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 z z\')
0.00/0.00	    (RULES
0.00/0.00	      plus(0,y) -> y
0.00/0.00	      plus(s(x),y) -> plus(x,s(y))
0.00/0.00	      f(x,y) -> z | plus(x,y) == plus(z,z\')
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/3-540-58216-9_40 [45] Example 4.1.a 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 z z\')
0.00/0.00	    (RULES
0.00/0.00	      plus(0,y) -> y
0.00/0.00	      plus(s(x),y) -> plus(x,s(y))
0.00/0.00	      f(x,y) -> z | plus(x,y) == plus(z,z\')
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/3-540-58216-9_40 [45] Example 4.1.a 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 z z\')
0.00/0.00	    (RULES
0.00/0.00	      plus(0,y) -> y
0.00/0.00	      plus(s(x),y) -> plus(x,s(y))
0.00/0.00	      f(x,y) -> z | plus(x,y) == plus(z,z\')
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/3-540-58216-9_40 [45] Example 4.1.a 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 z z\')
0.00/0.00	    (RULES
0.00/0.00	      plus(0,y) -> y
0.00/0.00	      plus(s(x),y) -> plus(x,s(y))
0.00/0.00	      f(x,y) -> z | plus(x,y) == plus(z,z\')
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1007/3-540-58216-9_40 [45] Example 4.1.a 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	      plus(0,x1) -> x1
0.00/0.00	      plus(s(x1),x2) -> plus(x1,s(x2))
0.00/0.00	      f(x1,x2) -> u1(plus(x1,x2),x1,x2)
0.00/0.00	      u1(plus(x3,x4),x1,x2) -> x3
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	Succeeded in proving operational termination of R.
0.00/0.00	
0.00/0.00	Try to prove joinability of all (conditional) CPs.
0.00/0.00	
0.00/0.00	Failed to prove termination of U(R).
0.00/0.00	
0.00/0.00	MAYBE
0.00/0.00	EOF