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 x l1 z l y)
0.00/0.00	    (RULES
0.00/0.00	      f(cons(x,nil)) -> pair(x,nil)
0.00/0.00	      f(cons(x,cons(y,l))) -> pair(z,cons(x,l1)) | f(cons(y,l)) == pair(z,l1)
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/3-540-58216-9_40 [45] Example 2.1 ( a ) submitted by: Thomas Sternagel)
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 l1 z l y)
0.00/0.00	    (RULES
0.00/0.00	      f(cons(x,nil)) -> pair(x,nil)
0.00/0.00	      f(cons(x,cons(y,l))) -> pair(z,cons(x,l1)) | f(cons(y,l)) == pair(z,l1)
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/3-540-58216-9_40 [45] Example 2.1 ( a ) submitted by: Thomas Sternagel)
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 l1 z l y)
0.00/0.00	    (RULES
0.00/0.00	      f(cons(x,nil)) -> pair(x,nil)
0.00/0.00	      f(cons(x,cons(y,l))) -> pair(z,cons(x,l1)) | f(cons(y,l)) == pair(z,l1)
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/3-540-58216-9_40 [45] Example 2.1 ( a ) submitted by: Thomas Sternagel)
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 l1 z l y)
0.00/0.00	    (RULES
0.00/0.00	      f(cons(x,nil)) -> pair(x,nil)
0.00/0.00	      f(cons(x,cons(y,l))) -> pair(z,cons(x,l1)) | f(cons(y,l)) == pair(z,l1)
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/3-540-58216-9_40 [45] Example 2.1 ( a ) submitted by: Thomas Sternagel)
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 x3 x2 x5 x4)
0.00/0.00	    (RULES
0.00/0.00	      f(cons(x1,nil)) -> pair(x1,nil)
0.00/0.00	      f(cons(x1,cons(x2,x3))) -> u1(f(cons(x2,x3)),x1,x2,x3)
0.00/0.00	      u1(pair(x4,x5),x1,x2,x3) -> pair(x4,cons(x1,x5))
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