0.00/0.00	YES
0.00/0.00	
0.00/0.00	
0.00/0.00	Succeeded in reading "/export/starexec/sandbox2/benchmark/theBenchmark.trs".
0.00/0.00	    (CONDITIONTYPE ORIENTED)
0.00/0.00	    (VAR x)
0.00/0.00	    (RULES
0.00/0.00	      even(0) -> true
0.00/0.00	      even(s(x)) -> false | odd(x) == false
0.00/0.00	      even(s(x)) -> true | odd(x) == true
0.00/0.00	      odd(0) -> false
0.00/0.00	      odd(s(x)) -> false | even(x) == false
0.00/0.00	      odd(s(x)) -> true | even(x) == true
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/978-3-540-31959-7_13 [67] Example 1 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 x)
0.00/0.00	    (RULES
0.00/0.00	      even(0) -> true
0.00/0.00	      even(s(x)) -> false | odd(x) == false
0.00/0.00	      even(s(x)) -> true | odd(x) == true
0.00/0.00	      odd(0) -> false
0.00/0.00	      odd(s(x)) -> false | even(x) == false
0.00/0.00	      odd(s(x)) -> true | even(x) == true
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/978-3-540-31959-7_13 [67] Example 1 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 x)
0.00/0.00	    (RULES
0.00/0.00	      even(0) -> true
0.00/0.00	      even(s(x)) -> false | odd(x) == false
0.00/0.00	      even(s(x)) -> true | odd(x) == true
0.00/0.00	      odd(0) -> false
0.00/0.00	      odd(s(x)) -> false | even(x) == false
0.00/0.00	      odd(s(x)) -> true | even(x) == true
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/978-3-540-31959-7_13 [67] Example 1 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 x)
0.00/0.00	    (RULES
0.00/0.00	      even(0) -> true
0.00/0.00	      even(s(x)) -> false | odd(x) == false
0.00/0.00	      even(s(x)) -> true | odd(x) == true
0.00/0.00	      odd(0) -> false
0.00/0.00	      odd(s(x)) -> false | even(x) == false
0.00/0.00	      odd(s(x)) -> true | even(x) == true
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/978-3-540-31959-7_13 [67] Example 1 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)
0.00/0.00	    (RULES
0.00/0.00	      even(0) -> true
0.00/0.00	      even(s(x1)) -> u1(odd(x1),x1)
0.00/0.00	      u1(false,x1) -> false
0.00/0.00	      u1(true,x1) -> true
0.00/0.00	      odd(0) -> false
0.00/0.00	      odd(s(x1)) -> u2(even(x1),x1)
0.00/0.00	      u2(false,x1) -> false
0.00/0.00	      u2(true,x1) -> true
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