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)
0.00/0.00	    (RULES
0.00/0.00	      p(q(x)) -> 0
0.00/0.00	      c -> c
0.00/0.00	      a(x) -> b | p(x) == 0
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/0022-0000 ( 86 ) 90033-4 [47] Example 2.6.2 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)
0.00/0.00	    (RULES
0.00/0.00	      p(q(x)) -> 0
0.00/0.00	      c -> c
0.00/0.00	      a(x) -> b | p(x) == 0
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/0022-0000 ( 86 ) 90033-4 [47] Example 2.6.2 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)
0.00/0.00	    (RULES
0.00/0.00	      p(q(x)) -> 0
0.00/0.00	      c -> c
0.00/0.00	      a(x) -> b | p(x) == 0
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/0022-0000 ( 86 ) 90033-4 [47] Example 2.6.2 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)
0.00/0.00	    (RULES
0.00/0.00	      p(q(x)) -> 0
0.00/0.00	      c -> c
0.00/0.00	      a(x) -> b | p(x) == 0
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/0022-0000 ( 86 ) 90033-4 [47] Example 2.6.2 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)
0.00/0.00	    (RULES
0.00/0.00	      p(q(x1)) -> 0
0.00/0.00	      c -> c
0.00/0.00	      a(x1) -> u1(p(x1),x1)
0.00/0.00	      u1(0,x1) -> b
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