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)
0.00/0.00	    (RULES
0.00/0.00	      s(p(x)) -> x
0.00/0.00	      p(s(x)) -> x
0.00/0.00	      pos(0) -> false
0.00/0.00	      pos(s(0)) -> true
0.00/0.00	      pos(s(x)) -> true | pos(x) == true
0.00/0.00	      pos(p(x)) -> false | pos(x) == false
0.00/0.00	    )
0.00/0.00	    (COMMENT [75] Example 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	      s(p(x)) -> x
0.00/0.00	      p(s(x)) -> x
0.00/0.00	      pos(0) -> false
0.00/0.00	      pos(s(0)) -> true
0.00/0.00	      pos(s(x)) -> true | pos(x) == true
0.00/0.00	      pos(p(x)) -> false | pos(x) == false
0.00/0.00	    )
0.00/0.00	    (COMMENT [75] Example 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	      s(p(x)) -> x
0.00/0.00	      p(s(x)) -> x
0.00/0.00	      pos(0) -> false
0.00/0.00	      pos(s(0)) -> true
0.00/0.00	      pos(s(x)) -> true | pos(x) == true
0.00/0.00	      pos(p(x)) -> false | pos(x) == false
0.00/0.00	    )
0.00/0.00	    (COMMENT [75] Example 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	      s(p(x)) -> x
0.00/0.00	      p(s(x)) -> x
0.00/0.00	      pos(0) -> false
0.00/0.00	      pos(s(0)) -> true
0.00/0.00	      pos(s(x)) -> true | pos(x) == true
0.00/0.00	      pos(p(x)) -> false | pos(x) == false
0.00/0.00	    )
0.00/0.00	    (COMMENT [75] Example 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	      s(p(x1)) -> x1
0.00/0.00	      p(s(x1)) -> x1
0.00/0.00	      pos(0) -> false
0.00/0.00	      pos(s(0)) -> true
0.00/0.00	      pos(p(x1)) -> u1(pos(x1),x1)
0.00/0.00	      u1(false,x1) -> false
0.00/0.00	      pos(s(x1)) -> u2(pos(x1),x1)
0.00/0.00	      u2(true,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	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 joinability of conditional CPs (via narrowing trees).
0.00/0.00	
0.00/0.00	MAYBE
0.00/0.00	EOF