f_1(6)* 593 to 553 labelled f_1(6)* 593 to 590 labelled f_1(6)* 593 to 589 labelled f_1(6)* 593 to 591 labelled f_1(6)* 594 to 595 labelled down_1(6)* 594 to 584 labelled g_flat_1(5)* 594 to 582 labelled g_flat_1(5)* 594 to 592 labelled g_flat_1(6)* 594 to 594 labelled g_flat_1(6)* 594 to 599 labelled g_flat_1(7)* 595 to 546 labelled g_1(6)* 595 to 553 labelled g_1(6)* 595 to 590 labelled g_1(6)* 595 to 589 labelled g_1(6)* 595 to 591 labelled g_1(6)* 596 to 597 labelled down_1(6)* 596 to 586 labelled f_flat_1(5)* 596 to 582 labelled f_flat_1(5)* 596 to 596 labelled f_flat_1(6)* 596 to 592 labelled f_flat_1(6)* 596 to 599 labelled f_flat_1(7)* 597 to 598 labelled f_1(6)* 598 to 546 labelled f_1(6)* 598 to 553 labelled f_1(6)* 599 to 600 labelled down_1(7)* 599 to 592 labelled g_flat_1(6), f_flat_1(6)* 599 to 594 labelled g_flat_1(6), f_flat_1(6)* 599 to 603 labelled g_flat_1(8), f_flat_1(8)* 599 to 599 labelled g_flat_1(7), f_flat_1(7)* 599 to 586 labelled f_flat_1(5)* 599 to 582 labelled f_flat_1(5)* 599 to 596 labelled f_flat_1(6)* 600 to 553 labelled g_1(7), f_1(7)* 600 to 590 labelled g_1(7), f_1(7)* 600 to 589 labelled g_1(7), f_1(7)* 600 to 591 labelled g_1(7), f_1(7)* 603 to 604 labelled down_1(8)* 603 to 594 labelled f_flat_1(6)* 603 to 599 labelled f_flat_1(7), g_flat_1(7)* 603 to 603 labelled g_flat_1(8), f_flat_1(8)* 603 to 586 labelled f_flat_1(5)* 603 to 582 labelled f_flat_1(5)* 603 to 596 labelled f_flat_1(6)* 603 to 592 labelled f_flat_1(6)* 603 to 655 labelled f_flat_1(9)* 604 to 553 labelled f_1(8)* 604 to 590 labelled f_1(8)* 604 to 589 labelled g_1(8), f_1(8)* 604 to 591 labelled g_1(8), f_1(8)* 655 to 656 labelled down_1(9)* 655 to 596 labelled f_flat_1(6)* 655 to 592 labelled f_flat_1(6)* 655 to 603 labelled f_flat_1(8)* 655 to 655 labelled f_flat_1(9)* 655 to 599 labelled f_flat_1(7)* 656 to 657 labelled f_1(9)* 657 to 553 labelled f_1(9)* 657 to 590 labelled f_1(9)* 657 to 589 labelled f_1(9)* 657 to 591 labelled f_1(9)
4.56/1.78	
4.56/1.78	
4.56/1.78	----------------------------------------
4.56/1.78	
4.56/1.78	(31)
4.56/1.78	YES
4.69/1.83	EOF