NO

The TRS could be proven non-terminating. The proof took 60016 ms.

The following reduction sequence is a witness for non-termination:

isList# →* isList#

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (196ms).
 | – Problem 2 was processed with processor SubtermCriterion (1ms).
 | – Problem 3 was processed with processor ForwardNarrowing (2ms).
 |    | – Problem 5 was processed with processor ForwardNarrowing (4ms).
 |    |    | – Problem 7 was processed with processor ForwardNarrowing (5ms).
 |    |    |    | – Problem 8 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    | – Problem 9 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (8ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 was processed with processor ForwardNarrowing (10ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 28 was processed with processor ForwardNarrowing (41ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 29 was processed with processor ForwardNarrowing (15ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 30 was processed with processor ForwardNarrowing (17ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 31 was processed with processor ForwardNarrowing (23ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 32 was processed with processor ForwardNarrowing (24ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 33 was processed with processor ForwardNarrowing (66ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 34 was processed with processor ForwardNarrowing (24ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 35 was processed with processor ForwardNarrowing (54ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 36 was processed with processor ForwardNarrowing (101ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 37 was processed with processor ForwardNarrowing (43ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 38 was processed with processor ForwardNarrowing (74ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 39 was processed with processor ForwardNarrowing (58ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 40 was processed with processor ForwardNarrowing (52ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 41 was processed with processor ForwardNarrowing (51ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 42 was processed with processor ForwardNarrowing (45ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 43 was processed with processor ForwardNarrowing (62ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 44 was processed with processor ForwardNarrowing (66ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 45 remains open; application of the following processors failed [ForwardNarrowing (51ms), ForwardNarrowing (156ms), ForwardNarrowing (52ms), ForwardNarrowing (62ms), ForwardNarrowing (61ms), ForwardNarrowing (193ms), ForwardNarrowing (60ms), ForwardNarrowing (52ms), ForwardNarrowing (53ms), ForwardNarrowing (62ms), ForwardNarrowing (166ms), ForwardNarrowing (60ms), ForwardNarrowing (60ms), ForwardNarrowing (68ms), ForwardNarrowing (182ms), ForwardNarrowing (65ms), ForwardNarrowing (55ms), ForwardNarrowing (40ms), ForwardNarrowing (57ms), ForwardNarrowing (207ms), ForwardNarrowing (81ms), ForwardNarrowing (66ms), ForwardNarrowing (64ms), ForwardNarrowing (58ms), ForwardNarrowing (178ms), ForwardNarrowing (65ms), ForwardNarrowing (54ms), ForwardNarrowing (timeout)].
 | – Problem 4 was processed with processor ForwardNarrowing (2ms).
 |    | – Problem 6 remains open; application of the following processors failed [ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (2ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (3ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (32ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (34ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (4ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (3ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (4ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (3ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (3ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (4ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (3ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (3ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (3ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (3ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (3ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (3ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (46ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (4ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (43ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (61ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (37ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (3ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (4ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (4ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (4ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (6ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (6ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (6ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms)].

Problem 1: DependencyGraph



Dependency Pair Problem

Dependency Pairs

isList#isList#isList#isNeList#
isNeList#U51#(isNeList)__#(__(X, Y), Z)__#(Y, Z)
isNeList#isNeList#U51#(tt)U52#(isList)
isNeList#isList#isPal#isNePal#
isNePal#U61#(isQid)U21#(tt)U22#(isList)
U71#(tt)U72#(isPal)isNeList#U31#(isQid)
U41#(tt)U42#(isNeList)__#(__(X, Y), Z)__#(X, __(Y, Z))
U41#(tt)isNeList#U21#(tt)isList#
isList#U21#(isList)isNeList#isQid#
U51#(tt)isList#isNePal#isQid#
isNeList#U41#(isList)isList#U11#(isNeList)
U71#(tt)isPal#isNePal#U71#(isQid)
isPal#U81#(isNePal)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The following SCCs where found

U51#(tt) → isList#isList# → isList#
U41#(tt) → isNeList#isNeList# → isList#
isNeList#U41#(isList)U21#(tt) → isList#
isList# → isNeList#isList#U21#(isList)
isNeList#U51#(isNeList)isNeList# → isNeList#

isPal# → isNePal#U71#(tt) → isPal#
isNePal#U71#(isQid)

__#(__(X, Y), Z) → __#(X, __(Y, Z))__#(__(X, Y), Z) → __#(Y, Z)

Problem 2: SubtermCriterion



Dependency Pair Problem

Dependency Pairs

__#(__(X, Y), Z)__#(X, __(Y, Z))__#(__(X, Y), Z)__#(Y, Z)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


Projection

The following projection was used:

Thus, the following dependency pairs are removed:

__#(__(X, Y), Z)__#(X, __(Y, Z))__#(__(X, Y), Z)__#(Y, Z)

Problem 3: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U51#(tt)isList#isList#isList#
U41#(tt)isNeList#isNeList#isList#
isNeList#U41#(isList)U21#(tt)isList#
isList#isNeList#isList#U21#(isList)
isNeList#U51#(isNeList)isNeList#isNeList#

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U41#(isList) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U41#(U11(isNeList)) 
U41#(U21(isList)) 
U41#(tt) 
Thus, the rule isNeList#U41#(isList) is replaced by the following rules:
isNeList#U41#(U11(isNeList))isNeList#U41#(tt)
isNeList#U41#(U21(isList))

Problem 5: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U51#(tt)isList#isList#isList#
U41#(tt)isNeList#isNeList#isList#
isNeList#U41#(U11(isNeList))U21#(tt)isList#
isList#U21#(isList)isList#isNeList#
isNeList#U41#(tt)isNeList#U41#(U21(isList))
isNeList#U51#(isNeList)isNeList#isNeList#

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U81, U52, U11, isQid, U31, U21, nil, U22

Strategy


The right-hand side of the rule isNeList#U41#(U11(isNeList)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U41#(U11(U31(isQid))) 
U41#(U11(U51(isNeList))) 
U41#(U11(U41(isList))) 
Thus, the rule isNeList#U41#(U11(isNeList)) is replaced by the following rules:
isNeList#U41#(U11(U31(isQid)))isNeList#U41#(U11(U41(isList)))
isNeList#U41#(U11(U51(isNeList)))

Problem 7: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isList#isList#isNeList#U41#(U11(U31(isQid)))
U41#(tt)isNeList#U21#(tt)isList#
isList#isNeList#isList#U21#(isList)
isNeList#U41#(tt)isNeList#U41#(U21(isList))
isNeList#U51#(isNeList)isNeList#isNeList#
U51#(tt)isList#isNeList#isList#
isNeList#U41#(U11(U41(isList)))isNeList#U41#(U11(U51(isNeList)))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U41#(U11(U31(isQid))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U41#(U11(U31(tt))) 
Thus, the rule isNeList#U41#(U11(U31(isQid))) is replaced by the following rules:
isNeList#U41#(U11(U31(tt)))

Problem 8: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isNeList#U41#(U11(U31(tt)))isList#isList#
U41#(tt)isNeList#U21#(tt)isList#
isList#isNeList#isList#U21#(isList)
isNeList#U41#(tt)isNeList#U41#(U21(isList))
isNeList#U51#(isNeList)isNeList#isNeList#
U51#(tt)isList#isNeList#isList#
isNeList#U41#(U11(U41(isList)))isNeList#U41#(U11(U51(isNeList)))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U81, U52, U11, isQid, U31, U21, nil, U22

Strategy


The right-hand side of the rule isNeList#U41#(U11(U31(tt))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U41#(U11(tt)) 
Thus, the rule isNeList#U41#(U11(U31(tt))) is replaced by the following rules:
isNeList#U41#(U11(tt))

Problem 9: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isList#isList#U41#(tt)isNeList#
U21#(tt)isList#isList#isNeList#
isList#U21#(isList)isNeList#U41#(tt)
isNeList#U41#(U21(isList))isNeList#U51#(isNeList)
isNeList#isNeList#U51#(tt)isList#
isNeList#U41#(U11(tt))isNeList#isList#
isNeList#U41#(U11(U41(isList)))isNeList#U41#(U11(U51(isNeList)))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isList#U21#(isList) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U21#(U21(isList)) 
U21#(U11(isNeList)) 
U21#(tt) 
Thus, the rule isList#U21#(isList) is replaced by the following rules:
isList#U21#(U21(isList))isList#U21#(U11(isNeList))
isList#U21#(tt)

Problem 10: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isList#isList#U41#(tt)isNeList#
U21#(tt)isList#isList#isNeList#
isList#U21#(U21(isList))isNeList#U41#(tt)
isNeList#U41#(U21(isList))isNeList#U51#(isNeList)
isNeList#isNeList#isList#U21#(U11(isNeList))
U51#(tt)isList#isNeList#U41#(U11(tt))
isNeList#isList#isNeList#U41#(U11(U41(isList)))
isNeList#U41#(U11(U51(isNeList)))isList#U21#(tt)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U81, U52, U11, isQid, U31, U21, nil, U22

Strategy


The right-hand side of the rule isList#U21#(U21(isList)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U21#(U21(U21(isList))) 
U21#(U21(U11(isNeList))) 
U21#(U21(tt)) 
Thus, the rule isList#U21#(U21(isList)) is replaced by the following rules:
isList#U21#(U21(U11(isNeList)))isList#U21#(U21(tt))
isList#U21#(U21(U21(isList)))

Problem 11: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isList#isList#U41#(tt)isNeList#
U21#(tt)isList#isList#isNeList#
isNeList#U41#(tt)isNeList#U41#(U21(isList))
isNeList#U51#(isNeList)isNeList#isNeList#
isList#U21#(U11(isNeList))U51#(tt)isList#
isNeList#U41#(U11(tt))isList#U21#(U21(U11(isNeList)))
isNeList#isList#isList#U21#(U21(tt))
isNeList#U41#(U11(U41(isList)))isList#U21#(U21(U21(isList)))
isNeList#U41#(U11(U51(isNeList)))isList#U21#(tt)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U41#(U21(isList)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U41#(U21(U11(isNeList))) 
U41#(U21(U21(isList))) 
U41#(U21(tt)) 
Thus, the rule isNeList#U41#(U21(isList)) is replaced by the following rules:
isNeList#U41#(U21(tt))isNeList#U41#(U21(U21(isList)))
isNeList#U41#(U21(U11(isNeList)))

Problem 12: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isList#isList#U41#(tt)isNeList#
U21#(tt)isList#isList#isNeList#
isNeList#U41#(tt)isNeList#U51#(isNeList)
isNeList#isNeList#isList#U21#(U11(isNeList))
U51#(tt)isList#isNeList#U41#(U11(tt))
isList#U21#(U21(U11(isNeList)))isList#U21#(U21(tt))
isNeList#U41#(U21(tt))isNeList#isList#
isNeList#U41#(U11(U41(isList)))isList#U21#(U21(U21(isList)))
isNeList#U41#(U21(U21(isList)))isNeList#U41#(U11(U51(isNeList)))
isNeList#U41#(U21(U11(isNeList)))isList#U21#(tt)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U81, U52, U11, isQid, U31, U21, nil, U22

Strategy


The right-hand side of the rule isNeList#U51#(isNeList) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(U31(isQid)) 
U51#(U51(isNeList)) 
U51#(U41(isList)) 
Thus, the rule isNeList#U51#(isNeList) is replaced by the following rules:
isNeList#U51#(U51(isNeList))isNeList#U51#(U31(isQid))
isNeList#U51#(U41(isList))

Problem 13: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isList#isList#U41#(tt)isNeList#
isNeList#U51#(U31(isQid))U21#(tt)isList#
isList#isNeList#isNeList#U51#(U41(isList))
isNeList#U41#(tt)isNeList#isNeList#
isList#U21#(U11(isNeList))U51#(tt)isList#
isNeList#U41#(U11(tt))isList#U21#(U21(U11(isNeList)))
isNeList#isList#isNeList#U41#(U21(tt))
isList#U21#(U21(tt))isNeList#U41#(U11(U41(isList)))
isNeList#U51#(U51(isNeList))isList#U21#(U21(U21(isList)))
isNeList#U41#(U21(U21(isList)))isNeList#U41#(U21(U11(isNeList)))
isNeList#U41#(U11(U51(isNeList)))isList#U21#(tt)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U51#(U31(isQid)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(U31(tt)) 
Thus, the rule isNeList#U51#(U31(isQid)) is replaced by the following rules:
isNeList#U51#(U31(tt))

