0.00/0.01	YES
0.00/0.01	
0.00/0.01	
0.00/0.01	Succeeded in reading "/export/starexec/sandbox2/benchmark/theBenchmark.trs".
0.00/0.01	    (CONDITIONTYPE ORIENTED)
0.00/0.01	    (VAR x)
0.00/0.01	    (RULES
0.00/0.01	      zero(0) -> true
0.00/0.01	      zero(s(x)) -> false
0.00/0.01	      even(x) -> true | zero(x) == true
0.00/0.01	      even(s(x)) -> true | odd(x) == true
0.00/0.01	      even(s(x)) -> false | even(x) == true
0.00/0.01	      odd(x) -> false | zero(x) == true
0.00/0.01	      odd(s(x)) -> true | even(x) == true
0.00/0.01	      odd(s(x)) -> false | odd(x) == true
0.00/0.01	    )
0.00/0.01	    (COMMENT variant of COPS #489 and COPS #522 , presented by Naoki Nishida at the 50th TRS meeting in Atami , Japan submitted by: Naoki Nishida)
0.00/0.01	
0.00/0.01	No "->="-rules.
0.00/0.01	
0.00/0.01	Decomposed conditions if possible.
0.00/0.01	    (CONDITIONTYPE ORIENTED)
0.00/0.01	    (VAR x)
0.00/0.01	    (RULES
0.00/0.01	      zero(0) -> true
0.00/0.01	      zero(s(x)) -> false
0.00/0.01	      even(x) -> true | zero(x) == true
0.00/0.01	      even(s(x)) -> true | odd(x) == true
0.00/0.01	      even(s(x)) -> false | even(x) == true
0.00/0.01	      odd(x) -> false | zero(x) == true
0.00/0.01	      odd(s(x)) -> true | even(x) == true
0.00/0.01	      odd(s(x)) -> false | odd(x) == true
0.00/0.01	    )
0.00/0.01	    (COMMENT variant of COPS #489 and COPS #522 , presented by Naoki Nishida at the 50th TRS meeting in Atami , Japan submitted by: Naoki Nishida)
0.00/0.01	
0.00/0.01	Removed infeasible rules as much as possible.
0.00/0.01	    (CONDITIONTYPE ORIENTED)
0.00/0.01	    (VAR x)
0.00/0.01	    (RULES
0.00/0.01	      zero(0) -> true
0.00/0.01	      zero(s(x)) -> false
0.00/0.01	      even(x) -> true | zero(x) == true
0.00/0.01	      even(s(x)) -> true | odd(x) == true
0.00/0.01	      even(s(x)) -> false | even(x) == true
0.00/0.01	      odd(x) -> false | zero(x) == true
0.00/0.01	      odd(s(x)) -> true | even(x) == true
0.00/0.01	      odd(s(x)) -> false | odd(x) == true
0.00/0.01	    )
0.00/0.01	    (COMMENT variant of COPS #489 and COPS #522 , presented by Naoki Nishida at the 50th TRS meeting in Atami , Japan submitted by: Naoki Nishida)
0.00/0.01	
0.00/0.01	Try to disprove confluence of the following (C)TRS:
0.00/0.01	    (CONDITIONTYPE ORIENTED)
0.00/0.01	    (VAR x)
0.00/0.01	    (RULES
0.00/0.01	      zero(0) -> true
0.00/0.01	      zero(s(x)) -> false
0.00/0.01	      even(x) -> true | zero(x) == true
0.00/0.01	      even(s(x)) -> true | odd(x) == true
0.00/0.01	      even(s(x)) -> false | even(x) == true
0.00/0.01	      odd(x) -> false | zero(x) == true
0.00/0.01	      odd(s(x)) -> true | even(x) == true
0.00/0.01	      odd(s(x)) -> false | odd(x) == true
0.00/0.01	    )
0.00/0.01	    (COMMENT variant of COPS #489 and COPS #522 , presented by Naoki Nishida at the 50th TRS meeting in Atami , Japan submitted by: Naoki Nishida)
0.00/0.01	
0.00/0.01	Failed either to apply SR and U for normal 1CTRSs to the above CTRS or to prove confluence of any converted TRSs.
0.00/0.01	
0.00/0.01	Try to apply SR and U for 3DCTRSs to the above CTRS.
0.00/0.01	
0.00/0.01	Succeeded in applying U for 3DCTRSs to the above CTRS.
0.00/0.01	U(R) =
0.00/0.01	    (VAR x1)
0.00/0.01	    (RULES
0.00/0.01	      zero(0) -> true
0.00/0.01	      zero(s(x1)) -> false
0.00/0.01	      even(s(x1)) -> u1(odd(x1),x1)
0.00/0.01	      u1(true,x1) -> true
0.00/0.01	      even(s(x1)) -> u2(even(x1),x1)
0.00/0.01	      u2(true,x1) -> false
0.00/0.01	      even(x1) -> u3(zero(x1),x1)
0.00/0.01	      u3(true,x1) -> true
0.00/0.01	      odd(s(x1)) -> u4(even(x1),x1)
0.00/0.01	      u4(true,x1) -> true
0.00/0.01	      odd(s(x1)) -> u5(odd(x1),x1)
0.00/0.01	      u5(true,x1) -> false
0.00/0.01	      odd(x1) -> u6(zero(x1),x1)
0.00/0.01	      u6(true,x1) -> false
0.00/0.01	    )
0.00/0.01	
0.00/0.01	U for 3DCTRSs is sound for the above CTRS.
0.00/0.01	
0.00/0.01	Failed to prove confluence of U(R).
0.00/0.01	
0.00/0.01	Try to prove operational termination of R, i.e., termination of U(R).
0.00/0.01	
0.00/0.01	Succeeded in proving operational termination of R.
0.00/0.01	
0.00/0.01	Try to prove joinability of all (conditional) CPs.
0.00/0.01	
0.00/0.01	Succeeded in proving joinability of conditional CPs by means of narrowing trees.
0.00/0.01	
0.00/0.01	YES
0.00/0.01	EOF