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 Y W Z)
0.00/0.00	    (RULES
0.00/0.00	      plus(0,X) -> X
0.00/0.00	      plus(s(X),Y) -> plus(X,s(Y))
0.00/0.00	      fib(0) -> pair(s(0),0)
0.00/0.00	      fib(s(X)) -> pair(W,Y) | fib(X) == pair(Y,Z), plus(Y,Z) == W
0.00/0.00	    )
0.00/0.00	    (COMMENT [62] Example 4.2 http://www.w3.org/People/Massimo/papers/MIT-LCS-TM-405.pdf 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 Y W Z)
0.00/0.00	    (RULES
0.00/0.00	      plus(0,X) -> X
0.00/0.00	      plus(s(X),Y) -> plus(X,s(Y))
0.00/0.00	      fib(0) -> pair(s(0),0)
0.00/0.00	      fib(s(X)) -> pair(W,Y) | fib(X) == pair(Y,Z), plus(Y,Z) == W
0.00/0.00	    )
0.00/0.00	    (COMMENT [62] Example 4.2 http://www.w3.org/People/Massimo/papers/MIT-LCS-TM-405.pdf 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 Y W Z)
0.00/0.00	    (RULES
0.00/0.00	      plus(0,X) -> X
0.00/0.00	      plus(s(X),Y) -> plus(X,s(Y))
0.00/0.00	      fib(0) -> pair(s(0),0)
0.00/0.00	      fib(s(X)) -> pair(W,Y) | fib(X) == pair(Y,Z), plus(Y,Z) == W
0.00/0.00	    )
0.00/0.00	    (COMMENT [62] Example 4.2 http://www.w3.org/People/Massimo/papers/MIT-LCS-TM-405.pdf 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 Y W Z)
0.00/0.00	    (RULES
0.00/0.00	      plus(0,X) -> X
0.00/0.00	      plus(s(X),Y) -> plus(X,s(Y))
0.00/0.00	      fib(0) -> pair(s(0),0)
0.00/0.00	      fib(s(X)) -> pair(W,Y) | fib(X) == pair(Y,Z), plus(Y,Z) == W
0.00/0.00	    )
0.00/0.00	    (COMMENT [62] Example 4.2 http://www.w3.org/People/Massimo/papers/MIT-LCS-TM-405.pdf 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 x4)
0.00/0.00	    (RULES
0.00/0.00	      plus(0,x1) -> x1
0.00/0.00	      plus(s(x1),x2) -> plus(x1,s(x2))
0.00/0.00	      fib(0) -> pair(s(0),0)
0.00/0.00	      fib(s(x1)) -> u1(fib(x1),x1)
0.00/0.00	      u1(pair(x2,x3),x1) -> u2(plus(x2,x3),x2,x3,x1)
0.00/0.00	      u2(x4,x2,x3,x1) -> pair(x4,x2)
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