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 y x)
0.00/0.00	    (RULES
0.00/0.00	      size(empty) -> 0
0.00/0.00	      size(push(x,y)) -> s(size(x))
0.00/0.00	      m -> s(s(s(s(0))))
0.00/0.00	      pop(empty) -> empty
0.00/0.00	      pop(push(x,y)) -> x | le(size(x),m) == true
0.00/0.00	      top(empty) -> eentry
0.00/0.00	      top(push(x,y)) -> y | le(size(x),m) == true
0.00/0.00	      le(x,0) -> false
0.00/0.00	      le(0,s(x)) -> true
0.00/0.00	      le(s(x),s(y)) -> le(x,y)
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/0022-0000 ( 86 ) 90033-4 [47] Example 2.3.i 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 y x)
0.00/0.00	    (RULES
0.00/0.00	      size(empty) -> 0
0.00/0.00	      size(push(x,y)) -> s(size(x))
0.00/0.00	      m -> s(s(s(s(0))))
0.00/0.00	      pop(empty) -> empty
0.00/0.00	      pop(push(x,y)) -> x | le(size(x),m) == true
0.00/0.00	      top(empty) -> eentry
0.00/0.00	      top(push(x,y)) -> y | le(size(x),m) == true
0.00/0.00	      le(x,0) -> false
0.00/0.00	      le(0,s(x)) -> true
0.00/0.00	      le(s(x),s(y)) -> le(x,y)
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/0022-0000 ( 86 ) 90033-4 [47] Example 2.3.i 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 y x)
0.00/0.00	    (RULES
0.00/0.00	      size(empty) -> 0
0.00/0.00	      size(push(x,y)) -> s(size(x))
0.00/0.00	      m -> s(s(s(s(0))))
0.00/0.00	      pop(empty) -> empty
0.00/0.00	      pop(push(x,y)) -> x | le(size(x),m) == true
0.00/0.00	      top(empty) -> eentry
0.00/0.00	      top(push(x,y)) -> y | le(size(x),m) == true
0.00/0.00	      le(x,0) -> false
0.00/0.00	      le(0,s(x)) -> true
0.00/0.00	      le(s(x),s(y)) -> le(x,y)
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/0022-0000 ( 86 ) 90033-4 [47] Example 2.3.i 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 y x)
0.00/0.00	    (RULES
0.00/0.00	      size(empty) -> 0
0.00/0.00	      size(push(x,y)) -> s(size(x))
0.00/0.00	      m -> s(s(s(s(0))))
0.00/0.00	      pop(empty) -> empty
0.00/0.00	      pop(push(x,y)) -> x | le(size(x),m) == true
0.00/0.00	      top(empty) -> eentry
0.00/0.00	      top(push(x,y)) -> y | le(size(x),m) == true
0.00/0.00	      le(x,0) -> false
0.00/0.00	      le(0,s(x)) -> true
0.00/0.00	      le(s(x),s(y)) -> le(x,y)
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/0022-0000 ( 86 ) 90033-4 [47] Example 2.3.i 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 x2 x1)
0.00/0.00	    (RULES
0.00/0.00	      size(empty) -> 0
0.00/0.00	      size(push(x1,x2)) -> s(size(x1))
0.00/0.00	      m -> s(s(s(s(0))))
0.00/0.00	      pop(empty) -> empty
0.00/0.00	      pop(push(x1,x2)) -> u1(le(size(x1),m),x1,x2)
0.00/0.00	      u1(true,x1,x2) -> x1
0.00/0.00	      top(empty) -> eentry
0.00/0.00	      top(push(x1,x2)) -> u2(le(size(x1),m),x1,x2)
0.00/0.00	      u2(true,x1,x2) -> x2
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	    )
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