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 z x y)
0.00/0.00	    (RULES
0.00/0.00	      sub(z,0) -> z
0.00/0.00	      sub(s(z),s(y)) -> x | sub(z,y) == x
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/j.tcs.2012.09.005 [72] p. 73 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 z x y)
0.00/0.00	    (RULES
0.00/0.00	      sub(z,0) -> z
0.00/0.00	      sub(s(z),s(y)) -> x | sub(z,y) == x
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/j.tcs.2012.09.005 [72] p. 73 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	    (CONDITIONTYPE ORIENTED)
0.00/0.00	    (VAR z x y)
0.00/0.00	    (RULES
0.00/0.00	      sub(z,0) -> z
0.00/0.00	      sub(s(z),s(y)) -> x | sub(z,y) == x
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/j.tcs.2012.09.005 [72] p. 73 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	    (CONDITIONTYPE ORIENTED)
0.00/0.00	    (VAR z x y)
0.00/0.00	    (RULES
0.00/0.00	      sub(z,0) -> z
0.00/0.00	      sub(s(z),s(y)) -> x | sub(z,y) == x
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/j.tcs.2012.09.005 [72] p. 73 submitted by: Thomas Sternagel and Aart Middeldorp)
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 x1 x2 x3)
0.00/0.00	    (RULES
0.00/0.00	      sub(x1,0) -> x1
0.00/0.00	      sub(s(x1),s(x2)) -> u1(sub(x1,x2),x1,x2)
0.00/0.00	      u1(x3,x1,x2) -> x3
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	U(R) is confluent.
0.00/0.00	
0.00/0.00	YES
0.00/0.00	EOF