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 z y x)
0.00/0.00	    (RULES
0.00/0.00	      f(x) -> g(x,y,z) | h(a,x) == i(y), h(a,y) == i(z)
0.00/0.00	      h(a,a) -> i(b)
0.00/0.00	      h(a,b) -> i(c)
0.00/0.00	      h(b,b) -> i(d)
0.00/0.00	    )
0.00/0.00	    (COMMENT [68] Example 3.2 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 z y x)
0.00/0.00	    (RULES
0.00/0.00	      f(x) -> g(x,y,z) | h(a,x) == i(y), h(a,y) == i(z)
0.00/0.00	      h(a,a) -> i(b)
0.00/0.00	      h(a,b) -> i(c)
0.00/0.00	      h(b,b) -> i(d)
0.00/0.00	    )
0.00/0.00	    (COMMENT [68] Example 3.2 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 z y x)
0.00/0.00	    (RULES
0.00/0.00	      f(x) -> g(x,y,z) | h(a,x) == i(y), h(a,y) == i(z)
0.00/0.00	      h(a,a) -> i(b)
0.00/0.00	      h(a,b) -> i(c)
0.00/0.00	      h(b,b) -> i(d)
0.00/0.00	    )
0.00/0.00	    (COMMENT [68] Example 3.2 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 z y x)
0.00/0.00	    (RULES
0.00/0.00	      f(x) -> g(x,y,z) | h(a,x) == i(y), h(a,y) == i(z)
0.00/0.00	      h(a,a) -> i(b)
0.00/0.00	      h(a,b) -> i(c)
0.00/0.00	      h(b,b) -> i(d)
0.00/0.00	    )
0.00/0.00	    (COMMENT [68] Example 3.2 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 x3)
0.00/0.00	    (RULES
0.00/0.00	      f(x1) -> u1(h(a,x1),x1)
0.00/0.00	      u1(i(x2),x1) -> u2(h(a,x2),x2,x1)
0.00/0.00	      u2(i(x3),x2,x1) -> g(x1,x2,x3)
0.00/0.00	      h(a,a) -> i(b)
0.00/0.00	      h(a,b) -> i(c)
0.00/0.00	      h(b,b) -> i(d)
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