946.49/273.45	YES
955.19/275.64	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
955.19/275.64	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
955.19/275.64	
955.19/275.64	
955.19/275.64	Termination w.r.t. Q of the given QTRS could be proven:
955.19/275.64	
955.19/275.64	(0) QTRS
955.19/275.64	(1) DependencyPairsProof [EQUIVALENT, 9 ms]
955.19/275.64	(2) QDP
955.19/275.64	(3) QDPOrderProof [EQUIVALENT, 7620 ms]
955.19/275.64	(4) QDP
955.19/275.64	(5) QDPOrderProof [EQUIVALENT, 4101 ms]
955.19/275.64	(6) QDP
955.19/275.64	(7) PisEmptyProof [EQUIVALENT, 0 ms]
955.19/275.64	(8) YES
955.19/275.64	
955.19/275.64	
955.19/275.64	----------------------------------------
955.19/275.64	
955.19/275.64	(0)
955.19/275.64	Obligation:
955.19/275.64	Q restricted rewrite system:
955.19/275.64	The TRS R consists of the following rules:
955.19/275.64	
955.19/275.64	   b(a(a(b(b(a(a(b(a(x1))))))))) -> a(a(b(b(a(a(b(a(a(b(b(a(x1))))))))))))
955.19/275.64	
955.19/275.64	Q is empty.
955.19/275.64	
955.19/275.64	----------------------------------------
955.19/275.64	
955.19/275.64	(1) DependencyPairsProof (EQUIVALENT)
955.19/275.64	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
955.19/275.64	----------------------------------------
955.19/275.64	
955.19/275.64	(2)
955.19/275.64	Obligation:
955.19/275.64	Q DP problem:
955.19/275.64	The TRS P consists of the following rules:
955.19/275.64	
955.19/275.64	   B(a(a(b(b(a(a(b(a(x1))))))))) -> B(b(a(a(b(a(a(b(b(a(x1))))))))))
955.19/275.64	   B(a(a(b(b(a(a(b(a(x1))))))))) -> B(a(a(b(a(a(b(b(a(x1)))))))))
955.19/275.64	   B(a(a(b(b(a(a(b(a(x1))))))))) -> B(a(a(b(b(a(x1))))))
955.19/275.64	   B(a(a(b(b(a(a(b(a(x1))))))))) -> B(b(a(x1)))
955.19/275.64	
955.19/275.64	The TRS R consists of the following rules:
955.19/275.64	
955.19/275.64	   b(a(a(b(b(a(a(b(a(x1))))))))) -> a(a(b(b(a(a(b(a(a(b(b(a(x1))))))))))))
955.19/275.64	
955.19/275.64	Q is empty.
955.19/275.64	We have to consider all minimal (P,Q,R)-chains.
955.19/275.64	----------------------------------------
955.19/275.64	
955.19/275.64	(3) QDPOrderProof (EQUIVALENT)
955.19/275.64	We use the reduction pair processor [LPAR04,JAR06].
955.19/275.64	
955.19/275.64	
955.19/275.64	The following pairs can be oriented strictly and are deleted.
955.19/275.64	
955.19/275.64	   B(a(a(b(b(a(a(b(a(x1))))))))) -> B(b(a(a(b(a(a(b(b(a(x1))))))))))
955.19/275.64	   B(a(a(b(b(a(a(b(a(x1))))))))) -> B(a(a(b(a(a(b(b(a(x1)))))))))
955.19/275.64	The remaining pairs can at least be oriented weakly.