Problem 14: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isList#isList#U41#(tt)isNeList#
U21#(tt)isList#isList#isNeList#
isNeList#U51#(U41(isList))isNeList#U41#(tt)
isNeList#U51#(U31(tt))isNeList#isNeList#
isList#U21#(U11(isNeList))U51#(tt)isList#
isNeList#U41#(U11(tt))isList#U21#(U21(U11(isNeList)))
isList#U21#(U21(tt))isNeList#U41#(U21(tt))
isNeList#isList#isNeList#U51#(U51(isNeList))
isNeList#U41#(U11(U41(isList)))isList#U21#(U21(U21(isList)))
isNeList#U41#(U21(U21(isList)))isNeList#U41#(U11(U51(isNeList)))
isNeList#U41#(U21(U11(isNeList)))isList#U21#(tt)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U81, U52, U11, isQid, U31, U21, nil, U22

Strategy


The right-hand side of the rule isNeList#U51#(U41(isList)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(U41(tt)) 
U51#(U41(U21(isList))) 
U51#(U41(U11(isNeList))) 
Thus, the rule isNeList#U51#(U41(isList)) is replaced by the following rules:
isNeList#U51#(U41(tt))isNeList#U51#(U41(U11(isNeList)))
isNeList#U51#(U41(U21(isList)))

Problem 15: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isNeList#U51#(U41(tt))isList#isList#
U41#(tt)isNeList#U21#(tt)isList#
isList#isNeList#isNeList#U41#(tt)
isNeList#U51#(U41(U11(isNeList)))isNeList#U51#(U31(tt))
isNeList#U51#(U41(U21(isList)))isNeList#isNeList#
isList#U21#(U11(isNeList))U51#(tt)isList#
isNeList#U41#(U11(tt))isList#U21#(U21(U11(isNeList)))
isNeList#isList#isNeList#U41#(U21(tt))
isList#U21#(U21(tt))isNeList#U41#(U11(U41(isList)))
isNeList#U51#(U51(isNeList))isList#U21#(U21(U21(isList)))
isNeList#U41#(U21(U21(isList)))isNeList#U41#(U21(U11(isNeList)))
isNeList#U41#(U11(U51(isNeList)))isList#U21#(tt)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U51#(U41(tt)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(U42(isNeList)) 
Thus, the rule isNeList#U51#(U41(tt)) is replaced by the following rules:
isNeList#U51#(U42(isNeList))

Problem 16: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isList#isList#U41#(tt)isNeList#
U21#(tt)isList#isList#isNeList#
isNeList#U41#(tt)isNeList#U51#(U41(U11(isNeList)))
isNeList#U51#(U31(tt))isNeList#U51#(U41(U21(isList)))
isNeList#isNeList#isList#U21#(U11(isNeList))
U51#(tt)isList#isNeList#U41#(U11(tt))
isNeList#U51#(U42(isNeList))isList#U21#(U21(U11(isNeList)))
isList#U21#(U21(tt))isNeList#U41#(U21(tt))
isNeList#isList#isNeList#U51#(U51(isNeList))
isNeList#U41#(U11(U41(isList)))isList#U21#(U21(U21(isList)))
isNeList#U41#(U21(U21(isList)))isNeList#U41#(U11(U51(isNeList)))
isNeList#U41#(U21(U11(isNeList)))isList#U21#(tt)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U81, U52, U11, isQid, U31, U21, nil, U22

Strategy


The right-hand side of the rule isNeList#U51#(U41(U11(isNeList))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(U41(U11(U31(isQid)))) 
U51#(U41(U11(U41(isList)))) 
U51#(U41(U11(U51(isNeList)))) 
Thus, the rule isNeList#U51#(U41(U11(isNeList))) is replaced by the following rules:
isNeList#U51#(U41(U11(U41(isList))))isNeList#U51#(U41(U11(U31(isQid))))
isNeList#U51#(U41(U11(U51(isNeList))))

Problem 17: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isNeList#U51#(U41(U11(U41(isList))))isList#isList#
isList#isNeList#isNeList#U51#(U31(tt))
isNeList#isNeList#isList#U21#(U11(isNeList))
isNeList#U51#(U41(U11(U31(isQid))))isList#U21#(U21(U11(isNeList)))
isNeList#U41#(U21(tt))isNeList#isList#
isNeList#U51#(U51(isNeList))isNeList#U41#(U11(U41(isList)))
isNeList#U51#(U41(U11(U51(isNeList))))isNeList#U41#(U21(U11(isNeList)))
isNeList#U41#(U11(U51(isNeList)))U41#(tt)isNeList#
U21#(tt)isList#isNeList#U41#(tt)
isNeList#U51#(U41(U21(isList)))U51#(tt)isList#
isNeList#U41#(U11(tt))isNeList#U51#(U42(isNeList))
isList#U21#(U21(tt))isList#U21#(U21(U21(isList)))
isNeList#U41#(U21(U21(isList)))isList#U21#(tt)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U51#(U41(U11(U41(isList)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(U41(U11(U41(U11(isNeList))))) 
U51#(U41(U11(U41(U21(isList))))) 
U51#(U41(U11(U41(tt)))) 
Thus, the rule isNeList#U51#(U41(U11(U41(isList)))) is replaced by the following rules:
isNeList#U51#(U41(U11(U41(U21(isList)))))isNeList#U51#(U41(U11(U41(tt))))
isNeList#U51#(U41(U11(U41(U11(isNeList)))))

Problem 18: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isList#isList#isNeList#U51#(U41(U11(U41(U21(isList)))))
isList#isNeList#isNeList#U51#(U31(tt))
isNeList#isNeList#isList#U21#(U11(isNeList))
isNeList#U51#(U41(U11(U41(tt))))isNeList#U51#(U41(U11(U31(isQid))))
isList#U21#(U21(U11(isNeList)))isNeList#isList#
isNeList#U41#(U21(tt))isNeList#U41#(U11(U41(isList)))
isNeList#U51#(U51(isNeList))isNeList#U51#(U41(U11(U51(isNeList))))
isNeList#U41#(U21(U11(isNeList)))isNeList#U41#(U11(U51(isNeList)))
U41#(tt)isNeList#U21#(tt)isList#
isNeList#U41#(tt)isNeList#U51#(U41(U21(isList)))
U51#(tt)isList#isNeList#U41#(U11(tt))
isNeList#U51#(U42(isNeList))isList#U21#(U21(tt))
isNeList#U51#(U41(U11(U41(U11(isNeList)))))isList#U21#(U21(U21(isList)))
isNeList#U41#(U21(U21(isList)))isList#U21#(tt)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U81, U52, U11, isQid, U31, U21, nil, U22

Strategy


The right-hand side of the rule isNeList#U51#(U41(U11(U41(U21(isList))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(U41(U11(U41(U21(tt))))) 
U51#(U41(U11(U41(U21(U21(isList)))))) 
U51#(U41(U11(U41(U21(U11(isNeList)))))) 
Thus, the rule isNeList#U51#(U41(U11(U41(U21(isList))))) is replaced by the following rules:
isNeList#U51#(U41(U11(U41(U21(U21(isList))))))isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))
isNeList#U51#(U41(U11(U41(U21(tt)))))

Problem 19: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isList#isList#isList#isNeList#
isNeList#U51#(U31(tt))isNeList#isNeList#
isList#U21#(U11(isNeList))isNeList#U51#(U41(U11(U41(U21(U21(isList))))))
isNeList#U51#(U41(U11(U41(tt))))isNeList#U51#(U41(U11(U31(isQid))))
isList#U21#(U21(U11(isNeList)))isNeList#U41#(U21(tt))
isNeList#isList#isNeList#U51#(U51(isNeList))
isNeList#U41#(U11(U41(isList)))isNeList#U51#(U41(U11(U51(isNeList))))
isNeList#U41#(U21(U11(isNeList)))isNeList#U41#(U11(U51(isNeList)))
isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))U41#(tt)isNeList#
U21#(tt)isList#isNeList#U41#(tt)
isNeList#U51#(U41(U21(isList)))U51#(tt)isList#
isNeList#U41#(U11(tt))isNeList#U51#(U42(isNeList))
isList#U21#(U21(tt))isNeList#U51#(U41(U11(U41(U11(isNeList)))))
isList#U21#(U21(U21(isList)))isNeList#U41#(U21(U21(isList)))
isNeList#U51#(U41(U11(U41(U21(tt)))))isList#U21#(tt)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U51#(U31(tt)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(tt) 
Thus, the rule isNeList#U51#(U31(tt)) is replaced by the following rules:
isNeList#U51#(tt)

Problem 20: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isList#isList#isList#isNeList#
isNeList#isNeList#isList#U21#(U11(isNeList))
isNeList#U51#(U41(U11(U41(U21(U21(isList))))))isNeList#U51#(U41(U11(U41(tt))))
isNeList#U51#(U41(U11(U31(isQid))))isList#U21#(U21(U11(isNeList)))
isNeList#isList#isNeList#U41#(U21(tt))
isNeList#U41#(U11(U41(isList)))isNeList#U51#(U51(isNeList))
isNeList#U51#(U41(U11(U51(isNeList))))isNeList#U41#(U21(U11(isNeList)))
isNeList#U41#(U11(U51(isNeList)))isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))
U41#(tt)isNeList#U21#(tt)isList#
isNeList#U41#(tt)isNeList#U51#(U41(U21(isList)))
isNeList#U51#(tt)U51#(tt)isList#
isNeList#U41#(U11(tt))isNeList#U51#(U42(isNeList))
isList#U21#(U21(tt))isNeList#U51#(U41(U11(U41(U11(isNeList)))))
isList#U21#(U21(U21(isList)))isNeList#U41#(U21(U21(isList)))
isNeList#U51#(U41(U11(U41(U21(tt)))))isList#U21#(tt)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U81, U52, U11, isQid, U31, U21, nil, U22

Strategy


The right-hand side of the rule isList#U21#(U11(isNeList)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U21#(U11(U41(isList))) 
U21#(U11(U51(isNeList))) 
U21#(U11(U31(isQid))) 
Thus, the rule isList#U21#(U11(isNeList)) is replaced by the following rules:
isList#U21#(U11(U41(isList)))isList#U21#(U11(U51(isNeList)))
isList#U21#(U11(U31(isQid)))

Problem 21: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isList#isList#isList#isNeList#
isNeList#isNeList#isList#U21#(U11(U31(isQid)))
isNeList#U51#(U41(U11(U41(U21(U21(isList))))))isNeList#U51#(U41(U11(U41(tt))))
isNeList#U51#(U41(U11(U31(isQid))))isList#U21#(U21(U11(isNeList)))
isNeList#U41#(U21(tt))isNeList#isList#
isNeList#U51#(U51(isNeList))isNeList#U41#(U11(U41(isList)))
isNeList#U51#(U41(U11(U51(isNeList))))isNeList#U41#(U21(U11(isNeList)))
isNeList#U41#(U11(U51(isNeList)))isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))
U41#(tt)isNeList#isList#U21#(U11(U41(isList)))
U21#(tt)isList#isNeList#U41#(tt)
isNeList#U51#(U41(U21(isList)))isNeList#U51#(tt)
U51#(tt)isList#isNeList#U41#(U11(tt))
isNeList#U51#(U42(isNeList))isList#U21#(U21(tt))
isNeList#U51#(U41(U11(U41(U11(isNeList)))))isList#U21#(U21(U21(isList)))
isNeList#U41#(U21(U21(isList)))isNeList#U51#(U41(U11(U41(U21(tt)))))
isList#U21#(U11(U51(isNeList)))isList#U21#(tt)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isList#U21#(U11(U31(isQid))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U21#(U11(U31(tt))) 
Thus, the rule isList#U21#(U11(U31(isQid))) is replaced by the following rules:
isList#U21#(U11(U31(tt)))

Problem 22: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isList#isList#isList#U21#(U11(U31(tt)))
isList#isNeList#isNeList#isNeList#
isNeList#U51#(U41(U11(U41(U21(U21(isList))))))isNeList#U51#(U41(U11(U41(tt))))
isNeList#U51#(U41(U11(U31(isQid))))isList#U21#(U21(U11(isNeList)))
isNeList#isList#isNeList#U41#(U21(tt))
isNeList#U41#(U11(U41(isList)))isNeList#U51#(U51(isNeList))
isNeList#U51#(U41(U11(U51(isNeList))))isNeList#U41#(U21(U11(isNeList)))
isNeList#U41#(U11(U51(isNeList)))isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))
U41#(tt)isNeList#isList#U21#(U11(U41(isList)))
U21#(tt)isList#isNeList#U41#(tt)
isNeList#U51#(U41(U21(isList)))isNeList#U51#(tt)
U51#(tt)isList#isNeList#U41#(U11(tt))
isNeList#U51#(U42(isNeList))isList#U21#(U21(tt))
isNeList#U51#(U41(U11(U41(U11(isNeList)))))isList#U21#(U21(U21(isList)))
isNeList#U41#(U21(U21(isList)))isNeList#U51#(U41(U11(U41(U21(tt)))))
isList#U21#(U11(U51(isNeList)))isList#U21#(tt)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U81, U52, U11, isQid, U31, U21, nil, U22

