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 y r q)
0.00/0.00	    (RULES
0.00/0.00	      lt(x,0) -> false
0.00/0.00	      lt(0,s(x)) -> true
0.00/0.00	      lt(s(x),s(y)) -> lt(x,y)
0.00/0.00	      m(0,s(y)) -> 0
0.00/0.00	      m(x,0) -> x
0.00/0.00	      m(s(x),s(y)) -> m(x,y)
0.00/0.00	      div(0,s(x)) -> pair(0,0)
0.00/0.00	      div(s(x),s(y)) -> pair(0,s(x)) | lt(x,y) == true
0.00/0.00	      div(s(x),s(y)) -> pair(s(q),r) | lt(x,y) == false, div(m(x,y),s(y)) == pair(q,r)
0.00/0.00	    )
0.00/0.00	    (COMMENT [68] p. 12 with rules for "lt" and "m" added doi:10.1007/3-540-59200-8_56 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 r q)
0.00/0.00	    (RULES
0.00/0.00	      lt(x,0) -> false
0.00/0.00	      lt(0,s(x)) -> true
0.00/0.00	      lt(s(x),s(y)) -> lt(x,y)
0.00/0.00	      m(0,s(y)) -> 0
0.00/0.00	      m(x,0) -> x
0.00/0.00	      m(s(x),s(y)) -> m(x,y)
0.00/0.00	      div(0,s(x)) -> pair(0,0)
0.00/0.00	      div(s(x),s(y)) -> pair(0,s(x)) | lt(x,y) == true
0.00/0.00	      div(s(x),s(y)) -> pair(s(q),r) | lt(x,y) == false, div(m(x,y),s(y)) == pair(q,r)
0.00/0.00	    )
0.00/0.00	    (COMMENT [68] p. 12 with rules for "lt" and "m" added doi:10.1007/3-540-59200-8_56 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 r q)
0.00/0.00	    (RULES
0.00/0.00	      lt(x,0) -> false
0.00/0.00	      lt(0,s(x)) -> true
0.00/0.00	      lt(s(x),s(y)) -> lt(x,y)
0.00/0.00	      m(0,s(y)) -> 0
0.00/0.00	      m(x,0) -> x
0.00/0.00	      m(s(x),s(y)) -> m(x,y)
0.00/0.00	      div(0,s(x)) -> pair(0,0)
0.00/0.00	      div(s(x),s(y)) -> pair(0,s(x)) | lt(x,y) == true
0.00/0.00	      div(s(x),s(y)) -> pair(s(q),r) | lt(x,y) == false, div(m(x,y),s(y)) == pair(q,r)
0.00/0.00	    )
0.00/0.00	    (COMMENT [68] p. 12 with rules for "lt" and "m" added doi:10.1007/3-540-59200-8_56 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 r q)
0.00/0.00	    (RULES
0.00/0.00	      lt(x,0) -> false
0.00/0.00	      lt(0,s(x)) -> true
0.00/0.00	      lt(s(x),s(y)) -> lt(x,y)
0.00/0.00	      m(0,s(y)) -> 0
0.00/0.00	      m(x,0) -> x
0.00/0.00	      m(s(x),s(y)) -> m(x,y)
0.00/0.00	      div(0,s(x)) -> pair(0,0)
0.00/0.00	      div(s(x),s(y)) -> pair(0,s(x)) | lt(x,y) == true
0.00/0.00	      div(s(x),s(y)) -> pair(s(q),r) | lt(x,y) == false, div(m(x,y),s(y)) == pair(q,r)
0.00/0.00	    )
0.00/0.00	    (COMMENT [68] p. 12 with rules for "lt" and "m" added doi:10.1007/3-540-59200-8_56 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 x4 x3)
0.00/0.00	    (RULES
0.00/0.00	      lt(x1,0) -> false
0.00/0.00	      lt(0,s(x1)) -> true
0.00/0.00	      lt(s(x1),s(x2)) -> lt(x1,x2)
0.00/0.00	      m(0,s(x1)) -> 0
0.00/0.00	      m(x1,0) -> x1
0.00/0.00	      m(s(x1),s(x2)) -> m(x1,x2)
0.00/0.00	      div(0,s(x1)) -> pair(0,0)
0.00/0.00	      div(s(x1),s(x2)) -> u1(lt(x1,x2),x1,x2)
0.00/0.00	      u1(true,x1,x2) -> pair(0,s(x1))
0.00/0.00	      u1(false,x1,x2) -> u2(div(m(x1,x2),s(x2)),x1,x2)
0.00/0.00	      u2(pair(x3,x4),x1,x2) -> pair(s(x3),x4)
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