0.00/0.09	YES
0.00/0.09	(ignored inputs)COMMENT doi:10.1006/jsco.1996.0002 [112] p. 31 ( signature extension and currying do not preserve NFP ) submitted by: Bertram Felgenhauer
0.00/0.09	input TRS:
0.00/0.09	   [ f(?x,?x) -> g,
0.00/0.09	     a -> b,
0.00/0.09	     a -> c,
0.00/0.09	     b -> b,
0.00/0.09	     c -> c,
0.00/0.09	     f(a,?x) -> g,
0.00/0.09	     f(b,?x) -> g,
0.00/0.09	     f(c,?x) -> g,
0.00/0.09	     f(?x,a) -> g,
0.00/0.09	     f(?x,b) -> g,
0.00/0.09	     f(?x,c) -> g ]
0.00/0.09	unknown Strongly Non-Overlapping
0.00/0.09	unknown Right-Reducible
0.00/0.09	Call a UNC decision procedure for shallow TRSs...
0.00/0.09	Input:
0.00/0.09	   [ f(?x,?x) -> g,
0.00/0.09	     a -> b,
0.00/0.09	     a -> c,
0.00/0.09	     b -> b,
0.00/0.09	     c -> c,
0.00/0.09	     f(a,?x) -> g,
0.00/0.09	     f(b,?x) -> g,
0.00/0.09	     f(c,?x) -> g,
0.00/0.09	     f(?x,a) -> g,
0.00/0.09	     f(?x,b) -> g,
0.00/0.09	     f(?x,c) -> g ]
0.00/0.09	
0.00/0.09	Make it flat:
0.00/0.09	   [ f(?x,?x) -> g,
0.00/0.09	     a -> b,
0.00/0.09	     a -> c,
0.00/0.09	     b -> b,
0.00/0.09	     c -> c,
0.00/0.09	     f(a,?x) -> g,
0.00/0.09	     f(b,?x) -> g,
0.00/0.09	     f(c,?x) -> g,
0.00/0.09	     f(?x,a) -> g,
0.00/0.09	     f(?x,b) -> g,
0.00/0.09	     f(?x,c) -> g ]
0.00/0.09	Time: 0.000 [s]
0.00/0.09	
0.00/0.09	Make it Complete (R^):
0.00/0.09	   [ f(?x,?x) = f(?x_1,c),
0.00/0.09	     f(?x,?x) = f(?x_1,b),
0.00/0.09	     f(?x,?x) = f(?x_1,a),
0.00/0.09	     f(?x,?x) = f(c,?x_1),
0.00/0.09	     f(?x,?x) = f(b,?x_1),
0.00/0.09	     f(?x,?x) = f(a,?x_1),
0.00/0.09	     f(?x,?x) = f(?x_1,?x_1),
0.00/0.09	     f(?x,?x) = g,
0.00/0.09	     b = c,
0.00/0.09	     a = b,
0.00/0.09	     a = c,
0.00/0.09	     f(a,?x) = f(?x_1,c),
0.00/0.09	     f(a,?x) = f(?x_1,b),
0.00/0.09	     f(a,?x) = f(?x_1,a),
0.00/0.09	     f(a,?x) = f(c,?x_1),
0.00/0.09	     f(a,?x) = f(b,?x_1),
0.00/0.09	     f(a,?x) = f(a,?x_1),
0.00/0.09	     f(a,?x) = g,
0.00/0.09	     f(b,?x) = f(?x_1,c),
0.00/0.09	     f(b,?x) = f(?x_1,b),
0.00/0.09	     f(b,?x) = f(?x_1,a),
0.00/0.09	     f(b,?x) = f(c,?x_1),
0.00/0.09	     f(b,?x) = f(b,?x_1),
0.00/0.09	     f(b,?x) = g,
0.00/0.09	     f(c,?x) = f(?x_1,c),
0.00/0.09	     f(c,?x) = f(?x_1,b),
0.00/0.09	     f(c,?x) = f(?x_1,a),
0.00/0.09	     f(c,?x) = f(c,?x_1),
0.00/0.09	     f(c,?x) = g,
0.00/0.09	     f(?x,a) = f(?x_1,c),
0.00/0.09	     f(?x,a) = f(?x_1,b),
0.00/0.09	     f(?x,a) = f(?x_1,a),
0.00/0.09	     f(?x,a) = g,
0.00/0.09	     f(?x,b) = f(?x_1,c),
0.00/0.09	     f(?x,b) = f(?x_1,b),
0.00/0.09	     f(?x,b) = g,
0.00/0.09	     f(?x,c) = f(?x_1,c),
0.00/0.09	     f(?x,c) = g ]
0.00/0.09	Time: 0.053 [s]
0.00/0.09	
0.00/0.09	CPNF:
0.00/0.09	   [ g … g ]
0.00/0.09	Time: 0.000 [s]
0.00/0.09	
0.00/0.09	Now checking all the pairs in CW...
0.00/0.09	
0.00/0.09	Time to check pairs: 0.000 [s]
0.00/0.09	
0.00/0.09	The TRS has Uniqueness of Normal Forms.
0.00/0.09	Total Time: 0.054 [s]
0.00/0.09	
0.00/0.09	...UNC found by the decision procedure (hence UNR).
0.00/0.09	/export/starexec/sandbox/benchmark/theBenchmark.trs: Success(UNR)
0.00/0.09	(54 msec.)
0.00/0.09	EOF