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 n m l)
0.00/0.00	    (RULES
0.00/0.00	      lte(0,n) -> true
0.00/0.00	      lte(s(m),0) -> false
0.00/0.00	      lte(s(m),s(n)) -> lte(m,n)
0.00/0.00	      insert(nil,m) -> cons(m,nil)
0.00/0.00	      insert(cons(n,l),m) -> cons(m,cons(n,l)) | lte(m,n) == true
0.00/0.00	      insert(cons(n,l),m) -> cons(n,insert(l,m)) | lte(m,n) == false
0.00/0.00	      ordered(nil) -> true
0.00/0.00	      ordered(cons(m,nil)) -> true
0.00/0.00	      ordered(cons(m,cons(n,l))) -> ordered(cons(n,l)) | lte(m,n) == true
0.00/0.00	      ordered(cons(m,cons(n,l))) -> false | lte(m,n) == false
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/3-540-54317-1_91 [48] p. 203 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 n m l)
0.00/0.00	    (RULES
0.00/0.00	      lte(0,n) -> true
0.00/0.00	      lte(s(m),0) -> false
0.00/0.00	      lte(s(m),s(n)) -> lte(m,n)
0.00/0.00	      insert(nil,m) -> cons(m,nil)
0.00/0.00	      insert(cons(n,l),m) -> cons(m,cons(n,l)) | lte(m,n) == true
0.00/0.00	      insert(cons(n,l),m) -> cons(n,insert(l,m)) | lte(m,n) == false
0.00/0.00	      ordered(nil) -> true
0.00/0.00	      ordered(cons(m,nil)) -> true
0.00/0.00	      ordered(cons(m,cons(n,l))) -> ordered(cons(n,l)) | lte(m,n) == true
0.00/0.00	      ordered(cons(m,cons(n,l))) -> false | lte(m,n) == false
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/3-540-54317-1_91 [48] p. 203 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 n m l)
0.00/0.00	    (RULES
0.00/0.00	      lte(0,n) -> true
0.00/0.00	      lte(s(m),0) -> false
0.00/0.00	      lte(s(m),s(n)) -> lte(m,n)
0.00/0.00	      insert(nil,m) -> cons(m,nil)
0.00/0.00	      insert(cons(n,l),m) -> cons(m,cons(n,l)) | lte(m,n) == true
0.00/0.00	      insert(cons(n,l),m) -> cons(n,insert(l,m)) | lte(m,n) == false
0.00/0.00	      ordered(nil) -> true
0.00/0.00	      ordered(cons(m,nil)) -> true
0.00/0.00	      ordered(cons(m,cons(n,l))) -> ordered(cons(n,l)) | lte(m,n) == true
0.00/0.00	      ordered(cons(m,cons(n,l))) -> false | lte(m,n) == false
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/3-540-54317-1_91 [48] p. 203 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 n m l)
0.00/0.00	    (RULES
0.00/0.00	      lte(0,n) -> true
0.00/0.00	      lte(s(m),0) -> false
0.00/0.00	      lte(s(m),s(n)) -> lte(m,n)
0.00/0.00	      insert(nil,m) -> cons(m,nil)
0.00/0.00	      insert(cons(n,l),m) -> cons(m,cons(n,l)) | lte(m,n) == true
0.00/0.00	      insert(cons(n,l),m) -> cons(n,insert(l,m)) | lte(m,n) == false
0.00/0.00	      ordered(nil) -> true
0.00/0.00	      ordered(cons(m,nil)) -> true
0.00/0.00	      ordered(cons(m,cons(n,l))) -> ordered(cons(n,l)) | lte(m,n) == true
0.00/0.00	      ordered(cons(m,cons(n,l))) -> false | lte(m,n) == false
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/3-540-54317-1_91 [48] p. 203 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)
0.00/0.00	    (RULES
0.00/0.00	      lte(0,x1) -> true
0.00/0.00	      lte(s(x1),0) -> false
0.00/0.00	      lte(s(x1),s(x2)) -> lte(x1,x2)
0.00/0.00	      insert(nil,x1) -> cons(x1,nil)
0.00/0.00	      insert(cons(x1,x2),x3) -> u1(lte(x3,x1),x1,x2,x3)
0.00/0.00	      u1(true,x1,x2,x3) -> cons(x3,cons(x1,x2))
0.00/0.00	      u1(false,x1,x2,x3) -> cons(x1,insert(x2,x3))
0.00/0.00	      ordered(nil) -> true
0.00/0.00	      ordered(cons(x1,nil)) -> true
0.00/0.00	      ordered(cons(x1,cons(x2,x3))) -> u2(lte(x1,x2),x1,x2,x3)
0.00/0.00	      u2(true,x1,x2,x3) -> ordered(cons(x2,x3))
0.00/0.00	      u2(false,x1,x2,x3) -> false
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