0.00/0.07 YES 0.00/0.07 (ignored inputs)COMMENT Cops #647 - #721: generated ground TRSs; evenly distributed in the UNR/UNC/NFP/CR hierarchy submitted by: Bertram Felgenhauer 0.00/0.07 input TRS: 0.00/0.07 [ a -> f(h(c,h(h(h(h(f(h(a,b)),a),h(h(h(f(f(a)),c),h(f(b),a)),a)),b),c))), 0.00/0.07 h(f(f(b)),h(c,h(f(f(h(h(b,h(c,c)),h(f(a),c)))),f(a)))) -> h(b,b), 0.00/0.07 f(c) -> c, 0.00/0.07 f(f(h(f(h(c,h(a,f(a)))),f(c)))) -> b ] 0.00/0.07 Try persistent and layer-preserving decomposition... 0.00/0.07 Sort Assignment: 0.00/0.07 a : =>9 0.00/0.07 b : =>9 0.00/0.07 c : =>9 0.00/0.07 f : 9=>9 0.00/0.07 h : 9*9=>9 0.00/0.07 maximal types: {9} 0.00/0.07 ...decomposition failed. 0.00/0.07 TRS: 0.00/0.07 [ a -> f(h(c,h(h(h(h(f(h(a,b)),a),h(h(h(f(f(a)),c),h(f(b),a)),a)),b),c))), 0.00/0.07 h(f(f(b)),h(c,h(f(f(h(h(b,h(c,c)),h(f(a),c)))),f(a)))) -> h(b,b), 0.00/0.07 f(c) -> c, 0.00/0.07 f(f(h(f(h(c,h(a,f(a)))),f(c)))) -> b ] 0.00/0.07 Input: 0.00/0.07 [ a -> f(h(c,h(h(h(h(f(h(a,b)),a),h(h(h(f(f(a)),c),h(f(b),a)),a)),b),c))), 0.00/0.07 h(f(f(b)),h(c,h(f(f(h(h(b,h(c,c)),h(f(a),c)))),f(a)))) -> h(b,b), 0.00/0.07 f(c) -> c, 0.00/0.07 f(f(h(f(h(c,h(a,f(a)))),f(c)))) -> b ] 0.00/0.07 0.00/0.07 Make it flat: 0.00/0.07 [ h(!cl_3,!cl_16) -> h(b,b), 0.00/0.07 !cl_16 -> !cl_16, 0.00/0.07 h(c,!cl_15) -> !cl_16, 0.00/0.07 !cl_14 -> !cl_14, 0.00/0.07 f(!cl_13) -> !cl_14, 0.00/0.07 !cl_12 -> !cl_12, 0.00/0.07 f(!cl_10) -> !cl_12, 0.00/0.07 !cl_10 -> !cl_10, 0.00/0.07 h(!cl_6,!cl_8) -> !cl_10, 0.00/0.07 !cl_8 -> !cl_8, 0.00/0.07 f(c) -> !cl_8, 0.00/0.07 !cl_6 -> !cl_6, 0.00/0.07 f(!cl_4) -> !cl_6, 0.00/0.07 !cl_4 -> !cl_4, 0.00/0.07 h(c,!cl_2) -> !cl_4, 0.00/0.07 !cl_2 -> !cl_2, 0.00/0.07 h(a,!cl_0) -> !cl_2, 0.00/0.07 a -> f(!cr_13), 0.00/0.07 !cr_13 -> h(c,!cr_12), 0.00/0.07 !cr_12 -> h(!cr_11,c), 0.00/0.07 !cr_11 -> h(!cr_10,b), 0.00/0.07 !cr_10 -> h(!cr_2,!cr_9), 0.00/0.07 !cr_9 -> h(!cr_8,a), 0.00/0.07 !cr_8 -> h(!cr_5,!cr_7), 0.00/0.07 !cr_7 -> h(!cr_6,a), 0.00/0.07 !cr_6 -> f(b), 0.00/0.07 !cr_5 -> h(!cr_4,c), 0.00/0.07 !cr_4 -> f(!cr_3), 0.00/0.07 !cr_3 -> f(a), 0.00/0.07 !cr_2 -> h(!cr_1,a), 0.00/0.07 !cr_1 -> f(!cr_0), 0.00/0.07 !cr_0 -> h(a,b), 0.00/0.07 !cl_0 -> !cl_0, 0.00/0.07 f(a) -> !cl_0, 0.00/0.07 f(b) -> !cl_1, 0.00/0.07 f(!cl_1) -> !cl_3, 0.00/0.07 h(c,c) -> !cl_5, 0.00/0.07 h(b,!cl_5) -> !cl_7, 0.00/0.07 h(!cl_0,c) -> !cl_9, 0.00/0.07 !cl_9 -> !cl_9, 0.00/0.07 h(!cl_7,!cl_9) -> !cl_11, 0.00/0.07 !cl_11 -> !cl_11, 0.00/0.07 f(!cl_11) -> !cl_13, 0.00/0.07 !cl_13 -> !cl_13, 0.00/0.07 f(!cl_12) -> b, 0.00/0.07 !cl_8 -> c, 0.00/0.07 h(!cl_14,!cl_0) -> !cl_15, 0.00/0.07 !cl_15 -> !cl_15 ] 0.00/0.07 Time: 0.009 [s] 0.00/0.07 0.00/0.07 Make it Complete (R^): 0.00/0.07 [ h(!cl_3,!cl_16) = h(b,b), 0.00/0.07 h(!cl_8,!cl_15) = h(c,!cl_15), 0.00/0.07 h(!cl_8,!cl_15) = !cl_16, 0.00/0.07 h(c,!cl_15) = !cl_16, 0.00/0.07 f(!cl_13) = !cl_14, 0.00/0.07 f(!cl_10) = !cl_12, 0.00/0.07 h(!cl_6,c) = h(!cl_6,!cl_8), 0.00/0.07 h(!cl_6,c) = !cl_10, 0.00/0.07 h(!cl_6,!cl_8) = !cl_10, 0.00/0.07 c = f(c), 0.00/0.07 c = f(!cl_8), 0.00/0.07 f(!cl_8) = f(c), 0.00/0.07 f(!cl_8) = !cl_8, 0.00/0.07 f(c) = !cl_8, 0.00/0.07 f(!cl_4) = !cl_6, 0.00/0.07 h(!cl_8,!cl_2) = h(c,!cl_2), 0.00/0.07 h(!cl_8,!cl_2) = !cl_4, 0.00/0.07 h(c,!cl_2) = !cl_4, 0.00/0.07 h(a,!cr_3) = h(a,!cl_0), 0.00/0.07 h(a,!cr_3) = !cl_2, 0.00/0.07 h(a,!cl_0) = !cl_2, 0.00/0.07 a = f(!cr_13), 0.00/0.07 h(!cl_8,!cr_12) = h(c,!cr_12), 0.00/0.07 h(!cl_8,!cr_12) = !cr_13, 0.00/0.07 !cr_13 = h(c,!cr_12), 0.00/0.07 h(!cr_11,!cl_8) = h(!cr_11,c), 0.00/0.07 h(!cr_11,!cl_8) = !cr_12, 0.00/0.07 !cr_12 = h(!cr_11,c), 0.00/0.07 !cr_11 = h(!cr_10,b), 0.00/0.07 !cr_10 = h(!cr_2,!cr_9), 0.00/0.07 !cr_9 = h(!cr_8,a), 0.00/0.07 !cr_8 = h(!cr_5,!cr_7), 0.00/0.07 h(!cl_1,a) = h(!cr_6,a), 0.00/0.07 h(!cl_1,a) = !cr_7, 0.00/0.07 !cr_7 = h(!cr_6,a), 0.00/0.07 f(!cr_6) = f(!cl_1), 0.00/0.07 f(!cr_6) = !cl_3, 