0.00/0.01	MAYBE
0.00/0.01	
0.00/0.01	
0.00/0.01	Succeeded in reading "/export/starexec/sandbox/benchmark/theBenchmark.trs".
0.00/0.01	    (CONDITIONTYPE ORIENTED)
0.00/0.01	    (VAR xs ys\' v ws y\' w xs\' x\' zs z ys y)
0.00/0.01	    (RULES
0.00/0.01	      ssp\'(xs,0) -> nil
0.00/0.01	      ssp\'(cons(y\',ws),v) -> cons(y\',ys\') | sub(v,y\') == w, ssp\'(ws,w) == ys\'
0.00/0.01	      ssp\'(cons(x\',xs\'),v) -> cons(y\',ys\') | get(xs\') == tp2(y\',zs), sub(v,y\') == w, ssp\'(cons(x\',zs),w) == ys\'
0.00/0.01	      sub(z,0) -> z
0.00/0.01	      sub(s(v),s(w)) -> z | sub(v,w) == z
0.00/0.01	      get(cons(y,ys)) -> tp2(y,ys)
0.00/0.01	      get(cons(x\',xs\')) -> tp2(y,cons(x\',zs)) | get(xs\') == tp2(y,zs)
0.00/0.01	    )
0.00/0.01	    (COMMENT doi:10.1016/j.tcs.2012.09.005 [72] Example 10 ( R'_ssp ) submitted by: Thomas Sternagel and Aart Middeldorp)
0.00/0.01	
0.00/0.01	No "->="-rules.
0.00/0.01	
0.00/0.01	Decomposed conditions if possible.
0.00/0.01	    (CONDITIONTYPE ORIENTED)
0.00/0.01	    (VAR xs ys\' v ws y\' w xs\' x\' zs z ys y)
0.00/0.01	    (RULES
0.00/0.01	      ssp\'(xs,0) -> nil
0.00/0.01	      ssp\'(cons(y\',ws),v) -> cons(y\',ys\') | sub(v,y\') == w, ssp\'(ws,w) == ys\'
0.00/0.01	      ssp\'(cons(x\',xs\'),v) -> cons(y\',ys\') | get(xs\') == tp2(y\',zs), sub(v,y\') == w, ssp\'(cons(x\',zs),w) == ys\'
0.00/0.01	      sub(z,0) -> z
0.00/0.01	      sub(s(v),s(w)) -> z | sub(v,w) == z
0.00/0.01	      get(cons(y,ys)) -> tp2(y,ys)
0.00/0.01	      get(cons(x\',xs\')) -> tp2(y,cons(x\',zs)) | get(xs\') == tp2(y,zs)
0.00/0.01	    )
0.00/0.01	    (COMMENT doi:10.1016/j.tcs.2012.09.005 [72] Example 10 ( R'_ssp ) submitted by: Thomas Sternagel and Aart Middeldorp)
0.00/0.01	
0.00/0.01	Removed infeasible rules as much as possible.