955.19/275.64	Used ordering:  Matrix interpretation [MATRO] with arctic integers [ARCTIC,STERNAGEL_THIEMANN_RTA14]:
955.19/275.64	
955.19/275.64	   <<<
955.19/275.64	 POL(B(x_1)) =  	[[0A]] 	 +  	[[-I, 0A, 2A]] 	* 	x_1
955.19/275.64	>>>
955.19/275.64	
955.19/275.64	   <<<
955.19/275.64	 POL(a(x_1)) =  	[[-I], [-I], [-I]] 	 +  	[[0A, -I, -I], [-I, -I, -I], [-I, 0A, -1A]] 	* 	x_1
955.19/275.64	>>>
955.19/275.64	
955.19/275.64	   <<<
955.19/275.64	 POL(b(x_1)) =  	[[-1A], [-I], [-I]] 	 +  	[[0A, -1A, 0A], [-1A, 2A, -I], [-I, -I, 0A]] 	* 	x_1
955.19/275.64	>>>
955.19/275.64	
955.19/275.64	
955.19/275.64	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
955.19/275.64	
955.19/275.64	   b(a(a(b(b(a(a(b(a(x1))))))))) -> a(a(b(b(a(a(b(a(a(b(b(a(x1))))))))))))
955.19/275.64	
955.19/275.64	
955.19/275.64	----------------------------------------
955.19/275.64	
955.19/275.64	(4)
955.19/275.64	Obligation:
955.19/275.64	Q DP problem:
955.19/275.64	The TRS P consists of the following rules:
955.19/275.64	
955.19/275.64	   B(a(a(b(b(a(a(b(a(x1))))))))) -> B(a(a(b(b(a(x1))))))
955.19/275.64	   B(a(a(b(b(a(a(b(a(x1))))))))) -> B(b(a(x1)))
955.19/275.64	
955.19/275.64	The TRS R consists of the following rules:
955.19/275.64	
955.19/275.64	   b(a(a(b(b(a(a(b(a(x1))))))))) -> a(a(b(b(a(a(b(a(a(b(b(a(x1))))))))))))
955.19/275.64	
955.19/275.64	Q is empty.
955.19/275.64	We have to consider all minimal (P,Q,R)-chains.
955.19/275.64	----------------------------------------
955.19/275.64	
955.19/275.64	(5) QDPOrderProof (EQUIVALENT)
955.19/275.64	We use the reduction pair processor [LPAR04,JAR06].
955.19/275.64	
955.19/275.64	
955.19/275.64	The following pairs can be oriented strictly and are deleted.
955.19/275.64	
955.19/275.64	   B(a(a(b(b(a(a(b(a(x1))))))))) -> B(a(a(b(b(a(x1))))))
955.19/275.64	   B(a(a(b(b(a(a(b(a(x1))))))))) -> B(b(a(x1)))
955.19/275.64	The remaining pairs can at least be oriented weakly.
955.19/275.64	Used ordering:  Polynomial interpretation [POLO,RATPOLO]:
955.19/275.64	
955.19/275.64	   POL(B(x_1)) = [1/4]x_1
955.19/275.64	   POL(a(x_1)) = [1/2]x_1
955.19/275.64	   POL(b(x_1)) = [1/2] + [4]x_1
955.19/275.64	The value of delta used in the strict ordering is 1/8.
955.19/275.64	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
955.19/275.64	
955.19/275.64	   b(a(a(b(b(a(a(b(a(x1))))))))) -> a(a(b(b(a(a(b(a(a(b(b(a(x1))))))))))))
955.19/275.64	
955.19/275.64	
955.19/275.64	----------------------------------------
955.19/275.64	
955.19/275.64	(6)
955.19/275.64	Obligation:
955.19/275.64	Q DP problem:
955.19/275.64	P is empty.
955.19/275.64	The TRS R consists of the following rules:
955.19/275.64	
955.19/275.64	   b(a(a(b(b(a(a(b(a(x1))))))))) -> a(a(b(b(a(a(b(a(a(b(b(a(x1))))))))))))
955.19/275.64	
955.19/275.64	Q is empty.
955.19/275.64	We have to consider all minimal (P,Q,R)-chains.
955.19/275.64	----------------------------------------
955.19/275.64	
955.19/275.64	(7) PisEmptyProof (EQUIVALENT)
955.19/275.64	The TRS P is empty. Hence, there is no (P,Q,R) chain.
955.19/275.64	----------------------------------------
955.19/275.64	
955.19/275.64	(8)
955.19/275.64	YES
955.39/275.71	EOF