0.00/0.07 !cr_6 = !cl_1, 0.00/0.07 !cr_6 = f(b), 0.00/0.07 h(!cr_4,!cl_8) = h(!cr_4,c), 0.00/0.07 h(!cr_4,!cl_8) = !cr_5, 0.00/0.07 !cr_5 = h(!cr_4,c), 0.00/0.07 f(!cl_0) = f(!cr_3), 0.00/0.07 f(!cl_0) = !cr_4, 0.00/0.07 !cr_4 = f(!cr_3), 0.00/0.07 h(!cl_14,!cr_3) = h(!cl_14,!cl_0), 0.00/0.07 h(!cl_14,!cr_3) = !cl_15, 0.00/0.07 h(!cr_3,c) = !cl_9, 0.00/0.07 h(!cr_3,!cl_8) = !cl_9, 0.00/0.07 h(!cr_3,c) = h(!cl_0,!cl_8), 0.00/0.07 h(!cl_0,!cl_8) = h(!cr_3,!cl_8), 0.00/0.07 h(!cr_3,c) = h(!cr_3,!cl_8), 0.00/0.07 h(!cr_3,c) = h(!cl_0,c), 0.00/0.07 h(!cr_3,!cl_8) = h(!cl_0,c), 0.00/0.07 !cr_3 = !cl_0, 0.00/0.07 !cr_3 = f(a), 0.00/0.07 !cr_2 = h(!cr_1,a), 0.00/0.07 !cr_1 = f(!cr_0), 0.00/0.07 !cr_0 = h(a,b), 0.00/0.07 f(a) = !cl_0, 0.00/0.07 f(b) = !cl_1, 0.00/0.07 f(!cl_1) = !cl_3, 0.00/0.07 h(c,!cl_8) = !cl_5, 0.00/0.07 h(!cl_8,!cl_8) = !cl_5, 0.00/0.07 h(c,!cl_8) = h(!cl_8,c), 0.00/0.07 h(c,!cl_8) = h(!cl_8,!cl_8), 0.00/0.07 h(!cl_8,c) = h(!cl_8,!cl_8), 0.00/0.07 h(c,!cl_8) = h(c,c), 0.00/0.07 h(!cl_8,!cl_8) = h(c,c), 0.00/0.07 h(!cl_8,c) = h(c,c), 0.00/0.07 h(!cl_8,c) = !cl_5, 0.00/0.07 h(c,c) = !cl_5, 0.00/0.07 h(b,!cl_5) = !cl_7, 0.00/0.07 h(!cl_0,!cl_8) = h(!cl_0,c), 0.00/0.07 h(!cl_0,!cl_8) = !cl_9, 0.00/0.07 h(!cl_0,c) = !cl_9, 0.00/0.07 h(!cl_7,!cl_9) = !cl_11, 0.00/0.07 f(!cl_11) = !cl_13, 0.00/0.07 f(!cl_12) = b, 0.00/0.07 !cl_8 = c, 0.00/0.07 h(!cl_14,!cl_0) = !cl_15 ] 0.00/0.07 Time: 0.015 [s] 0.00/0.07 0.00/0.07 CPNF: 0.00/0.07 [ !cl_1 … !cl_1, 0.00/0.07 !cl_3 … !cl_3, 0.00/0.07 !cl_5 … !cl_5, 0.00/0.07 !cl_7 … !cl_7, 0.00/0.07 b … b, 0.00/0.07 !cl_8 … c ] 0.00/0.07 Time: 0.000 [s] 0.00/0.07 0.00/0.07 Now checking all the pairs in CW... 0.00/0.07 0.00/0.07 Time to check pairs: 0.000 [s] 0.00/0.07 0.00/0.07 The TRS has Uniqueness of Normal Forms. 0.00/0.07 Total Time: 0.028 [s] 0.00/0.07 0.00/0.07 /export/starexec/sandbox/benchmark/theBenchmark.trs: Success(UNC) 0.00/0.07 (28 msec.) 0.00/0.07 EOF