0.00/0.00	YES
0.00/0.00	
0.00/0.00	
0.00/0.00	Succeeded in reading "/export/starexec/sandbox/benchmark/theBenchmark.trs".
0.00/0.00	    (CONDITIONTYPE ORIENTED)
0.00/0.00	    (VAR r n xs x q y)
0.00/0.00	    (RULES
0.00/0.00	      filter(n,r,nil) -> pair(mo,nil)
0.00/0.00	      filter(n,r,cons(x,xs)) -> pair(x,xs) | eq(div(x,n),pair(q,r)) == true
0.00/0.00	      filter(n,r,cons(x,xs)) -> pair(y,cons(x,ys)) | filter(n,r,xs) == pair(y,ys), eq(div(x,n),pair(q,r)) == false
0.00/0.00	    )
0.00/0.00	    (COMMENT [68] p. 13 doi:10.1007/3-540-59200-8_56 submitted by: Thomas Sternagel and Aart Middeldorp)
0.00/0.00	
0.00/0.00	No "->="-rules.
0.00/0.00	
0.00/0.00	Decomposed conditions if possible.
0.00/0.00	    (CONDITIONTYPE ORIENTED)
0.00/0.00	    (VAR r n xs x q y)
0.00/0.00	    (RULES
0.00/0.00	      filter(n,r,nil) -> pair(mo,nil)
0.00/0.00	      filter(n,r,cons(x,xs)) -> pair(x,xs) | eq(div(x,n),pair(q,r)) == true
0.00/0.00	      filter(n,r,cons(x,xs)) -> pair(y,cons(x,ys)) | filter(n,r,xs) == pair(y,ys), eq(div(x,n),pair(q,r)) == false
0.00/0.00	    )
0.00/0.00	    (COMMENT [68] p. 13 doi:10.1007/3-540-59200-8_56 submitted by: Thomas Sternagel and Aart Middeldorp)
0.00/0.00	
0.00/0.00	Removed infeasible rules as much as possible.
0.00/0.00	    (VAR r n xs x q y)
0.00/0.00	    (RULES
0.00/0.00	      filter(n,r,nil) -> pair(mo,nil)
0.00/0.00	    )
0.00/0.00	    (COMMENT [68] p. 13 doi:10.1007/3-540-59200-8_56 submitted by: Thomas Sternagel and Aart Middeldorp)
0.00/0.00	
0.00/0.00	Try to disprove confluence of the following (C)TRS:
0.00/0.00	    (VAR r n xs x q y)
0.00/0.00	    (RULES
0.00/0.00	      filter(n,r,nil) -> pair(mo,nil)
0.00/0.00	    )
0.00/0.00	    (COMMENT [68] p. 13 doi:10.1007/3-540-59200-8_56 submitted by: Thomas Sternagel and Aart Middeldorp)
0.00/0.00	
0.00/0.00	Try to prove confluence of the following TRS:
0.00/0.00	    (VAR r n xs x q y)
0.00/0.00	    (RULES
0.00/0.00	      filter(n,r,nil) -> pair(mo,nil)
0.00/0.00	    )
0.00/0.00	    (COMMENT [68] p. 13 doi:10.1007/3-540-59200-8_56 submitted by: Thomas Sternagel and Aart Middeldorp)
0.00/0.00	
0.00/0.00	Succeeded in proving confluence due to orthogonality.
0.00/0.00	
0.00/0.00	Proved via the following orthogonal TRS:
0.00/0.00	(VAR r n xs x q y)
0.00/0.00	(RULES
0.00/0.00	  filter(n,r,nil) -> pair(mo,nil)
0.00/0.00	)
0.00/0.00	(COMMENT [68] p. 13 doi:10.1007/3-540-59200-8_56 submitted by: Thomas Sternagel and Aart Middeldorp)
0.00/0.00	
0.00/0.00	YES
0.00/0.00	EOF