Strategy


The right-hand side of the rule isList#U21#(U11(U31(tt))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U21#(U11(tt)) 
Thus, the rule isList#U21#(U11(U31(tt))) is replaced by the following rules:
isList#U21#(U11(tt))

Problem 23: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isList#isList#isList#isNeList#
isNeList#isNeList#isNeList#U51#(U41(U11(U41(U21(U21(isList))))))
isNeList#U51#(U41(U11(U41(tt))))isNeList#U51#(U41(U11(U31(isQid))))
isList#U21#(U21(U11(isNeList)))isNeList#U41#(U21(tt))
isNeList#isList#isNeList#U51#(U51(isNeList))
isNeList#U41#(U11(U41(isList)))isNeList#U41#(U21(U11(isNeList)))
isNeList#U51#(U41(U11(U51(isNeList))))isNeList#U41#(U11(U51(isNeList)))
isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))U41#(tt)isNeList#
isList#U21#(U11(U41(isList)))U21#(tt)isList#
isNeList#U41#(tt)isNeList#U51#(U41(U21(isList)))
isNeList#U51#(tt)U51#(tt)isList#
isNeList#U41#(U11(tt))isList#U21#(U11(tt))
isNeList#U51#(U42(isNeList))isList#U21#(U21(tt))
isNeList#U51#(U41(U11(U41(U11(isNeList)))))isList#U21#(U21(U21(isList)))
isNeList#U41#(U21(U21(isList)))isNeList#U51#(U41(U11(U41(U21(tt)))))
isList#U21#(U11(U51(isNeList)))isList#U21#(tt)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U51#(U41(U11(U41(U21(U21(isList)))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(U41(U11(U41(U21(U21(U21(isList))))))) 
U51#(U41(U11(U41(U21(U21(U11(isNeList))))))) 
U51#(U41(U11(U41(U21(U21(tt)))))) 
Thus, the rule isNeList#U51#(U41(U11(U41(U21(U21(isList)))))) is replaced by the following rules:
isNeList#U51#(U41(U11(U41(U21(U21(U21(isList)))))))isNeList#U51#(U41(U11(U41(U21(U21(U11(isNeList)))))))
isNeList#U51#(U41(U11(U41(U21(U21(tt))))))

Problem 24: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isList#isList#isList#isNeList#
isNeList#isNeList#isNeList#U51#(U41(U11(U41(U21(U21(tt))))))
isNeList#U51#(U41(U11(U41(tt))))isNeList#U51#(U41(U11(U31(isQid))))
isList#U21#(U21(U11(isNeList)))isNeList#isList#
isNeList#U41#(U21(tt))isNeList#U41#(U11(U41(isList)))
isNeList#U51#(U51(isNeList))isNeList#U51#(U41(U11(U51(isNeList))))
isNeList#U41#(U21(U11(isNeList)))isNeList#U41#(U11(U51(isNeList)))
isNeList#U51#(U41(U11(U41(U21(U21(U11(isNeList)))))))isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))
U41#(tt)isNeList#isList#U21#(U11(U41(isList)))
U21#(tt)isList#isNeList#U41#(tt)
isNeList#U51#(U41(U21(isList)))isNeList#U51#(tt)
U51#(tt)isList#isNeList#U41#(U11(tt))
isNeList#U51#(U42(isNeList))isList#U21#(U11(tt))
isNeList#U51#(U41(U11(U41(U21(U21(U21(isList)))))))isList#U21#(U21(tt))
isNeList#U51#(U41(U11(U41(U11(isNeList)))))isList#U21#(U21(U21(isList)))
isNeList#U41#(U21(U21(isList)))isNeList#U51#(U41(U11(U41(U21(tt)))))
isList#U21#(U11(U51(isNeList)))isList#U21#(tt)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U81, U52, U11, isQid, U31, U21, nil, U22

Strategy


The right-hand side of the rule isNeList#U51#(U41(U11(U41(U21(U21(tt)))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(U41(U11(U41(U21(U22(isList)))))) 
Thus, the rule isNeList#U51#(U41(U11(U41(U21(U21(tt)))))) is replaced by the following rules:
isNeList#U51#(U41(U11(U41(U21(U22(isList))))))

Problem 25: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isNeList#U51#(U51(U31(isQid)))isNeList#U41#(U22(U11(isNeList)))
U41#(tt)isNeList#isNeList#U51#(U41(U11(tt)))
isList#U21#(U11(U41(isList)))U21#(tt)isList#
isNeList#U41#(tt)isNeList#U51#(U41(U21(isList)))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(isNeList))))))))isNeList#U51#(tt)
isNeList#U41#(U11(U41(U21(U11(U51(U31(isQid)))))))isNeList#U41#(U11(U41(tt)))
isList#U21#(U11(tt))isNeList#U41#(U22(U21(U11(U41(isList)))))
isList#U21#(U21(U11(U51(U41(isList)))))isNeList#U51#(U41(U11(U41(U11(isNeList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U31(isQid)))))))isList#U21#(U21(U21(isList)))
isNeList#U41#(U11(U41(U21(U21(U11(U41(tt)))))))isNeList#U41#(U22(U21(tt)))
isNeList#U41#(U21(U11(U51(isNeList))))isNeList#U41#(U11(U41(U21(U21(tt)))))
isNeList#U41#(U11(U41(U11(isNeList))))isList#isList#
isNeList#U41#(U11(U41(U21(tt))))isNeList#U41#(U11(U41(U21(U11(U51(U41(U21(isList))))))))
isNeList#U41#(U21(U11(U41(isList))))isNeList#U41#(U22(U21(U21(isList))))
isList#isNeList#isNeList#U41#(U11(U41(U21(U11(U51(U42(isNeList)))))))
isNeList#isNeList#isNeList#U41#(U21(U11(U31(isQid))))
isNeList#isList#isNeList#U41#(U11(U41(U21(U21(U11(U41(U21(isList))))))))
isNeList#U51#(U51(U51(isNeList)))isList#U21#(U21(U11(U41(U11(U41(U22(U11(isNeList))))))))
isList#U21#(U21(U11(U41(U21(isList)))))isList#U21#(U21(U11(U41(U11(U41(tt))))))
isNeList#U51#(U41(U11(U51(isNeList))))isList#U21#(U21(U11(U51(tt))))
isList#U21#(U21(U11(U51(U51(isNeList)))))isNeList#U41#(U11(U51(isNeList)))
isNeList#U41#(U22(U21(U11(U51(isNeList)))))isNeList#U41#(U11(U41(U21(U21(U11(U51(isNeList)))))))
isNeList#U41#(U22(U21(U11(U31(isQid)))))isNeList#U41#(U11(U41(U21(U11(U41(isList))))))
isNeList#U51#(U41(U11(U42(isNeList))))isNeList#U51#(U41(U11(U41(U21(U22(isList))))))
isNeList#U51#(U41(U11(U41(U21(U21(U11(isNeList)))))))isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))
isNeList#U41#(U11(U41(U21(U21(U21(isList))))))isList#U21#(U21(U11(U41(tt))))
isList#U21#(U21(U11(U41(U11(U41(U11(isNeList)))))))isList#U21#(U21(U11(U41(U11(U31(isQid))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U21(isList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U41(U11(isNeList))))))))
U51#(tt)isList#isNeList#U41#(U11(tt))
isNeList#U51#(U51(U41(isList)))isNeList#U51#(U42(isNeList))
isNeList#U51#(U41(U11(U41(U21(U21(U21(isList)))))))isList#U21#(U21(U11(U41(U11(U51(isNeList))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(isNeList)))))))isList#U21#(U21(U11(U31(isQid))))
isList#U21#(U21(tt))isNeList#U41#(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))
isNeList#U41#(U11(U41(U21(U11(U31(tt))))))isList#U21#(U21(U11(U41(U11(U41(U22(U21(isList))))))))
isNeList#U41#(U21(U21(isList)))isNeList#U51#(U41(U11(U41(U21(tt)))))
isList#U21#(U11(U51(isNeList)))isList#U21#(tt)
isNeList#U41#(U22(tt))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U51#(U51(U31(isQid))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(U51(U31(tt))) 
Thus, the rule isNeList#U51#(U51(U31(isQid))) is replaced by the following rules:
isNeList#U51#(U51(U31(tt)))

Problem 26: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(isList))))))))U21#(tt)isList#
isNeList#U51#(U41(U21(U11(U51(U51(U51(U31(isQid))))))))isNeList#U41#(U11(U41(U21(U21(tt)))))
isNeList#U51#(U41(U21(U11(U41(tt)))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(isNeList)))))))))
isNeList#U41#(U11(U41(U21(tt))))isNeList#U51#(U41(U21(U11(U51(tt)))))
isNeList#U41#(U22(U21(U21(isList))))isNeList#U51#(U41(U21(U11(U41(U11(isNeList))))))
isList#isNeList#isNeList#U41#(U11(U41(U21(U11(U51(U42(isNeList)))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(isNeList))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(isNeList))))))))
isNeList#U41#(U22(U21(U11(U41(U22(isList))))))isNeList#isNeList#
isNeList#U41#(U22(U21(U11(U41(U21(U21(isList)))))))isNeList#U51#(U41(U21(U11(U31(tt)))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(isNeList)))))))isNeList#isList#
isNeList#U41#(U21(U11(U31(isQid))))isNeList#U51#(U41(U11(U41(U11(U31(isQid))))))
isList#U21#(U21(U11(U41(U21(isList)))))isNeList#U41#(U22(U11(U41(isList))))
isList#U21#(U21(U21(U21(tt))))isNeList#U41#(U11(U51(isNeList)))
isList#U21#(U21(U11(U51(U51(isNeList)))))isNeList#U41#(U22(U21(U11(U51(isNeList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(isNeList)))))))isNeList#U51#(U41(U11(U41(U21(U21(U11(isNeList)))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U51(isNeList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(isNeList)))))))))))
isList#U21#(U21(U21(U21(U11(isNeList)))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U41(isList)))))))))
isNeList#U41#(U11(U41(U21(U21(U21(isList))))))isList#U21#(U21(U11(U41(tt))))
isList#U21#(U21(U11(U41(U11(U41(U11(isNeList)))))))isNeList#U51#(U41(U11(U41(U11(U51(isNeList))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(isNeList)))))))isList#U21#(U21(U11(U41(U11(U41(U21(U21(isList))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(U21(isList))))))))U51#(tt)isList#
isNeList#U51#(U42(isNeList))isNeList#U51#(U51(U41(isList)))
isNeList#U41#(U11(U41(U21(U11(U51(U51(isNeList)))))))isNeList#U51#(U41(U11(U41(U21(U21(U21(isList)))))))
isNeList#U51#(U41(U21(U11(U51(U41(isList))))))isNeList#U41#(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U31(isQid))))))))isNeList#U41#(U21(U21(isList)))
isList#U21#(U21(U21(tt)))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(isList)))))))))))
isList#U21#(tt)isNeList#U51#(U41(U21(U11(U41(U21(tt))))))
isNeList#U41#(U22(U22(isList)))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(tt)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(isNeList)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(tt)))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(tt)))))))))U41#(tt)isNeList#
isNeList#U41#(U11(U41(U21(U21(U11(U42(U51(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U11(U41(U11(isNeList))))))))
isNeList#U41#(tt)isNeList#U51#(tt)
isList#U21#(U21(U11(U51(U41(isList)))))isNeList#U41#(U11(U41(U21(U21(U11(U31(isQid)))))))
isNeList#U41#(U21(U11(U51(isNeList))))isNeList#U41#(U22(U11(U51(isNeList))))
isList#U21#(U21(U21(U11(isNeList))))isNeList#U51#(U41(U21(U11(U41(U21(U21(isList)))))))
isNeList#U41#(U11(U41(U11(isNeList))))isList#isList#
isNeList#U41#(U11(U41(U21(U11(U51(U41(U21(isList))))))))isNeList#U41#(U21(U11(U41(isList))))
isNeList#U41#(U22(U21(U11(U41(tt)))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U21(isList))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U31(isQid)))))))isList#U21#(U11(U41(U11(isNeList))))
isNeList#U51#(U41(U21(U21(isList))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(isList)))))))))
isNeList#U51#(U41(U11(U41(U11(U41(isList))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(isList))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(isList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U41(U21(isList))))))))
isNeList#U51#(U51(U51(isNeList)))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(tt))))))))
isList#U21#(U21(U11(U41(U11(U41(U22(U11(isNeList))))))))isList#U21#(U21(U11(U41(U11(U41(tt))))))
isList#U21#(U11(U41(U21(isList))))isNeList#U51#(U41(U11(U51(isNeList))))
isList#U21#(U21(U11(U51(tt))))isNeList#U41#(U22(U21(U11(U31(isQid)))))
isNeList#U51#(U41(tt))isNeList#U41#(U11(U41(U21(U11(U41(isList))))))
isNeList#U51#(U41(U11(U42(isNeList))))isNeList#U41#(U22(U21(U11(U41(U11(U41(tt)))))))
isNeList#U51#(U51(tt))isNeList#U51#(U41(U11(U41(U21(U22(isList))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(tt))))))))isNeList#U41#(U11(U42(isNeList)))
isNeList#U41#(U11(U41(U21(U11(U51(U31(tt)))))))isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U11(isNeList))))))))))))isList#U21#(U11(U41(tt)))
isList#U21#(U21(U11(U41(U11(U31(isQid))))))isList#U21#(U21(U21(U21(U21(isList)))))
isNeList#U41#(U22(U11(U31(isQid))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(tt)))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U41(U11(isNeList))))))))
isNeList#U41#(U11(tt))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U31(tt)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U31(isQid)))))))))))isList#U21#(U21(U11(U41(U11(U51(isNeList))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(tt))))))))))isList#U21#(U21(U11(U31(isQid))))
isList#U21#(U21(tt))isNeList#U41#(U11(U41(U21(U11(U31(tt))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U21(isList)))))))))isNeList#U51#(U41(U21(U11(U51(U51(U41(isList)))))))
isList#U21#(U21(U11(U41(U11(U41(U22(U21(isList))))))))isNeList#U51#(U41(U11(U41(U21(tt)))))
isList#U21#(U11(U51(isNeList)))isNeList#U41#(U22(tt))
isNeList#U51#(U41(U21(tt)))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(isList)))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(U41(U21(U11(U41(U21(U11(U41(U21(isList))))))))) 
U51#(U41(U21(U11(U41(U21(U11(U41(tt)))))))) 
U51#(U41(U21(U11(U41(U21(U11(U41(U11(isNeList))))))))) 
Thus, the rule isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(isList)))))))) is replaced by the following rules:
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U21(isList)))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(tt))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(isNeList)))))))))

