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 y x z)
0.00/0.00	    (RULES
0.00/0.00	      f(x,y) -> x | g(x) == z, g(y) == z
0.00/0.00	      g(x) -> c | d == c
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.2168/LMCS-8 ( 3:4 ) 2012 [64] Example 3.4 ( R_4 ) 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 y x z)
0.00/0.00	    (RULES
0.00/0.00	      f(x,y) -> x | g(x) == z, g(y) == z
0.00/0.00	      g(x) -> c | d == c
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.2168/LMCS-8 ( 3:4 ) 2012 [64] Example 3.4 ( R_4 ) 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 y x z)
0.00/0.00	    (RULES
0.00/0.00	      f(x,y) -> x | g(x) == z, g(y) == z
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.2168/LMCS-8 ( 3:4 ) 2012 [64] Example 3.4 ( R_4 ) 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 y x z)
0.00/0.00	    (RULES
0.00/0.00	      f(x,y) -> x | g(x) == z, g(y) == z
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.2168/LMCS-8 ( 3:4 ) 2012 [64] Example 3.4 ( R_4 ) 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 x2 x1 x3)
0.00/0.00	    (RULES
0.00/0.00	      f(x1,x2) -> u1(g(x1),x1,x2)
0.00/0.00	      u1(x3,x1,x2) -> u2(g(x2),x3,x1,x2)
0.00/0.00	      u2(x3,x3,x1,x2) -> x1
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