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 y x r q)
0.00/0.00	    (RULES
0.00/0.00	      div(x,y) -> pair(0,y) | greater(y,x) == true
0.00/0.00	      div(x,y) -> pair(s(q),r) | leq(y,x) == true, div(m(x,y),y) == pair(q,r)
0.00/0.00	      m(x,0) -> x
0.00/0.00	      m(0,y) -> 0
0.00/0.00	      m(s(x),s(y)) -> m(x,y)
0.00/0.00	      greater(s(x),s(y)) -> greater(x,y)
0.00/0.00	      greater(s(x),0) -> true
0.00/0.00	      leq(s(x),s(y)) -> leq(x,y)
0.00/0.00	      leq(0,x) -> true
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/j.jlap.2009.08.001 [73] Example 9 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 r q)
0.00/0.00	    (RULES
0.00/0.00	      div(x,y) -> pair(0,y) | greater(y,x) == true
0.00/0.00	      div(x,y) -> pair(s(q),r) | leq(y,x) == true, div(m(x,y),y) == pair(q,r)
0.00/0.00	      m(x,0) -> x
0.00/0.00	      m(0,y) -> 0
0.00/0.00	      m(s(x),s(y)) -> m(x,y)
0.00/0.00	      greater(s(x),s(y)) -> greater(x,y)
0.00/0.00	      greater(s(x),0) -> true
0.00/0.00	      leq(s(x),s(y)) -> leq(x,y)
0.00/0.00	      leq(0,x) -> true
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/j.jlap.2009.08.001 [73] Example 9 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 r q)
0.00/0.00	    (RULES
0.00/0.00	      div(x,y) -> pair(0,y) | greater(y,x) == true
0.00/0.00	      div(x,y) -> pair(s(q),r) | leq(y,x) == true, div(m(x,y),y) == pair(q,r)
0.00/0.00	      m(x,0) -> x
0.00/0.00	      m(0,y) -> 0
0.00/0.00	      m(s(x),s(y)) -> m(x,y)
0.00/0.00	      greater(s(x),s(y)) -> greater(x,y)
0.00/0.00	      greater(s(x),0) -> true
0.00/0.00	      leq(s(x),s(y)) -> leq(x,y)
0.00/0.00	      leq(0,x) -> true
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/j.jlap.2009.08.001 [73] Example 9 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 r q)
0.00/0.00	    (RULES
0.00/0.00	      div(x,y) -> pair(0,y) | greater(y,x) == true
0.00/0.00	      div(x,y) -> pair(s(q),r) | leq(y,x) == true, div(m(x,y),y) == pair(q,r)
0.00/0.00	      m(x,0) -> x
0.00/0.00	      m(0,y) -> 0
0.00/0.00	      m(s(x),s(y)) -> m(x,y)
0.00/0.00	      greater(s(x),s(y)) -> greater(x,y)
0.00/0.00	      greater(s(x),0) -> true
0.00/0.00	      leq(s(x),s(y)) -> leq(x,y)
0.00/0.00	      leq(0,x) -> true
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/j.jlap.2009.08.001 [73] Example 9 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 x4 x3)
0.00/0.00	    (RULES
0.00/0.00	      div(x1,x2) -> u1(greater(x2,x1),x1,x2)
0.00/0.00	      u1(true,x1,x2) -> pair(0,x2)
0.00/0.00	      div(x1,x2) -> u2(leq(x2,x1),x1,x2)
0.00/0.00	      u2(true,x1,x2) -> u3(div(m(x1,x2),x2),x1,x2)
0.00/0.00	      u3(pair(x3,x4),x1,x2) -> pair(s(x3),x4)
0.00/0.00	      m(x1,0) -> x1
0.00/0.00	      m(0,x1) -> 0
0.00/0.00	      m(s(x1),s(x2)) -> m(x1,x2)
0.00/0.00	      greater(s(x1),s(x2)) -> greater(x1,x2)
0.00/0.00	      greater(s(x1),0) -> true
0.00/0.00	      leq(s(x1),s(x2)) -> leq(x1,x2)
0.00/0.00	      leq(0,x1) -> true
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	Failed to prove operational termination of R.
0.00/0.00	
0.00/0.00	MAYBE
0.00/0.00	EOF