Problem 27: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isNeList#U41#(U11(U51(U41(U11(isNeList)))))
isList#isNeList#isNeList#isNeList#
isNeList#isList#isNeList#U41#(U22(U21(U11(U51(isNeList)))))
isNeList#U41#(U11(U51(U41(tt))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(isNeList)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(isNeList)))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U11(isNeList)))))))))))
isNeList#U51#(U41(U21(U11(U52(isList)))))isNeList#U51#(U41(U11(U41(U21(U21(U11(isNeList)))))))
isList#U21#(U21(U11(U41(U21(tt)))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U51(isNeList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(isNeList)))))))))))isList#U21#(U21(U11(U51(U51(U31(isQid))))))
isList#U21#(U21(U21(U21(U11(isNeList)))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U41(isList)))))))))
isNeList#U41#(U11(U41(U21(U21(U21(isList))))))isList#U21#(U21(U11(U41(tt))))
isList#U21#(U21(U11(U41(U11(U41(U11(isNeList)))))))isNeList#U51#(U41(U11(U41(U11(U51(isNeList))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(isNeList)))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(tt))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U41(tt)))))))))))isList#U21#(U21(U11(U41(U21(U11(isNeList))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(tt))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U21(isList))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(U21(isList))))))))U51#(tt)isList#
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(isNeList)))))))))))isNeList#U51#(U42(isNeList))
isNeList#U51#(U51(U41(isList)))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(isNeList)))))))isNeList#U51#(U41(U11(U41(U21(U21(U21(isList)))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(tt)))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U21(isList)))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U21(isList))))))))isNeList#U51#(U41(U21(U11(U51(U41(isList))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U31(tt)))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U31(isQid))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))isList#U21#(U21(U11(U51(U51(U41(isList))))))
isNeList#U41#(U22(U21(U11(U41(U21(U22(isList)))))))isNeList#U41#(U21(U21(isList)))
isList#U21#(U21(U21(tt)))isNeList#U41#(U22(U11(U41(U11(isNeList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(isList)))))))))))isNeList#U41#(U11(U51(U31(isQid))))
isList#U21#(tt)isList#U21#(U21(U11(U51(U51(U51(U41(isList)))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U41(U11(isNeList))))))))))))isNeList#U51#(U41(U21(U11(U42(U41(isList))))))
isNeList#U51#(U41(U21(U11(U41(U21(tt))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(isNeList)))))))))
isNeList#U41#(U22(U11(U41(U21(isList)))))isList#U21#(U21(U11(U41(U21(U21(isList))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U51(isNeList)))))))))))isNeList#U41#(U22(U22(isList)))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(tt)))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U31(isQid))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(tt)))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U22(U21(isList)))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(isList)))))))))))isList#U21#(U21(U11(U51(U51(U51(U51(isNeList)))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(tt)))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(isNeList)))))))))))isNeList#U41#(U21(tt))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U31(isQid)))))))))))isList#U21#(U21(U11(U51(U51(U51(U31(isQid)))))))
isNeList#U51#(U41(U21(U11(U42(U51(U41(isList)))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(isNeList)))))))
isNeList#U41#(U11(U41(U22(isList))))isNeList#U41#(U11(U41(U21(U21(U11(U42(tt)))))))
isNeList#U41#(U22(U21(U21(U21(isList)))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(tt)))))))))
U41#(tt)isNeList#isNeList#U41#(U11(U41(U21(U21(U11(U42(U51(isNeList))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(U11(isNeList))))))))isNeList#U41#(tt)
isNeList#U51#(U41(U21(U11(U41(U11(U31(isQid)))))))isNeList#U41#(U11(U41(U21(U22(isList)))))
isNeList#U51#(tt)isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U41(isList)))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U41(U21(isList))))))))))))isList#U21#(U21(U11(U51(U41(isList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U31(isQid)))))))isNeList#U41#(U21(U11(U51(isNeList))))
isNeList#U41#(U22(U11(U51(isNeList))))isNeList#U41#(U11(U51(U51(isNeList))))
isList#U21#(U21(U21(U11(isNeList))))isNeList#U51#(U41(U21(U11(U42(U51(U31(isQid)))))))
isNeList#U51#(U41(U21(U11(U41(U21(U21(isList)))))))isNeList#U41#(U11(U41(U11(isNeList))))
isNeList#U51#(U41(U21(U11(U42(U51(U51(isNeList)))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U41(isList))))))))))))))
isList#isList#isNeList#U51#(U41(U11(U41(U11(U31(tt))))))
isNeList#U41#(U11(U41(U21(U11(U51(U41(U21(isList))))))))isNeList#U41#(U21(U11(U41(isList))))
isNeList#U41#(U22(U21(U11(U41(tt)))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(isNeList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U31(tt)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U21(isList))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U31(isQid)))))))isNeList#U51#(U41(U21(U11(U41(U11(U51(isNeList)))))))
isNeList#U51#(U41(U21(U21(isList))))isList#U21#(U11(U41(U11(isNeList))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U31(isQid))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(isList)))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(tt))))))))))isNeList#U41#(U22(U21(U21(U11(isNeList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U41(isList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U51(isNeList))))))))))))))
isNeList#U41#(U11(U51(U41(U21(isList)))))isNeList#U51#(U41(U21(U11(U41(U11(U41(isList)))))))
isNeList#U51#(U41(U11(U41(U11(U41(isList))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(isList))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(isList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U41(U21(isList))))))))
isNeList#U51#(U51(U51(isNeList)))isList#U21#(U21(U11(U41(U11(U41(U22(U11(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(tt))))))))isList#U21#(U21(U11(U41(U11(U41(tt))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U31(tt))))))))))))))isList#U21#(U11(U41(U21(isList))))
isNeList#U51#(U41(U11(U51(isNeList))))isList#U21#(U21(U11(U51(tt))))
isNeList#U51#(U41(U21(U11(tt))))isNeList#U41#(U22(U21(U11(U31(isQid)))))
isNeList#U51#(U41(U11(U42(isNeList))))isNeList#U51#(U41(tt))
isNeList#U41#(U11(U41(U21(U11(U41(isList))))))isNeList#U41#(U22(U21(U11(U41(U11(U41(tt)))))))
isNeList#U51#(U51(tt))isNeList#U51#(U41(U11(U41(U21(U22(isList))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(tt))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U11(isNeList))))))))))))
isNeList#U41#(U11(U42(isNeList)))isNeList#U41#(U11(U41(U21(U11(U51(U31(tt)))))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(isNeList))))))))isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U11(isNeList))))))))))))isList#U21#(U11(U41(tt)))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U31(isQid))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U41(isList)))))))))
isList#U21#(U21(U11(U41(U11(U31(isQid))))))isList#U21#(U21(U21(U22(isList))))
isList#U21#(U21(U21(U21(U21(isList)))))isNeList#U41#(U22(U11(U31(isQid))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(tt)))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U41(U11(isNeList))))))))
isNeList#U41#(U11(tt))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U31(tt)))))))))
isNeList#U51#(U41(U21(U11(U42(U31(isQid))))))isNeList#U41#(U22(U21(U22(isList))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U31(isQid)))))))))))isList#U21#(U21(U11(U41(U11(U51(isNeList))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(tt))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U21(isList)))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U21(isList))))))))isList#U21#(U21(U11(U31(isQid))))
isList#U21#(U21(tt))isNeList#U41#(U11(U41(U21(U11(U31(tt))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U21(isList)))))))))isNeList#U51#(U41(U21(U11(U51(U51(U41(isList)))))))
isList#U21#(U21(U11(U41(U11(U41(U22(U21(isList))))))))isNeList#U41#(U22(U21(U11(U41(U21(U11(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U22(U11(isNeList)))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U51(isNeList))))))))
isNeList#U51#(U41(U11(U41(U21(tt)))))isList#U21#(U11(U51(isNeList)))
isNeList#U41#(U22(U11(U41(tt))))isNeList#U41#(U22(tt))
isNeList#U51#(U41(U21(tt)))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U41#(U11(U51(U41(U11(isNeList))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U41#(U11(U51(U41(U11(U41(isList)))))) 
U41#(U11(U51(U41(U11(U51(isNeList)))))) 
U41#(U11(U51(U41(U11(U31(isQid)))))) 
Thus, the rule isNeList#U41#(U11(U51(U41(U11(isNeList))))) is replaced by the following rules:
isNeList#U41#(U11(U51(U41(U11(U31(isQid))))))isNeList#U41#(U11(U51(U41(U11(U41(isList))))))
isNeList#U41#(U11(U51(U41(U11(U51(isNeList))))))

