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 x y)
0.00/0.00	    (RULES
0.00/0.00	      +(0,x) -> x
0.00/0.00	      +(x,0) -> 0 | x == 0
0.00/0.00	      +(x,y) -> +(y,x)
0.00/0.00	    )
0.00/0.00	    (COMMENT submitted by: Nao Hirokawa)
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 x y)
0.00/0.00	    (RULES
0.00/0.00	      +(0,x) -> x
0.00/0.00	      +(x,0) -> 0 | x == 0
0.00/0.00	      +(x,y) -> +(y,x)
0.00/0.00	    )
0.00/0.00	    (COMMENT submitted by: Nao Hirokawa)
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 x y)
0.00/0.00	    (RULES
0.00/0.00	      +(0,x) -> x
0.00/0.00	      +(x,0) -> 0 | x == 0
0.00/0.00	      +(x,y) -> +(y,x)
0.00/0.00	    )
0.00/0.00	    (COMMENT submitted by: Nao Hirokawa)
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 x y)
0.00/0.00	    (RULES
0.00/0.00	      +(0,x) -> x
0.00/0.00	      +(x,0) -> 0 | x == 0
0.00/0.00	      +(x,y) -> +(y,x)
0.00/0.00	    )
0.00/0.00	    (COMMENT submitted by: Nao Hirokawa)
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)
0.00/0.00	    (RULES
0.00/0.00	      +(0,x1) -> x1
0.00/0.00	      +(x1,x2) -> +(x2,x1)
0.00/0.00	      +(x1,0) -> u1(x1,x1)
0.00/0.00	      u1(0,x1) -> 0
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