0.00/0.00	MAYBE
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 l y x)
0.00/0.00	    (RULES
0.00/0.00	      dot(x,dot(y,l)) -> dot(y,dot(x,l)) | les(x,y) == true
0.00/0.00	      les(0,0) -> false
0.00/0.00	      les(0,s(0)) -> true
0.00/0.00	      les(0,s(s(x))) -> les(0,s(x))
0.00/0.00	      les(s(0),0) -> false
0.00/0.00	      les(s(s(x)),0) -> les(s(x),0)
0.00/0.00	      les(s(x),s(y)) -> les(x,y)
0.00/0.00	    )
0.00/0.00	    (COMMENT [79] Example 9)
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 l y x)
0.00/0.00	    (RULES
0.00/0.00	      dot(x,dot(y,l)) -> dot(y,dot(x,l)) | les(x,y) == true
0.00/0.00	      les(0,0) -> false
0.00/0.00	      les(0,s(0)) -> true
0.00/0.00	      les(0,s(s(x))) -> les(0,s(x))
0.00/0.00	      les(s(0),0) -> false
0.00/0.00	      les(s(s(x)),0) -> les(s(x),0)
0.00/0.00	      les(s(x),s(y)) -> les(x,y)
0.00/0.00	    )
0.00/0.00	    (COMMENT [79] Example 9)
0.00/0.00	
0.00/0.00	Removed infeasible rules as much as possible.
0.00/0.00	    (CONDITIONTYPE ORIENTED)
0.00/0.00	    (VAR l y x)
0.00/0.00	    (RULES
0.00/0.00	      dot(x,dot(y,l)) -> dot(y,dot(x,l)) | les(x,y) == true
0.00/0.00	      les(0,0) -> false
0.00/0.00	      les(0,s(0)) -> true
0.00/0.00	      les(0,s(s(x))) -> les(0,s(x))
0.00/0.00	      les(s(0),0) -> false
0.00/0.00	      les(s(s(x)),0) -> les(s(x),0)
0.00/0.00	      les(s(x),s(y)) -> les(x,y)
0.00/0.00	    )
0.00/0.00	    (COMMENT [79] Example 9)
0.00/0.00	
0.00/0.00	Try to disprove confluence of the following (C)TRS:
0.00/0.00	    (CONDITIONTYPE ORIENTED)
0.00/0.00	    (VAR l y x)
0.00/0.00	    (RULES
0.00/0.00	      dot(x,dot(y,l)) -> dot(y,dot(x,l)) | les(x,y) == true
0.00/0.00	      les(0,0) -> false
0.00/0.00	      les(0,s(0)) -> true
0.00/0.00	      les(0,s(s(x))) -> les(0,s(x))
0.00/0.00	      les(s(0),0) -> false
0.00/0.00	      les(s(s(x)),0) -> les(s(x),0)
0.00/0.00	      les(s(x),s(y)) -> les(x,y)
0.00/0.00	    )
0.00/0.00	    (COMMENT [79] Example 9)
0.00/0.00	
0.00/0.00	Failed either to apply SR and U for normal 1CTRSs to the above CTRS or to prove confluence of any converted TRSs.
0.00/0.00	
0.00/0.00	Try to apply SR and U for 3DCTRSs to the above CTRS.
0.00/0.00	
0.00/0.00	Succeeded in applying U for 3DCTRSs to the above CTRS.
0.00/0.00	U(R) =
0.00/0.00	    (VAR x3 x2 x1)
0.00/0.00	    (RULES
0.00/0.00	      dot(x1,dot(x2,x3)) -> u1(les(x1,x2),x1,x2,x3)
0.00/0.00	      u1(true,x1,x2,x3) -> dot(x2,dot(x1,x3))
0.00/0.00	      les(0,0) -> false
0.00/0.00	      les(0,s(0)) -> true
0.00/0.00	      les(0,s(s(x1))) -> les(0,s(x1))
0.00/0.00	      les(s(0),0) -> false
0.00/0.00	      les(s(s(x1)),0) -> les(s(x1),0)
0.00/0.00	      les(s(x1),s(x2)) -> les(x1,x2)
0.00/0.00	    )
0.00/0.00	
0.00/0.00	U for 3DCTRSs is sound for the above CTRS.
0.00/0.00	
0.00/0.00	Failed to prove confluence of U(R).
0.00/0.00	
0.00/0.00	Try to prove operational termination of R, i.e., termination of U(R).
0.00/0.00	
0.00/0.00	Failed to prove operational termination of R.
0.00/0.00	
0.00/0.00	MAYBE
0.00/0.00	EOF