Problem 28: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isNeList#isNeList#isNeList#isList#
isList#U21#(U21(U21(U21(U11(U51(U41(tt)))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(isList)))))))))))
isList#U21#(tt)isList#U21#(U21(U11(U51(U51(U51(U41(isList)))))))
isNeList#U51#(U41(U21(U11(U42(U41(isList))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(isNeList)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(tt)))))))))isNeList#U41#(U11(U51(U41(U11(U41(tt))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U31(isQid))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(isList)))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(tt)))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(isNeList)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U31(isQid))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(isList))))))))
isList#U21#(U21(U11(U51(U51(U51(U31(isQid)))))))isList#U21#(U21(U11(U51(U51(U31(tt))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(isNeList)))))))isNeList#U41#(U11(U41(U22(isList))))
isNeList#U51#(U42(U41(U11(isNeList))))isList#U21#(U21(U11(U41(U21(U11(U51(isNeList)))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(isNeList))))))))isNeList#U41#(U11(U51(U41(U11(U31(isQid))))))
isList#U21#(U21(U11(U41(U21(U11(U42(isNeList)))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(isNeList))))))))
isNeList#U51#(U41(U21(U11(U52(U11(isNeList))))))isNeList#U51#(U51(U41(U11(U42(isNeList)))))
isNeList#U51#(U41(U21(U11(U41(U11(U31(isQid)))))))isNeList#U51#(tt)
isNeList#U41#(U22(U21(U11(U41(U21(U22(U21(isList))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U41(U21(isList))))))))))))
isNeList#U51#(U41(U21(U11(U52(tt)))))isNeList#U41#(U21(U21(U11(U41(isList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U31(isQid)))))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U51(isNeList))))))))
isList#U21#(U21(U21(U11(isNeList))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(isNeList)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U31(tt)))))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U21(isList)))))))
isList#isList#isNeList#U51#(U42(U31(isQid)))
isNeList#U41#(U11(U41(U21(U11(U51(U41(U21(isList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U31(tt)))))))))))
isList#U21#(U21(U21(U21(U11(U41(isList))))))isList#U21#(U11(U41(U11(isNeList))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U31(isQid))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(isList)))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(tt))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U41(isList)))))))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(isList)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(isList))))))))))
isNeList#U51#(U41(U11(U41(U11(U41(isList))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(isList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U41(U21(isList))))))))isList#U21#(U21(U11(U41(U11(U41(U11(U31(isQid))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U31(isQid))))))))isList#U21#(U11(U41(U21(isList))))
isNeList#U41#(U22(U21(U11(U41(U21(U22(tt)))))))isNeList#U51#(U41(U11(U51(isNeList))))
isNeList#U51#(U41(U21(U11(tt))))isNeList#U51#(U51(tt))
isNeList#U41#(U11(U41(U21(U11(U51(U31(tt)))))))isNeList#U41#(U11(U42(isNeList)))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U41(isList)))))))))isList#U21#(U11(U41(tt)))
isList#U21#(U21(U11(U41(U11(U31(isQid))))))isList#U21#(U21(U21(U21(U21(isList)))))
isList#U21#(U21(U21(U22(isList))))isNeList#U41#(U22(U11(U31(isQid))))
isNeList#U41#(U11(U51(U42(U51(isNeList)))))isNeList#U41#(U11(U41(U21(U21(U11(U41(U11(isNeList))))))))
isNeList#U51#(U41(U21(U11(U42(U31(isQid))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U31(tt)))))))))
isNeList#U41#(U11(tt))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U31(isQid)))))))))))
isList#U21#(U21(U11(U41(U11(U51(isNeList))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U21(isList)))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U21(isList))))))))isNeList#U41#(U22(U21(U11(U41(U21(U11(U41(isList))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U41(isList)))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U21(isList)))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U51(isNeList))))))))isNeList#U41#(U21(U21(U11(U51(isNeList)))))
isNeList#U41#(U11(U51(U42(U31(isQid)))))isNeList#U51#(U41(U21(tt)))
isNeList#U41#(U22(tt))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(tt))))))))))
isNeList#U51#(U51(U41(U11(U41(U11(isNeList))))))isNeList#U51#(U51(U41(U11(U51(U31(tt))))))
isNeList#U51#(U51(U41(U11(U51(U51(isNeList))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U31(isQid))))))))
isNeList#U51#(U51(U41(U21(isList))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(tt))))))))
isNeList#U41#(U21(U21(U11(U31(isQid)))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U31(isQid)))))))))
isNeList#U51#(U42(U51(isNeList)))isList#U21#(U21(U21(U21(U11(U51(U51(isNeList)))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U21(U11(isNeList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(isNeList)))))))))))))
isNeList#U51#(U42(U41(U21(isList))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U42(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(U31(isQid))))))))isNeList#U41#(U22(U21(U11(U41(U21(U22(U11(isNeList))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(U21(isList))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U41(isList))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U41(isList))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U31(isQid))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U11(isNeList)))))))))))isList#U21#(U21(U11(U41(U22(isList)))))
isNeList#U51#(U41(U11(U41(U21(U21(U11(isNeList)))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U51(isNeList))))))))))
isNeList#U41#(U11(U41(U21(U21(U21(isList))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U41(isList)))))))))
isList#U21#(U21(U11(U41(tt))))isNeList#U51#(U41(U11(U41(U11(U51(isNeList))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(tt))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U21(isList))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(U21(isList))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U41(isList))))))))
U51#(tt)isList#isNeList#U51#(U41(U11(U41(U21(U21(U21(isList)))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(tt)))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U21(isList)))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U21(isList))))))))isNeList#U51#(U41(U21(U11(U51(U41(isList))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U31(tt)))))))))isNeList#U41#(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U21(U21(isList))))))))))isList#U21#(U21(U11(U41(U11(U41(U11(U41(isList))))))))
isNeList#U51#(U51(U41(U11(U41(U21(isList))))))isList#U21#(U21(U11(U51(U51(U41(isList))))))
isNeList#U41#(U22(U11(U41(U11(isNeList)))))isNeList#U41#(U11(U51(U31(isQid))))
isNeList#U51#(U42(U42(isNeList)))isNeList#U51#(U41(U21(U11(U41(U21(tt))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U41(U11(isNeList))))))))))))isList#U21#(U21(U11(U41(U21(U21(isList))))))
isNeList#U41#(U22(U11(U41(U21(isList)))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U51(isNeList)))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U21(tt)))))))))isNeList#U51#(U51(U41(U11(U31(isQid)))))
isNeList#U41#(U22(U22(isList)))isNeList#U41#(U22(U21(U11(U51(U51(U31(isQid)))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(tt)))))))isNeList#U41#(U22(U21(U11(U51(U31(tt))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U22(U21(isList)))))))))))))isList#U21#(U21(U11(U51(U51(U51(U51(isNeList)))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U31(isQid))))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U31(tt))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U31(isQid)))))))))))isNeList#U41#(U21(tt))
isList#U21#(U21(U11(U41(U11(U41(U11(U51(isNeList))))))))isNeList#U51#(U41(U21(U11(U42(U51(U41(isList)))))))
isNeList#U51#(U51(U41(tt)))isList#U21#(U21(U11(U41(U21(U11(U41(U21(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(tt)))))))isNeList#U41#(U22(U21(U21(U21(isList)))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(tt)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U51(U51(isNeList))))))))
isNeList#U41#(U11(U51(U41(U11(U41(U21(isList)))))))U41#(tt)isNeList#
isNeList#U41#(U11(U41(U21(U21(U11(U42(U51(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U11(U41(U11(isNeList))))))))
isNeList#U41#(tt)isNeList#U41#(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))
isNeList#U41#(U11(U41(U21(U22(isList)))))isNeList#U41#(U21(U21(tt)))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U51(isNeList)))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U41(isList)))))))))
isList#U21#(U21(U11(U51(U41(isList)))))isList#U21#(U21(U22(isList)))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U11(isNeList)))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U41(tt)))))))
isNeList#U41#(U22(U21(U11(U51(U41(isList))))))isNeList#U41#(U21(U11(U51(isNeList))))
isNeList#U41#(U22(U11(U51(isNeList))))isNeList#U41#(U11(U51(U51(isNeList))))
isNeList#U41#(U11(U41(U11(isNeList))))isNeList#U51#(U41(U21(U11(U42(U51(U31(isQid)))))))
isNeList#U51#(U41(U21(U11(U42(U51(U51(isNeList)))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U41(isList))))))))))))))
isNeList#U51#(U41(U11(U41(U11(U31(tt))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))
isNeList#U51#(U41(U21(U11(U52(U21(isList))))))isNeList#U41#(U21(U11(U41(isList))))
isNeList#U51#(U51(U41(U11(U51(U41(isList))))))isList#U21#(U21(U21(U21(U11(U31(isQid))))))
isNeList#U41#(U22(U21(U11(U41(tt)))))isNeList#U41#(U21(U21(U21(isList))))
isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(isNeList))))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U41(isList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U21(isList))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U31(isQid)))))))isNeList#U51#(U41(U21(U11(U41(U11(U51(isNeList)))))))
isNeList#U51#(U41(U21(U21(isList))))isNeList#U41#(U11(U41(U21(U21(U11(U51(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U41(isList))))))))))isNeList#U41#(U22(U21(U21(U11(isNeList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U51(isNeList))))))))))))))isNeList#U41#(U11(U51(U41(U21(isList)))))
isNeList#U51#(U41(U21(U11(U41(U11(U41(isList)))))))isNeList#U51#(U51(U51(isNeList)))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(tt))))))))isList#U21#(U21(U11(U41(U11(U41(U22(U11(isNeList))))))))
isList#U21#(U21(U11(U41(U11(U41(tt))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U31(tt))))))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))isList#U21#(U21(U11(U51(tt))))
isNeList#U41#(U22(U21(U11(U31(isQid)))))isNeList#U41#(U11(U41(U21(U11(U41(isList))))))
isNeList#U51#(U41(U11(U42(isNeList))))isNeList#U51#(U41(tt))
isNeList#U51#(U41(U11(U41(U21(U22(isList))))))isNeList#U41#(U22(U21(U11(U41(U11(U41(tt)))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(tt))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U51(isNeList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U11(isNeList))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U51(isNeList))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(isNeList))))))))isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U11(isNeList))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U31(isQid))))))))
isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(tt)))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))
isNeList#U41#(U11(U51(U41(U11(U41(U11(isNeList)))))))isNeList#U41#(U22(U21(U22(isList))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(tt))))))))))isList#U21#(U21(tt))
isList#U21#(U21(U11(U31(isQid))))isNeList#U41#(U11(U41(U21(U11(U31(tt))))))
isList#U21#(U21(U11(U41(U11(U41(U22(U21(isList))))))))isList#U21#(U21(U11(U41(U21(U11(U31(isQid)))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U22(U11(isNeList)))))))))))))isNeList#U41#(U11(U51(U42(U41(isList)))))
isNeList#U51#(U41(U11(U41(U21(tt)))))isNeList#U41#(U11(U51(U41(U11(U51(isNeList))))))
isList#U21#(U11(U51(isNeList)))isNeList#U41#(U22(U11(U41(tt))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isList#U21#(U21(U21(U21(U11(U51(U41(tt))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U21#(U21(U21(U21(U11(U51(U42(isNeList))))))) 
Thus, the rule isList#U21#(U21(U21(U21(U11(U51(U41(tt))))))) is replaced by the following rules:
isList#U21#(U21(U21(U21(U11(U51(U42(isNeList)))))))

