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 xs v ys\' y xs\' w z)
0.00/0.00	    (RULES
0.00/0.00	      ssp(nil,0) -> nil
0.00/0.00	      ssp(cons(y,ys\'),v) -> xs | ssp(ys\',v) == xs
0.00/0.00	      ssp(cons(y,ys\'),v) -> cons(y,xs\') | sub(v,y) == w, ssp(ys\',w) == xs\'
0.00/0.00	      sub(z,0) -> z
0.00/0.00	      sub(s(v),s(w)) -> z | sub(v,w) == z
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/j.tcs.2012.09.005 [72] Example 9 ( R_ssp ) 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 xs v ys\' y xs\' w z)
0.00/0.00	    (RULES
0.00/0.00	      ssp(nil,0) -> nil
0.00/0.00	      ssp(cons(y,ys\'),v) -> xs | ssp(ys\',v) == xs
0.00/0.00	      ssp(cons(y,ys\'),v) -> cons(y,xs\') | sub(v,y) == w, ssp(ys\',w) == xs\'
0.00/0.00	      sub(z,0) -> z
0.00/0.00	      sub(s(v),s(w)) -> z | sub(v,w) == z
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/j.tcs.2012.09.005 [72] Example 9 ( R_ssp ) 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 xs v ys\' y xs\' w z)
0.00/0.00	    (RULES
0.00/0.00	      ssp(nil,0) -> nil
0.00/0.00	      ssp(cons(y,ys\'),v) -> xs | ssp(ys\',v) == xs
0.00/0.00	      ssp(cons(y,ys\'),v) -> cons(y,xs\') | sub(v,y) == w, ssp(ys\',w) == xs\'
0.00/0.00	      sub(z,0) -> z
0.00/0.00	      sub(s(v),s(w)) -> z | sub(v,w) == z
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/j.tcs.2012.09.005 [72] Example 9 ( R_ssp ) 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 xs v ys\' y xs\' w z)
0.00/0.00	    (RULES
0.00/0.00	      ssp(nil,0) -> nil
0.00/0.00	      ssp(cons(y,ys\'),v) -> xs | ssp(ys\',v) == xs
0.00/0.00	      ssp(cons(y,ys\'),v) -> cons(y,xs\') | sub(v,y) == w, ssp(ys\',w) == xs\'
0.00/0.00	      sub(z,0) -> z
0.00/0.00	      sub(s(v),s(w)) -> z | sub(v,w) == z
0.00/0.00	    )
0.00/0.00	    (COMMENT doi:10.1016/j.tcs.2012.09.005 [72] Example 9 ( R_ssp ) 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 x3 x2 x1 x4 x5)
0.00/0.00	    (RULES
0.00/0.00	      ssp(nil,0) -> nil
0.00/0.00	      ssp(cons(x1,x2),x3) -> u1(ssp(x2,x3),x1,x2,x3)
0.00/0.00	      u1(x4,x1,x2,x3) -> x4
0.00/0.00	      ssp(cons(x1,x2),x3) -> u2(sub(x3,x1),x1,x2,x3)
0.00/0.00	      u2(x4,x1,x2,x3) -> u3(ssp(x2,x4),x4,x1,x2,x3)
0.00/0.00	      u3(x5,x4,x1,x2,x3) -> cons(x1,x5)
0.00/0.00	      sub(x1,0) -> x1
0.00/0.00	      sub(s(x1),s(x2)) -> u4(sub(x1,x2),x1,x2)
0.00/0.00	      u4(x3,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	Failed to prove operational termination of R.
0.00/0.00	
0.00/0.00	MAYBE
0.00/0.00	EOF