0.00/0.01	    (CONDITIONTYPE ORIENTED)
0.00/0.01	    (VAR xs ys\' v ws y\' w xs\' x\' zs z ys y)
0.00/0.01	    (RULES
0.00/0.01	      ssp\'(xs,0) -> nil
0.00/0.01	      ssp\'(cons(y\',ws),v) -> cons(y\',ys\') | sub(v,y\') == w, ssp\'(ws,w) == ys\'
0.00/0.01	      ssp\'(cons(x\',xs\'),v) -> cons(y\',ys\') | get(xs\') == tp2(y\',zs), sub(v,y\') == w, ssp\'(cons(x\',zs),w) == ys\'
0.00/0.01	      sub(z,0) -> z
0.00/0.01	      sub(s(v),s(w)) -> z | sub(v,w) == z
0.00/0.01	      get(cons(y,ys)) -> tp2(y,ys)
0.00/0.01	      get(cons(x\',xs\')) -> tp2(y,cons(x\',zs)) | get(xs\') == tp2(y,zs)
0.00/0.01	    )
0.00/0.01	    (COMMENT doi:10.1016/j.tcs.2012.09.005 [72] Example 10 ( R'_ssp ) submitted by: Thomas Sternagel and Aart Middeldorp)
0.00/0.01	
0.00/0.01	Try to disprove confluence of the following (C)TRS:
0.00/0.01	    (CONDITIONTYPE ORIENTED)
0.00/0.01	    (VAR xs ys\' v ws y\' w xs\' x\' zs z ys y)
0.00/0.01	    (RULES
0.00/0.01	      ssp\'(xs,0) -> nil
0.00/0.01	      ssp\'(cons(y\',ws),v) -> cons(y\',ys\') | sub(v,y\') == w, ssp\'(ws,w) == ys\'
0.00/0.01	      ssp\'(cons(x\',xs\'),v) -> cons(y\',ys\') | get(xs\') == tp2(y\',zs), sub(v,y\') == w, ssp\'(cons(x\',zs),w) == ys\'
0.00/0.01	      sub(z,0) -> z
0.00/0.01	      sub(s(v),s(w)) -> z | sub(v,w) == z
0.00/0.01	      get(cons(y,ys)) -> tp2(y,ys)
0.00/0.01	      get(cons(x\',xs\')) -> tp2(y,cons(x\',zs)) | get(xs\') == tp2(y,zs)
0.00/0.01	    )
0.00/0.01	    (COMMENT doi:10.1016/j.tcs.2012.09.005 [72] Example 10 ( R'_ssp ) submitted by: Thomas Sternagel and Aart Middeldorp)
0.00/0.01	
0.00/0.01	Failed either to apply SR and U for normal 1CTRSs to the above CTRS or to prove confluence of any converted TRSs.
0.00/0.01	
0.00/0.01	Try to apply SR and U for 3DCTRSs to the above CTRS.
0.00/0.01	
0.00/0.01	Succeeded in applying U for 3DCTRSs to the above CTRS.
0.00/0.01	U(R) =
0.00/0.01	    (VAR x1 x3 x2 x4 x5 x6 x7)
0.00/0.01	    (RULES
0.00/0.01	      ssp\'(x1,0) -> nil
0.00/0.01	      ssp\'(cons(x1,x2),x3) -> u1(sub(x3,x1),x1,x2,x3)
0.00/0.01	      u1(x4,x1,x2,x3) -> u5(ssp\'(x2,x4),x4,x1,x2,x3)
0.00/0.02	      u5(x5,x4,x1,x2,x3) -> cons(x1,x5)
0.00/0.02	      ssp\'(cons(x1,x2),x3) -> u2(get(x2),x1,x2,x3)
0.00/0.02	      u2(tp2(x4,x5),x1,x2,x3) -> u3(sub(x3,x4),x4,x5,x1,x2,x3)
0.00/0.02	      u3(x6,x4,x5,x1,x2,x3) -> u4(ssp\'(cons(x1,x5),x6),x6,x4,x5,x1,x2,x3)
0.00/0.02	      u4(x7,x6,x4,x5,x1,x2,x3) -> cons(x4,x7)
0.00/0.02	      sub(x1,0) -> x1
0.00/0.02	      sub(s(x1),s(x2)) -> u6(sub(x1,x2),x1,x2)
0.00/0.02	      u6(x3,x1,x2) -> x3
0.00/0.02	      get(cons(x1,x2)) -> tp2(x1,x2)
0.00/0.02	      get(cons(x1,x2)) -> u7(get(x2),x1,x2)
0.00/0.02	      u7(tp2(x3,x4),x1,x2) -> tp2(x3,cons(x1,x4))
0.00/0.02	    )
0.00/0.02	
0.00/0.02	U for 3DCTRSs is sound for the above CTRS.
0.00/0.02	
0.00/0.02	Failed to prove confluence of U(R).
0.00/0.02	
0.00/0.02	Try to prove operational termination of R, i.e., termination of U(R).
0.00/0.02	
0.00/0.02	Failed to prove operational termination of R.
0.00/0.02	
0.00/0.02	MAYBE
0.00/0.02	EOF