Problem 29: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isNeList#isNeList#isNeList#isList#
isList#U21#(tt)isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(isList))))))))
isList#U21#(U21(U11(U51(U51(U51(U31(isQid)))))))isList#U21#(U21(U11(U51(U51(U31(tt))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(isNeList)))))))isNeList#U41#(U11(U41(U22(isList))))
isNeList#U51#(U42(U41(U11(isNeList))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(tt))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(tt)))))))))))isList#U21#(U21(U11(U41(U21(U11(U51(isNeList)))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(isNeList))))))))isNeList#U41#(U11(U51(U41(U11(U31(isQid))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(isNeList))))))))isList#U21#(U21(U11(U41(U21(U11(U42(isNeList)))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(isNeList)))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(tt)))))))))
isNeList#U51#(U41(U21(U11(U42(U41(U11(isNeList)))))))isNeList#U51#(U41(U21(U11(U52(U11(isNeList))))))
isNeList#U51#(U51(U41(U11(U42(isNeList)))))isNeList#U51#(U41(U21(U11(U41(U11(U31(isQid)))))))
isNeList#U51#(tt)isList#U21#(U21(U21(U21(U11(U51(U42(isNeList)))))))
isNeList#U41#(U22(U21(U11(U41(U21(U22(U21(isList))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U41(U21(isList))))))))))))
isNeList#U51#(U41(U21(U11(U52(tt)))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U41(isList)))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U31(isQid)))))))))isNeList#U41#(U21(U21(U11(U41(isList)))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(tt)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U31(isQid)))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U51(isNeList))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U41(U11(isNeList))))))))))))isList#U21#(U21(U21(U11(isNeList))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(isNeList)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U31(tt)))))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U21(isList)))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U51(U41(isList))))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U21(isList))))))))))isList#isList#
isNeList#U51#(U42(U31(isQid)))isNeList#U41#(U11(U41(U21(U11(U51(U41(U21(isList))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U51(isNeList)))))))))))isList#U21#(U21(U21(U21(U11(U41(isList))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U31(tt)))))))))))isList#U21#(U11(U41(U11(isNeList))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U31(isQid))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U11(isNeList))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(isList)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(isList)))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(tt))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U41(isList)))))))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(isList)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(isList))))))))))
isNeList#U51#(U41(U11(U41(U11(U41(isList))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(isList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U41(U21(isList))))))))isList#U21#(U21(U11(U41(U11(U41(U11(U31(isQid))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U31(isQid))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U21(isList)))))))))))))))
isList#U21#(U11(U41(U21(isList))))isNeList#U41#(U22(U21(U11(U41(U21(U22(tt)))))))
isNeList#U51#(U41(U11(U51(isNeList))))isNeList#U51#(U41(U21(U11(tt))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U11(isNeList))))))))))isNeList#U51#(U51(tt))
isNeList#U41#(U11(U41(U21(U11(U51(U31(tt)))))))isNeList#U41#(U11(U42(isNeList)))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U41(isList)))))))))isList#U21#(U11(U41(tt)))
isList#U21#(U21(U11(U41(U11(U31(isQid))))))isList#U21#(U21(U21(U21(U21(isList)))))
isList#U21#(U21(U21(U22(isList))))isNeList#U41#(U22(U11(U31(isQid))))
isNeList#U41#(U11(U51(U42(U51(isNeList)))))isNeList#U41#(U11(U41(U21(U21(U11(U41(U11(isNeList))))))))
isNeList#U51#(U41(U21(U11(U42(U31(isQid))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U31(tt)))))))))
isNeList#U41#(U11(tt))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U31(isQid)))))))))))
isList#U21#(U21(U11(U41(U11(U51(isNeList))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U42(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U21(isList)))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U21(isList))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U41(isList))))))))isNeList#U51#(U41(U21(U11(U51(U51(U41(isList)))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U21(isList)))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U51(isNeList))))))))
isNeList#U41#(U21(U21(U11(U51(isNeList)))))isNeList#U41#(U22(tt))
isNeList#U41#(U11(U51(U42(U31(isQid)))))isNeList#U51#(U41(U21(tt)))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U42(isNeList)))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(tt))))))))))
isNeList#U51#(U51(U41(U11(U41(U11(isNeList))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(isNeList))))))))))))
isNeList#U51#(U51(U41(U11(U51(U31(tt))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U31(tt)))))))))
isNeList#U51#(U51(U41(U11(U51(U51(isNeList))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U31(isQid))))))))
isNeList#U51#(U51(U41(U21(isList))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(isNeList))))))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(isNeList)))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(isList))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(tt))))))))isNeList#U41#(U21(U21(U11(U31(isQid)))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U31(isQid))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(isNeList))))))))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U31(isQid)))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U21(isList))))))))))
isNeList#U51#(U42(U51(isNeList)))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U51(isNeList)))))))))
isList#U21#(U21(U21(U21(U11(U51(U51(isNeList)))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U21(U11(isNeList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(isNeList)))))))))))))isNeList#U51#(U42(U41(U21(isList))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(isNeList)))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U31(isQid)))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U31(tt)))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U31(isQid)))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(U21(isList))))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U42(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(U31(isQid))))))))isNeList#U41#(U22(U21(U11(U41(U21(U22(U11(isNeList))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(isList)))))))))isNeList#U41#(U22(U21(U11(U51(U51(U41(U21(isList))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U31(isQid)))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U51(isNeList))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U51(U51(isNeList))))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U51(U31(isQid))))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U41(isList))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U41(isList))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U22(isList)))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U31(isQid))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U11(isNeList)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(tt)))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U11(isNeList)))))))))))isList#U21#(U21(U11(U41(U22(isList)))))
isNeList#U51#(U41(U11(U41(U21(U21(U11(isNeList)))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U51(isNeList))))))))))
isNeList#U41#(U11(U41(U21(U21(U21(isList))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U41(isList)))))))))
isList#U21#(U21(U11(U41(tt))))isNeList#U51#(U41(U11(U41(U11(U51(isNeList))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(isList))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(tt)))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U21(isList))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(U21(isList))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U41(isList))))))))
U51#(tt)isList#isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U21(isList)))))))))
isNeList#U51#(U41(U11(U41(U21(U21(U21(isList)))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(tt)))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U21(isList)))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U21(isList))))))))
isNeList#U51#(U41(U21(U11(U51(U41(isList))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U31(tt)))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U41(isList))))))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U21(U21(isList))))))))))isList#U21#(U21(U11(U41(U11(U41(U11(U41(isList))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U31(isQid)))))))))))isNeList#U51#(U51(U41(U11(U41(U21(isList))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(tt))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U41(isList))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U51(isNeList)))))))isList#U21#(U21(U11(U51(U51(U41(isList))))))
isNeList#U41#(U22(U11(U41(U11(isNeList)))))isNeList#U41#(U11(U51(U31(isQid))))
isNeList#U51#(U42(U42(isNeList)))isNeList#U51#(U41(U21(U11(U41(U21(tt))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U41(U11(isNeList))))))))))))isList#U21#(U21(U11(U41(U21(U21(isList))))))
isNeList#U41#(U22(U11(U41(U21(isList)))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U51(isNeList)))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U21(tt)))))))))isNeList#U51#(U51(U41(U11(U31(isQid)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U11(isNeList)))))))))))))isNeList#U41#(U22(U22(isList)))
isNeList#U41#(U22(U21(U11(U51(U51(U31(isQid)))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(tt)))))))
isNeList#U41#(U22(U21(U11(U51(U31(tt))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U22(U21(isList)))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U51(isNeList)))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U21(isList))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U31(isQid))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U31(tt))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U31(tt))))))))))isNeList#U41#(U21(tt))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U31(isQid)))))))))))isNeList#U51#(U41(U21(U11(U42(U41(U21(isList)))))))
isNeList#U51#(U41(U21(U11(U42(U51(U41(isList)))))))isList#U21#(U21(U11(U41(U11(U41(U11(U51(isNeList))))))))
isNeList#U51#(U51(U41(tt)))isList#U21#(U21(U11(U41(U21(U11(U41(U21(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(tt)))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U41(U21(isList))))))))))))
isNeList#U41#(U22(U21(U21(U21(isList)))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(tt)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(U51(isNeList))))))))isNeList#U41#(U11(U51(U41(U11(U41(U21(isList)))))))
U41#(tt)isNeList#isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U11(isNeList)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U51(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U11(U41(U11(isNeList))))))))
isNeList#U41#(tt)isNeList#U41#(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U21(isList))))))))isNeList#U41#(U11(U41(U21(U22(isList)))))
isNeList#U41#(U21(U21(tt)))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U51(isNeList)))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U41(isList)))))))))isList#U21#(U21(U11(U51(U41(isList)))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U41(isList)))))))))))isList#U21#(U21(U22(isList)))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U11(isNeList)))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U51(isNeList)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(tt)))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U41(tt)))))))
isNeList#U41#(U22(U21(U11(U51(U41(isList))))))isNeList#U51#(U41(U21(U11(U42(U41(tt))))))
isNeList#U41#(U21(U11(U51(isNeList))))isNeList#U41#(U22(U11(U51(isNeList))))
isNeList#U41#(U11(U51(U51(isNeList))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(isList))))))))))))
isNeList#U41#(U11(U41(U11(isNeList))))isNeList#U51#(U41(U21(U11(U42(U51(U31(isQid)))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U11(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U41(isList))))))))))))))
isNeList#U51#(U41(U21(U11(U42(U51(U51(isNeList)))))))isNeList#U51#(U41(U11(U41(U11(U31(tt))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))isNeList#U51#(U41(U21(U11(U52(U21(isList))))))
isList#U21#(U21(U11(U51(U51(U51(U41(tt)))))))isNeList#U41#(U21(U11(U41(isList))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(tt))))))))isNeList#U41#(U22(U21(U11(U41(tt)))))
isList#U21#(U21(U21(U21(U11(U31(isQid))))))isNeList#U51#(U51(U41(U11(U51(U41(isList))))))
isNeList#U41#(U21(U21(U21(isList))))isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(isNeList))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U21(isList))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U31(isQid)))))))
isNeList#U51#(U41(U21(U11(U41(U11(U51(isNeList)))))))isNeList#U51#(U41(U21(U21(isList))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(U41(isList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U31(isQid))))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U41(isList))))))))))isNeList#U41#(U22(U21(U21(U11(isNeList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U51(isNeList))))))))))))))isNeList#U41#(U11(U51(U41(U21(isList)))))
isNeList#U51#(U41(U21(U11(U41(U11(U41(isList)))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(tt)))))))))))
isNeList#U51#(U51(U51(isNeList)))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(tt))))))))
isList#U21#(U21(U11(U41(U11(U41(U22(U11(isNeList))))))))isList#U21#(U21(U11(U41(U11(U41(tt))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U31(tt))))))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U31(tt))))))))))))isList#U21#(U21(U11(U51(tt))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U31(isQid)))))))))))))isNeList#U41#(U22(U21(U11(U31(isQid)))))
isNeList#U41#(U11(U41(U21(U11(U41(isList))))))isNeList#U51#(U41(U11(U42(isNeList))))
isNeList#U51#(U41(tt))isNeList#U51#(U41(U11(U41(U21(U22(isList))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(tt)))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(tt))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U51(isNeList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U11(isNeList))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U51(isNeList))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U11(isNeList))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U31(isQid))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U41(isList))))))))))
isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(tt)))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))
isNeList#U41#(U11(U51(U41(U11(U41(U11(isNeList)))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U51(isNeList)))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))isNeList#U41#(U22(U21(U22(isList))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(tt))))))))))isList#U21#(U21(tt))
isList#U21#(U21(U11(U31(isQid))))isNeList#U41#(U11(U41(U21(U11(U31(tt))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(tt)))))))))isList#U21#(U21(U11(U41(U11(U41(U22(U21(isList))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U51(isNeList))))))))))isList#U21#(U21(U11(U41(U21(U11(U31(isQid)))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U22(U11(isNeList)))))))))))))isNeList#U41#(U11(U51(U42(U41(isList)))))
isNeList#U51#(U41(U11(U41(U21(tt)))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(U11(isNeList))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U31(tt))))))))))))isNeList#U41#(U11(U51(U41(U11(U51(isNeList))))))
isList#U21#(U11(U51(isNeList)))isNeList#U41#(U22(U11(U41(tt))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(isList)))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U41#(U11(U41(U21(U11(U51(U51(U41(U21(isList))))))))) 
U41#(U11(U41(U21(U11(U51(U51(U41(tt)))))))) 
U41#(U11(U41(U21(U11(U51(U51(U41(U11(isNeList))))))))) 
Thus, the rule isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(isList)))))))) is replaced by the following rules:
isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(isList)))))))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(tt))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U11(isNeList)))))))))

