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 r n xs r\' n\')
0.00/0.00	    (RULES
0.00/0.00	      eq(0,0) -> true
0.00/0.00	      eq(s(x),0) -> false
0.00/0.00	      eq(0,s(y)) -> false
0.00/0.00	      eq(s(x),s(y)) -> eq(x,y)
0.00/0.00	      lte(0,y) -> true
0.00/0.00	      lte(s(x),0) -> false
0.00/0.00	      lte(s(x),s(y)) -> lte(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	      mod(0,y) -> 0
0.00/0.00	      mod(s(x),0) -> 0
0.00/0.00	      mod(s(x),s(y)) -> mod(m(x,y),s(y)) | lte(y,x) == true
0.00/0.00	      mod(s(x),s(y)) -> s(x) | lte(y,x) == false
0.00/0.00	      filter(n,r,nil) -> nil
0.00/0.00	      filter(n,r,cons(x,xs)) -> cons(x,filter(n,r,xs)) | mod(x,n) == r\', eq(r,r\') == true
0.00/0.00	      filter(n,r,cons(x,xs)) -> filter(n,r,xs) | mod(x,n) == n\', eq(r,r\') == false
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/978-1-4757-3661-8 [18] Example 7.4.9 with typo; corrected as Cops #493 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 n xs r\' n\')
0.00/0.00	    (RULES
0.00/0.00	      eq(0,0) -> true
0.00/0.00	      eq(s(x),0) -> false
0.00/0.00	      eq(0,s(y)) -> false
0.00/0.00	      eq(s(x),s(y)) -> eq(x,y)
0.00/0.00	      lte(0,y) -> true
0.00/0.00	      lte(s(x),0) -> false
0.00/0.00	      lte(s(x),s(y)) -> lte(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	      mod(0,y) -> 0
0.00/0.00	      mod(s(x),0) -> 0
0.00/0.00	      mod(s(x),s(y)) -> mod(m(x,y),s(y)) | lte(y,x) == true
0.00/0.00	      mod(s(x),s(y)) -> s(x) | lte(y,x) == false
0.00/0.00	      filter(n,r,nil) -> nil
0.00/0.00	      filter(n,r,cons(x,xs)) -> cons(x,filter(n,r,xs)) | mod(x,n) == r\', eq(r,r\') == true
0.00/0.00	      filter(n,r,cons(x,xs)) -> filter(n,r,xs) | mod(x,n) == n\', eq(r,r\') == false
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/978-1-4757-3661-8 [18] Example 7.4.9 with typo; corrected as Cops #493 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 n xs r\' n\')
0.00/0.00	    (RULES
0.00/0.00	      eq(0,0) -> true
0.00/0.00	      eq(s(x),0) -> false
0.00/0.00	      eq(0,s(y)) -> false
0.00/0.00	      eq(s(x),s(y)) -> eq(x,y)
0.00/0.00	      lte(0,y) -> true
0.00/0.00	      lte(s(x),0) -> false
0.00/0.00	      lte(s(x),s(y)) -> lte(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	      mod(0,y) -> 0
0.00/0.00	      mod(s(x),0) -> 0
0.00/0.00	      mod(s(x),s(y)) -> mod(m(x,y),s(y)) | lte(y,x) == true
0.00/0.00	      mod(s(x),s(y)) -> s(x) | lte(y,x) == false
0.00/0.00	      filter(n,r,nil) -> nil
0.00/0.00	      filter(n,r,cons(x,xs)) -> cons(x,filter(n,r,xs)) | mod(x,n) == r\', eq(r,r\') == true
0.00/0.00	      filter(n,r,cons(x,xs)) -> filter(n,r,xs) | mod(x,n) == n\', eq(r,r\') == false
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/978-1-4757-3661-8 [18] Example 7.4.9 with typo; corrected as Cops #493 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 n xs r\' n\')
0.00/0.00	    (RULES
0.00/0.00	      eq(0,0) -> true
0.00/0.00	      eq(s(x),0) -> false
0.00/0.00	      eq(0,s(y)) -> false
0.00/0.00	      eq(s(x),s(y)) -> eq(x,y)
0.00/0.00	      lte(0,y) -> true
0.00/0.00	      lte(s(x),0) -> false
0.00/0.00	      lte(s(x),s(y)) -> lte(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	      mod(0,y) -> 0
0.00/0.00	      mod(s(x),0) -> 0
0.00/0.00	      mod(s(x),s(y)) -> mod(m(x,y),s(y)) | lte(y,x) == true
0.00/0.00	      mod(s(x),s(y)) -> s(x) | lte(y,x) == false
0.00/0.00	      filter(n,r,nil) -> nil
0.00/0.00	      filter(n,r,cons(x,xs)) -> cons(x,filter(n,r,xs)) | mod(x,n) == r\', eq(r,r\') == true
0.00/0.00	      filter(n,r,cons(x,xs)) -> filter(n,r,xs) | mod(x,n) == n\', eq(r,r\') == false
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/978-1-4757-3661-8 [18] Example 7.4.9 with typo; corrected as Cops #493 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	EOF