0.00/0.06	NO
0.00/0.06	(ignored inputs)COMMENT Cops #647 - #721: generated ground TRSs; evenly distributed in the UNR/UNC/NFP/CR hierarchy submitted by: Bertram Felgenhauer
0.00/0.06	input TRS:
0.00/0.06	   [ b -> a,
0.00/0.06	     f(h(b,f(a))) -> f(c),
0.00/0.06	     c -> h(c,c),
0.00/0.06	     h(f(f(b)),a) -> c,
0.00/0.06	     h(a,a) -> a ]
0.00/0.06	Try persistent and layer-preserving decomposition...
0.00/0.06	Sort Assignment:
0.00/0.06	 a : =>9
0.00/0.06	 b : =>9
0.00/0.06	 c : =>9
0.00/0.06	 f : 9=>9
0.00/0.06	 h : 9*9=>9
0.00/0.06	maximal types: {9}
0.00/0.06	...decomposition failed.
0.00/0.06	TRS:
0.00/0.06	   [ b -> a,
0.00/0.06	     f(h(b,f(a))) -> f(c),
0.00/0.06	     c -> h(c,c),
0.00/0.06	     h(f(f(b)),a) -> c,
0.00/0.06	     h(a,a) -> a ]
0.00/0.06	Input:
0.00/0.06	   [ b -> a,
0.00/0.06	     f(h(b,f(a))) -> f(c),
0.00/0.06	     c -> h(c,c),
0.00/0.06	     h(f(f(b)),a) -> c,
0.00/0.06	     h(a,a) -> a ]
0.00/0.06	
0.00/0.06	Make it flat:
0.00/0.06	   [ f(!cl_3) -> f(c),
0.00/0.06	     c -> h(c,c),
0.00/0.06	     h(!cl_2,a) -> c,
0.00/0.06	     !cl_3 -> !cl_3,
0.00/0.06	     h(b,!cl_1) -> !cl_3,
0.00/0.06	     f(a) -> !cl_1,
0.00/0.06	     h(a,a) -> a,
0.00/0.06	     f(b) -> !cl_0,
0.00/0.06	     !cl_0 -> !cl_0,
0.00/0.06	     b -> a,
0.00/0.06	     f(!cl_0) -> !cl_2,
0.00/0.06	     !cl_2 -> !cl_2 ]
0.00/0.06	Time: 0.000 [s]
0.00/0.06	
0.00/0.06	Make it Complete (R^):
0.00/0.06	   [ f(!cl_3) = f(c),
0.00/0.06	     h(c,c) = h(!cl_2,a),
0.00/0.06	     h(c,c) = h(!cl_2,b),
0.00/0.06	     c = h(c,c),
0.00/0.06	     h(!cl_2,b) = h(!cl_2,a),
0.00/0.06	     h(!cl_2,b) = c,
0.00/0.06	     h(!cl_2,a) = c,
0.00/0.06	     h(a,!cl_1) = !cl_3,
0.00/0.06	     h(a,!cl_0) = !cl_3,
0.00/0.06	     h(a,!cl_1) = h(b,!cl_0),
0.00/0.06	     h(a,!cl_1) = h(a,!cl_0),
0.00/0.06	     h(b,!cl_0) = h(a,!cl_0),
0.00/0.06	     h(a,!cl_1) = h(b,!cl_1),
0.00/0.06	     h(a,!cl_0) = h(b,!cl_1),
0.00/0.06	     h(b,!cl_0) = h(b,!cl_1),
0.00/0.06	     h(b,!cl_0) = !cl_3,
0.00/0.06	     h(b,!cl_1) = !cl_3,
0.00/0.06	     f(b) = !cl_1,
0.00/0.06	     f(!cl_1) = f(!cl_0),
0.00/0.06	     f(!cl_1) = !cl_2,
0.00/0.06	     !cl_1 = !cl_0,
0.00/0.06	     f(a) = !cl_1,
0.00/0.06	     b = h(a,a),
0.00/0.06	     h(a,b) = a,
0.00/0.06	     b = h(b,a),
0.00/0.06	     h(a,b) = b,
0.00/0.06	     b = h(b,b),
0.00/0.06	     h(b,b) = a,
0.00/0.06	     h(a,b) = h(b,a),
0.00/0.06	     h(a,b) = h(b,b),
0.00/0.06	     h(b,a) = h(b,b),
0.00/0.06	     h(a,b) = h(a,a),
0.00/0.06	     h(b,b) = h(a,a),
0.00/0.06	     h(b,a) = h(a,a),
0.00/0.06	     h(b,a) = a,
0.00/0.06	     h(a,a) = a,
0.00/0.06	     f(a) = f(b),
0.00/0.06	     f(a) = !cl_0,
0.00/0.06	     f(b) = !cl_0,
0.00/0.06	     b = a,
0.00/0.06	     f(!cl_0) = !cl_2 ]
0.00/0.06	Time: 0.009 [s]
0.00/0.06	
0.00/0.06	CPNF:
0.00/0.06	   [ c … h(h(f(!cl_1),a),h(f(!cl_1),a)),
0.00/0.06	     c … h(f(!cl_1),a),
0.00/0.06	     !cl_3 … h(a,!cl_1),
0.00/0.06	     !cl_2 … f(!cl_1),
0.00/0.06	     !cl_0 … !cl_1,
0.00/0.06	     a … a ]
0.00/0.06	Time: 0.000 [s]
0.00/0.06	
0.00/0.06	The TRS doesn't have Uniqueness of Normal Forms.
0.00/0.06	Counter Example: 
0.00/0.06	     h(h(f(!cl_1),a),h(f(!cl_1),a))
0.00/0.06	<->* h(f(!cl_1),a)
0.00/0.06	
0.00/0.06	proof:
0.00/0.06	     h(h(f(!cl_1),a),h(f(!cl_1),a))
0.00/0.06	->R^ h(h(f(!cl_0),a),h(f(!cl_1),a))
0.00/0.06	->R^ h(h(f(!cl_0),a),h(f(!cl_0),a))
0.00/0.06	->R^ h(h(!cl_2,a),h(f(!cl_0),a))
0.00/0.06	->R^ h(h(!cl_2,a),h(!cl_2,a))
0.00/0.06	->R^ h(c,h(!cl_2,a))
0.00/0.06	->R^ h(c,c)
0.00/0.06	->R^ c
0.00/0.06	
0.00/0.06	     h(f(!cl_1),a)
0.00/0.06	->R^ h(f(!cl_0),a)
0.00/0.06	->R^ h(!cl_2,a)
0.00/0.06	->R^ c
0.00/0.06	Total Time: 0.010 [s]
0.00/0.06	
0.00/0.06	/export/starexec/sandbox/benchmark/theBenchmark.trs: Success(not UNC)
0.00/0.06	(10 msec.)
0.00/0.06	EOF