Problem 30: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isNeList#isNeList#isNeList#isList#
isList#U21#(tt)isList#U21#(U21(U21(U21(U11(U51(U41(U11(U31(isQid)))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(isNeList)))))))))isNeList#U51#(U41(U21(U11(U42(U41(U11(isNeList)))))))
isNeList#U51#(U41(U21(U11(U52(U11(isNeList))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(isNeList))))))))))
isNeList#U51#(U51(U41(U11(U42(isNeList)))))isNeList#U51#(U41(U21(U11(U41(U11(U31(isQid)))))))
isNeList#U51#(tt)isNeList#U41#(U22(U21(U11(U41(U21(U22(U21(isList))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(isNeList)))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U41(U21(isList))))))))))))
isNeList#U51#(U41(U21(U11(U52(tt)))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U31(isQid)))))))))
isNeList#U41#(U21(U21(U11(U41(isList)))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U41(isList)))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(tt)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U31(isQid)))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U51(isNeList))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U11(isNeList)))))))))isNeList#U41#(U11(U41(U22(U21(U21(U21(isList)))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U41(U11(isNeList))))))))))))isList#U21#(U21(U21(U11(isNeList))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(isNeList)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U31(tt)))))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U21(isList)))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U51(U41(isList))))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U21(isList))))))))))isList#isList#
isNeList#U51#(U42(U31(isQid)))isNeList#U41#(U11(U41(U21(U11(U51(U41(U21(isList))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U51(isNeList)))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U41(isList))))))))
isList#U21#(U21(U21(U21(U11(U41(isList))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U31(tt)))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(tt))))))))))isNeList#U41#(U11(U41(U22(U21(U22(tt))))))
isList#U21#(U11(U41(U11(isNeList))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U11(isNeList))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U31(isQid))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(isList)))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(tt))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(isList)))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(tt))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(isList)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U41(isList)))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(isList))))))))))
isNeList#U51#(U41(U11(U41(U11(U41(isList))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(isList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U41(U21(isList))))))))isList#U21#(U21(U11(U41(U11(U41(U11(U31(isQid))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U31(isQid))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U21(isList)))))))))))))))
isList#U21#(U11(U41(U21(isList))))isNeList#U41#(U22(U21(U11(U41(U21(U22(tt)))))))
isNeList#U51#(U41(U11(U51(isNeList))))isNeList#U51#(U41(U21(U11(tt))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U21(U11(isNeList)))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U11(isNeList))))))))))
isNeList#U51#(U51(tt))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U22(isList)))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U31(tt)))))))isNeList#U41#(U11(U42(isNeList)))
isNeList#U41#(U11(U41(U22(U21(U22(U11(isNeList)))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U41(isList)))))))))
isList#U21#(U11(U41(tt)))isList#U21#(U21(U11(U41(U11(U31(isQid))))))
isNeList#U41#(U11(U41(U22(U21(U21(U11(U51(U51(isNeList)))))))))isList#U21#(U21(U21(U21(U21(isList)))))
isList#U21#(U21(U21(U22(isList))))isNeList#U41#(U22(U11(U31(isQid))))
isList#U21#(U21(U11(U51(U51(U51(U31(tt)))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U22(isList))))))))))))))
isNeList#U41#(U11(U51(U42(U51(isNeList)))))isNeList#U41#(U11(U41(U21(U21(U11(U41(U11(isNeList))))))))
isNeList#U51#(U41(U21(U11(U42(U31(isQid))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U31(tt)))))))))
isNeList#U41#(U11(tt))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U31(isQid)))))))))))
isList#U21#(U21(U11(U41(U11(U51(isNeList))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U42(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U21(isList)))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(isNeList))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U31(isQid))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U21(isList))))))))
isNeList#U51#(U42(U41(U11(U41(U21(isList))))))isNeList#U41#(U22(U21(U11(U41(U21(U11(U41(isList))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U21(isList)))))))))isNeList#U51#(U41(U21(U11(U51(U51(U41(isList)))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U51(isNeList))))))))isNeList#U41#(U21(U21(U11(U51(isNeList)))))
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U51#(tt)isList#isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U21(isList)))))))))
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isNeList#U51#(U41(U21(U11(U51(U41(isList))))))isNeList#U41#(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))
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isNeList#U41#(U11(U41(U22(U11(isNeList)))))isNeList#U41#(U22(U11(U41(U11(isNeList)))))
isNeList#U41#(U11(U51(U31(isQid))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(isNeList)))))))))))
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isNeList#U41#(U22(U21(U11(U41(U22(U21(tt)))))))isNeList#U41#(U22(U21(U11(U51(U31(tt))))))
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isNeList#U41#(U11(U51(U41(U11(U41(U21(isList)))))))U41#(tt)isNeList#
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isNeList#U41#(tt)isNeList#U41#(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U21(isList))))))))isNeList#U41#(U11(U41(U21(U22(isList)))))
isNeList#U41#(U21(U21(tt)))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U51(isNeList)))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U41(isList)))))))))isList#U21#(U21(U11(U51(U41(isList)))))
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isNeList#U41#(U22(U21(U11(U51(U41(isList))))))isNeList#U51#(U41(U21(U11(U42(U41(tt))))))
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isNeList#U51#(U41(U21(U21(isList))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U31(isQid))))))))
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isNeList#U51#(U41(U21(U11(U41(U11(U41(isList)))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(isList)))))))))
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isNeList#U51#(U51(U51(isNeList)))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(tt))))))))
isList#U21#(U21(U11(U41(U11(U41(U22(U11(isNeList))))))))isList#U21#(U21(U11(U41(U11(U41(tt))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U31(tt))))))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U31(tt))))))))))))isList#U21#(U21(U11(U51(tt))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U31(isQid)))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U51(isNeList))))))))))))
isNeList#U41#(U22(U21(U11(U31(isQid)))))isNeList#U41#(U11(U41(U21(U11(U41(isList))))))
isNeList#U51#(U41(U11(U42(isNeList))))isNeList#U51#(U41(tt))
isNeList#U51#(U41(U11(U41(U21(U22(isList))))))isNeList#U41#(U22(U21(U11(U41(U11(U41(tt)))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(tt))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U51(isNeList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U11(isNeList))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U11(isNeList)))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U51(isNeList))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U11(isNeList))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U31(isQid))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U41(isList))))))))))
isNeList#U41#(U11(U41(U22(tt))))isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(tt)))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))isNeList#U41#(U11(U51(U41(U11(U41(U11(isNeList)))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U51(isNeList)))))))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(tt))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))isNeList#U41#(U22(U21(U22(isList))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(tt))))))))))isList#U21#(U21(tt))
isList#U21#(U21(U11(U31(isQid))))isNeList#U41#(U11(U41(U21(U11(U31(tt))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(tt)))))))))isList#U21#(U21(U11(U41(U11(U41(U22(U21(isList))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U51(isNeList))))))))))isList#U21#(U21(U11(U41(U21(U11(U31(isQid)))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U22(U11(isNeList)))))))))))))isNeList#U41#(U11(U51(U42(U41(isList)))))
isNeList#U51#(U42(U41(U11(U51(isNeList)))))isNeList#U51#(U41(U11(U41(U21(tt)))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(U11(isNeList))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U31(tt))))))))))))isNeList#U41#(U11(U51(U41(U11(U51(isNeList))))))
isList#U21#(U11(U51(isNeList)))isNeList#U41#(U22(U11(U41(tt))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isList#U21#(U21(U21(U21(U11(U51(U41(U11(U31(isQid))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U21#(U21(U21(U21(U11(U51(U41(U11(U31(tt))))))))) 
Thus, the rule isList#U21#(U21(U21(U21(U11(U51(U41(U11(U31(isQid))))))))) is replaced by the following rules:
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U31(tt)))))))))

Problem 31: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isNeList#isList#isNeList#U51#(tt)
isList#isList#isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(isList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U41(U21(isList))))))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U31(isQid))))))))
isNeList#U51#(U41(U11(U51(isNeList))))isNeList#U51#(U41(U21(U11(tt))))
isNeList#U41#(U11(U41(U21(U11(U51(U31(tt)))))))isList#U21#(U11(U41(tt)))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U21(tt))))))))))isList#U21#(U21(U11(U41(U11(U31(isQid))))))
isList#U21#(U21(U21(U21(U21(isList)))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U51(U31(isQid))))))))))))
isNeList#U51#(U41(U21(U11(U52(U11(U41(U21(isList))))))))isNeList#U41#(U22(U11(U31(isQid))))
isList#U21#(U21(U11(U51(U51(U51(U31(tt)))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U22(isList))))))))))))))
isNeList#U41#(U11(U51(U42(U51(isNeList)))))isNeList#U41#(U11(tt))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U31(isQid)))))))))))isList#U21#(U21(U11(U41(U11(U51(isNeList))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(isNeList))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U31(isQid))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U51(isNeList))))))))isNeList#U41#(U22(tt))
isNeList#U41#(U11(U51(U42(U31(isQid)))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(isList)))))))))))
isNeList#U51#(U51(U41(U11(U41(U11(isNeList))))))isNeList#U41#(U22(U21(U11(U41(U21(U11(U31(tt))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(isNeList))))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(isList))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U31(tt)))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U31(isQid))))))))
isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(isList))))))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(isList)))))))))
isNeList#U51#(U51(U41(U21(isList))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(isNeList))))))))))))))))
isNeList#U41#(U11(U41(U22(U21(tt)))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(isList))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(isNeList)))))))))))isList#U21#(U21(U21(U11(U51(isNeList)))))
isNeList#U51#(U41(U11(U41(U11(U41(U21(U11(isNeList))))))))isNeList#U41#(U21(U21(U11(U31(isQid)))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U31(isQid)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(isNeList))))))))))))))
isNeList#U51#(U42(U51(isNeList)))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U21(isList))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U51(isNeList)))))))))isList#U21#(U21(U21(U21(U11(U51(U51(isNeList)))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U31(isQid)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(tt)))))))
isNeList#U41#(U11(U41(U22(U21(U21(U11(U51(U31(isQid)))))))))isList#U21#(U21(U11(U41(U21(U11(U51(U31(tt))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(isNeList)))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(tt)))))))))
isNeList#U51#(U42(U41(U21(isList))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(isNeList)))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U51(U31(tt))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U51(U31(isQid)))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(isNeList))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U31(tt)))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(isList)))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U42(isNeList))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(tt)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U51(U31(isQid))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(isList)))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U41(isList))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U31(isQid)))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U41(isList))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U51(U31(isQid))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(isNeList))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(isList))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(isList)))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(tt))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(tt)))))))))))
isList#U21#(U21(U11(U41(U22(isList)))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U31(isQid))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U51(isNeList)))))))))isNeList#U51#(U41(U11(U41(U21(U21(U11(isNeList)))))))
isNeList#U41#(U11(U41(U21(U21(U21(isList))))))isList#U21#(U21(U11(U41(tt))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(isNeList)))))))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(isNeList)))))))))))
isNeList#U51#(U41(U11(U41(U11(U51(isNeList))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U11(U51(isNeList)))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(tt))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(isList))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(tt)))))))))))U51#(tt)isList#
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U31(tt)))))))))isNeList#U51#(U51(U41(U11(U41(U21(isList))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U41(U21(U11(U31(isQid)))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(tt))))))))))
isList#U21#(U21(U11(U51(U51(U41(isList))))))isNeList#U41#(U11(U41(U22(U11(isNeList)))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U21(isList))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(isNeList)))))))))))
isNeList#U51#(U42(U42(isNeList)))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U21(U21(isList)))))))))))))
isNeList#U51#(U41(U21(U11(U52(U11(U42(U31(tt))))))))isNeList#U51#(U41(U21(U11(U41(U21(tt))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U11(isNeList))))))))))isList#U21#(U21(U11(U41(U21(U11(U42(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U51(isNeList)))))))))))isNeList#U41#(U22(U22(isList)))
isList#U21#(U21(U11(U41(U21(U11(U51(U51(isNeList))))))))isList#U21#(U21(U11(U51(U51(U51(U51(isNeList)))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U31(isQid))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U21(isList))))))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U51(U31(isQid)))))))))))))isNeList#U41#(U21(tt))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U41(U21(isList))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(tt)))))))
isNeList#U41#(U22(U21(U21(U21(isList)))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(isList))))))))))))
isNeList#U41#(U11(U51(U41(U11(U41(U21(isList)))))))U41#(tt)isNeList#
isNeList#U41#(U11(U41(U21(U21(U11(U42(U51(isNeList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(U11(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(isNeList))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(tt))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U31(isQid)))))))))
isNeList#U41#(tt)isNeList#U41#(U21(U21(tt)))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U11(isNeList)))))))))))isList#U21#(U21(U22(isList)))
isNeList#U41#(U22(U21(U11(U51(U41(isList))))))isNeList#U51#(U41(U21(U11(U42(U41(tt))))))
isNeList#U41#(U21(U11(U51(isNeList))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U31(isQid)))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U11(isNeList))))))))))isNeList#U41#(U22(U11(U51(isNeList))))
isNeList#U41#(U11(U51(U51(isNeList))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U41(isList)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(isList))))))))))))isNeList#U51#(U41(U21(U11(U42(U51(U31(isQid)))))))
isNeList#U41#(U11(U41(U11(isNeList))))isNeList#U51#(U41(U21(U11(U42(U51(U51(isNeList)))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U41(isList))))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U11(isNeList))))))))
isList#U21#(U21(U11(U51(U52(isList)))))isNeList#U51#(U41(U21(U11(U52(U11(U42(U51(isNeList))))))))
isNeList#U51#(U41(U11(U41(U11(U31(tt))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(tt))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(tt)))))))isList#U21#(U21(U21(U21(U11(U31(isQid))))))
isNeList#U41#(U22(U21(U11(U41(tt)))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(isNeList))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U31(isQid))))))))isNeList#U51#(U41(U21(U11(U41(U11(U51(isNeList)))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(U41(isList))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U22(isList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U31(isQid))))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U41(U21(tt)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U51(isNeList))))))))))))))isNeList#U41#(U22(U21(U21(U11(isNeList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U41(isList))))))))))isNeList#U51#(U41(U21(U11(U52(U11(U31(isQid)))))))
isNeList#U51#(U42(U41(U11(U41(U11(U31(isQid)))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U51(U51(isNeList))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(isList)))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U41(U11(isNeList)))))))))))
isList#U21#(U21(U21(U21(U11(U41(U11(U51(isNeList))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(tt)))))))))
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isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U31(isQid)))))))))))isNeList#U51#(U41(U21(U11(U42(U41(U21(isList)))))))
isNeList#U51#(U42(U41(U11(U31(isQid)))))isList#U21#(U21(U11(U41(U21(U11(U42(U31(isQid))))))))
isNeList#U51#(U41(U21(U11(U42(U51(U41(isList)))))))isList#U21#(U21(U11(U41(U11(U41(U11(U51(isNeList))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(tt))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U21(isList))))))))
isNeList#U51#(U51(U41(tt)))isNeList#U51#(U41(U21(U11(U42(U41(U11(U51(isNeList))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(tt)))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U11(isNeList)))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))isNeList#U41#(U11(U41(U21(U22(isList)))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U21(isList))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U51(isNeList)))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U41(isList)))))))))isList#U21#(U21(U11(U51(U41(isList)))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U41(isList)))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U51(isNeList)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(tt)))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U21(tt)))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(tt)))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U11(isNeList)))))))))))
isNeList#U51#(U41(U21(U11(U52(U21(isList))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))
isNeList#U41#(U21(U11(U41(isList))))isNeList#U51#(U51(U41(U11(U51(U41(isList))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))isNeList#U41#(U21(U21(U21(isList))))
isNeList#U51#(U41(U21(U11(U51(U51(U31(isQid)))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U21(isList))))))))))))isNeList#U51#(U41(U21(U21(isList))))
isNeList#U41#(U11(U51(U41(U21(isList)))))isNeList#U51#(U41(U21(U11(U41(U11(U41(isList)))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U21(isList)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(tt)))))))))))
isNeList#U51#(U51(U51(isNeList)))isList#U21#(U21(U11(U41(U11(U41(U22(U11(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(tt))))))))isList#U21#(U21(U11(U41(U11(U41(tt))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U31(isQid)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U31(tt))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U51(isNeList))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U22(U21(tt))))))))isNeList#U51#(U41(tt))
isNeList#U51#(U41(U11(U41(U21(U22(isList))))))isNeList#U41#(U22(U21(U11(U41(U11(U41(tt)))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U51(isNeList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(tt)))))))))))))
isNeList#U41#(U11(U41(U22(tt))))isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(tt)))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(tt))))))))))
isList#U21#(U21(U11(U31(isQid))))isNeList#U41#(U11(U41(U21(U11(U31(tt))))))
isList#U21#(U21(U11(U41(U11(U41(U22(U21(isList))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U21(isList)))))))))))
isNeList#U51#(U42(U41(U11(U51(isNeList)))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(tt)))))))))
isNeList#U51#(U41(U11(U41(U21(tt)))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))
isNeList#U41#(U11(U51(U41(U11(U51(isNeList))))))isNeList#U41#(U22(U11(U41(tt))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(isList)))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(tt)))))))))) 
U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(U21(isList))))))))))) 
U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(U11(isNeList))))))))))) 
Thus, the rule isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(isList)))))))))) is replaced by the following rules:
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(tt))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(U11(isNeList)))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(U21(isList)))))))))))

