0.00/0.00	MAYBE
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 y xs)
0.00/0.00	    (RULES
0.00/0.00	      le(x,0) -> false
0.00/0.00	      le(0,s(y)) -> true
0.00/0.00	      le(s(x),s(y)) -> le(x,y)
0.00/0.00	      min(cons(x,nil)) -> x
0.00/0.00	      min(cons(x,xs)) -> x | min(xs) == y, le(x,y) == true
0.00/0.00	      min(cons(x,xs)) -> y | min(xs) == y, le(x,y) == false
0.00/0.00	    )
0.00/0.00	    (COMMENT [121] Example 9.6; adaptation of Cops #292 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 y xs)
0.00/0.00	    (RULES
0.00/0.00	      le(x,0) -> false
0.00/0.00	      le(0,s(y)) -> true
0.00/0.00	      le(s(x),s(y)) -> le(x,y)
0.00/0.00	      min(cons(x,nil)) -> x
0.00/0.00	      min(cons(x,xs)) -> x | min(xs) == y, le(x,y) == true
0.00/0.00	      min(cons(x,xs)) -> y | min(xs) == y, le(x,y) == false
0.00/0.00	    )
0.00/0.00	    (COMMENT [121] Example 9.6; adaptation of Cops #292 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 y xs)
0.00/0.00	    (RULES
0.00/0.00	      le(x,0) -> false
0.00/0.00	      le(0,s(y)) -> true
0.00/0.00	      le(s(x),s(y)) -> le(x,y)
0.00/0.00	      min(cons(x,nil)) -> x
0.00/0.00	      min(cons(x,xs)) -> x | min(xs) == y, le(x,y) == true
0.00/0.00	      min(cons(x,xs)) -> y | min(xs) == y, le(x,y) == false
0.00/0.00	    )
0.00/0.00	    (COMMENT [121] Example 9.6; adaptation of Cops #292 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 y xs)
0.00/0.00	    (RULES
0.00/0.00	      le(x,0) -> false
0.00/0.00	      le(0,s(y)) -> true
0.00/0.00	      le(s(x),s(y)) -> le(x,y)
0.00/0.00	      min(cons(x,nil)) -> x
0.00/0.00	      min(cons(x,xs)) -> x | min(xs) == y, le(x,y) == true
0.00/0.00	      min(cons(x,xs)) -> y | min(xs) == y, le(x,y) == false
0.00/0.00	    )
0.00/0.00	    (COMMENT [121] Example 9.6; adaptation of Cops #292 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 x2 x3)
0.00/0.00	    (RULES
0.00/0.00	      le(x1,0) -> false
0.00/0.00	      le(0,s(x1)) -> true
0.00/0.00	      le(s(x1),s(x2)) -> le(x1,x2)
0.00/0.00	      min(cons(x1,nil)) -> x1
0.00/0.00	      min(cons(x1,x2)) -> u1(min(x2),x1,x2)
0.00/0.00	      u1(x3,x1,x2) -> u2(le(x1,x3),x3,x1,x2)
0.00/0.00	      u2(true,x3,x1,x2) -> x1
0.00/0.00	      u2(false,x3,x1,x2) -> x3
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	Failed to prove confluence of U(R).
0.00/0.00	
0.00/0.00	Try to prove operational termination of R, i.e., termination of U(R).
0.00/0.00	
0.00/0.00	Succeeded in proving operational termination of R.
0.00/0.00	
0.00/0.00	Try to prove joinability of all (conditional) CPs.
0.00/0.00	
0.00/0.00	Failed to prove joinability of conditional CPs (via narrowing trees).
0.00/0.00	
0.00/0.00	MAYBE
0.00/0.00	EOF