Problem 32: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(U11(isNeList)))))))))
isList#isNeList#isNeList#isList#
isNeList#U51#(tt)isList#isList#
isNeList#U51#(U51(U41(U21(isList))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(isList)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(isNeList))))))))))))))))isNeList#U41#(U11(U41(U22(U21(tt)))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(isNeList)))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(isList))))))))))))
isList#U21#(U21(U21(U11(U51(isNeList)))))isList#U21#(U21(U11(U51(U51(U51(tt))))))
isNeList#U51#(U41(U11(U41(U11(U41(U21(U11(isNeList))))))))isList#U21#(U11(U42(U51(U41(isList)))))
isNeList#U41#(U21(U21(U11(U31(isQid)))))isNeList#U41#(U11(U41(U21(U11(U51(U51(tt)))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U31(isQid)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(isNeList))))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U21(isList))))))))))isNeList#U51#(U42(U51(isNeList)))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U31(isQid)))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U51(isNeList)))))))))
isList#U21#(U21(U21(U21(U11(U51(U51(isNeList)))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U31(isQid)))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(tt)))))))isNeList#U41#(U11(U41(U22(U21(U21(U11(U51(U31(isQid)))))))))
isList#U21#(U21(U11(U41(U21(U11(U51(U31(tt))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(isNeList)))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(tt)))))))))isNeList#U51#(U42(U41(U21(isList))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(isNeList)))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U51(U31(tt))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(isNeList)))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U51(U31(tt))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U51(U31(isQid)))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(isNeList))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U31(tt)))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(isList)))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U42(isNeList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(tt)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(U31(isQid))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(isList)))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U41(isList))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U31(isQid)))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U41(isList))))))))))))isList#U21#(U11(U42(U51(U51(isNeList)))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U51(U31(isQid))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(isList)))))))))))
isList#U21#(U21(U11(U41(U11(U51(U31(isQid)))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(isNeList))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(isList))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(isList)))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(tt))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U21(U21(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(tt)))))))))))isList#U21#(U21(U11(U41(U22(isList)))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U31(isQid))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U51(isNeList)))))))))
isNeList#U51#(U41(U11(U41(U21(U21(U11(isNeList)))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U51(U51(isNeList)))))))))
isNeList#U41#(U11(U41(U21(U21(U21(isList))))))isList#U21#(U21(U11(U41(tt))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(isNeList)))))))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(isNeList)))))))))))
isNeList#U51#(U41(U11(U41(U11(U51(isNeList))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U11(U51(isNeList)))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(tt))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(isList))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(tt)))))))))))U51#(tt)isList#
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U31(tt)))))))))isNeList#U51#(U51(U41(U11(U41(U21(isList))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U41(U21(U11(U31(isQid)))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(tt))))))))))
isList#U21#(U21(U11(U51(U51(U41(isList))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U21(isList))))))))))
isNeList#U41#(U11(U41(U22(U11(isNeList)))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(isNeList)))))))))))
isNeList#U51#(U42(U42(isNeList)))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U21(U21(isList)))))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(tt))))))isNeList#U51#(U41(U21(U11(U52(U11(U42(U31(tt))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U11(isNeList))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U31(tt))))))))
isList#U21#(U21(U11(U41(U21(U11(U42(U41(isList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U51(isNeList)))))))))))
isNeList#U41#(U11(U51(U42(U51(U31(isQid))))))isList#U21#(U11(U42(U31(isQid))))
isList#U21#(U21(U11(U41(U21(U11(U51(U51(isNeList))))))))isNeList#U41#(U22(U22(isList)))
isList#U21#(U21(U11(U51(U51(U51(U51(isNeList)))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U21(isList))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U31(isQid))))))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U51(U31(isQid)))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U11(U41(tt)))))))))))))isNeList#U41#(U21(tt))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U41(U21(isList))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(tt)))))))
isNeList#U41#(U22(U21(U21(U21(isList)))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(isList))))))))))))
isNeList#U41#(U11(U51(U41(U11(U41(U21(isList)))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U22(tt))))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(U11(isNeList)))))))))))U41#(tt)isNeList#
isNeList#U41#(U11(U41(U21(U21(U11(U42(U51(isNeList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(U11(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(isNeList))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(tt))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U31(isQid)))))))))
isNeList#U41#(tt)isNeList#U41#(U21(U21(tt)))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U11(isNeList)))))))))))isList#U21#(U21(U22(isList)))
isNeList#U41#(U22(U21(U11(U51(U41(isList))))))isNeList#U51#(U41(U21(U11(U42(U41(tt))))))
isNeList#U41#(U21(U11(U51(isNeList))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U31(isQid)))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U11(isNeList))))))))))isNeList#U41#(U22(U11(U51(isNeList))))
isNeList#U41#(U11(U51(U51(isNeList))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U41(isList)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(isList))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U31(isQid)))))))))))))
isNeList#U51#(U41(U21(U11(U42(U51(U31(isQid)))))))isNeList#U41#(U11(U41(U11(isNeList))))
isNeList#U51#(U41(U21(U11(U42(U51(U51(isNeList)))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U41(isList))))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U11(isNeList))))))))isList#U21#(U21(U11(U51(U52(isList)))))
isNeList#U51#(U41(U21(U11(U52(U11(U42(U51(isNeList))))))))isNeList#U51#(U41(U11(U41(U11(U31(tt))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(tt))))))))isList#U21#(U21(U11(U51(U51(U51(U41(tt)))))))
isList#U21#(U21(U21(U21(U11(U31(isQid))))))isNeList#U41#(U22(U21(U11(U41(tt)))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(isNeList))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U31(isQid))))))))
isNeList#U51#(U41(U21(U11(U41(U11(U51(isNeList)))))))isNeList#U41#(U11(U41(U21(U21(U11(U51(U41(isList))))))))
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isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U51(U41(isList))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U51(isNeList)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U41(isList))))))))))))isList#U21#(U11(U41(U11(U31(isQid)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U22(isList)))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U51(U51(isNeList))))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U21(U11(isNeList)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U41(U21(U11(isNeList)))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U31(isQid))))))))isList#U21#(U11(U42(U41(isList))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U42(isNeList)))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U11(isNeList)))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U11(isNeList)))))))))))isList#U21#(U11(U42(U51(U31(isQid)))))
isNeList#U51#(U41(U11(U41(U11(U41(tt))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U51(isNeList))))))))))
isList#U21#(U21(U11(U41(U11(U51(U41(isList)))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U41(isList)))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U21(isList))))))))isList#U21#(U21(U11(U41(U21(U11(U42(U51(isNeList))))))))
isNeList#U41#(U11(U41(U22(U21(U21(U11(U51(U41(isList)))))))))isNeList#U41#(U22(U21(U11(U41(U11(U41(U21(isList))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U41(isList))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U21(isList)))))))))
isNeList#U51#(U41(U11(U41(U21(U21(U21(isList)))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U21(isList))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U21(isList)))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(tt)))))))
isNeList#U51#(U41(U21(U11(U51(U41(isList))))))isNeList#U41#(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U21(U21(isList))))))))))isList#U21#(U21(U11(U41(U11(U41(U11(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U41(isList))))))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U31(isQid)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(tt))))))))))))isNeList#U51#(U51(U41(U11(U41(U11(U41(isList)))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U41(isList))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U51(isNeList)))))))
isNeList#U41#(U11(U41(U22(U21(U21(U11(U31(tt))))))))isNeList#U41#(U22(U11(U41(U11(isNeList)))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))))isNeList#U41#(U11(U51(U31(isQid))))
isList#U21#(U21(U11(U41(U21(U11(U51(U41(isList))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U41(U11(isNeList))))))))))))
isList#U21#(U21(U21(U21(U21(U11(isNeList))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(tt)))))))))
isList#U21#(U21(U11(U41(U21(U21(isList))))))isNeList#U41#(U22(U11(U41(U21(isList)))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U51(U51(isNeList))))))))))))))isNeList#U51#(U51(U41(U11(U31(isQid)))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U21(tt)))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(tt))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U22(isList))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U11(isNeList)))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U31(isQid)))))))isList#U21#(U21(U21(U21(U11(U41(U11(U31(isQid))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(tt)))))))isNeList#U41#(U22(U21(U11(U51(U31(tt))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U22(U21(isList)))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U41(isList)))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U51(U41(isList))))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U31(tt))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U31(tt))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U51(isNeList))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U31(tt)))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U31(isQid)))))))))))
isNeList#U51#(U41(U21(U11(U42(U41(U21(isList)))))))isNeList#U51#(U42(U41(U11(U31(isQid)))))
isNeList#U51#(U41(U11(U51(U31(tt)))))isList#U21#(U21(U11(U41(U21(U11(U42(U31(isQid))))))))
isNeList#U51#(U41(U21(U11(U42(U51(U41(isList)))))))isList#U21#(U21(U11(U41(U11(U41(U11(U51(isNeList))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(tt))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U21(isList))))))))
isNeList#U51#(U51(U41(tt)))isNeList#U51#(U41(U21(U11(U42(U41(U11(U51(isNeList))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(tt)))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U11(isNeList)))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))isNeList#U41#(U11(U41(U21(U22(isList)))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U21(isList))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U51(isNeList)))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U41(isList)))))))))isList#U21#(U21(U11(U51(U41(isList)))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(U11(isNeList)))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U41(isList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U51(isNeList)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(tt)))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U21(tt)))))))))))))isList#U21#(U21(U21(U21(U21(U21(isList))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(tt)))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U11(isNeList)))))))))))
isNeList#U51#(U41(U21(U11(U52(U21(isList))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))
isNeList#U41#(U21(U11(U41(isList))))isNeList#U51#(U51(U41(U11(U51(U41(isList))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))isNeList#U41#(U21(U21(U21(isList))))
isNeList#U51#(U41(U21(U11(U51(U51(U31(isQid)))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U21(isList))))))))))))isNeList#U51#(U41(U21(U21(isList))))
isNeList#U41#(U11(U51(U41(U21(isList)))))isNeList#U51#(U41(U21(U11(U41(U11(U41(isList)))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U21(isList)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(tt)))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(tt))))))))))isNeList#U51#(U51(U51(isNeList)))
isList#U21#(U21(U11(U41(U11(U41(U22(U11(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(tt))))))))
isList#U21#(U21(U11(U41(U11(U41(tt))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U31(isQid)))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U31(tt))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U51(isNeList))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U22(U21(tt))))))))
isNeList#U51#(U41(tt))isNeList#U51#(U41(U11(U41(U21(U22(isList))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(tt)))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U51(isNeList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(tt)))))))))))))isNeList#U51#(U51(U41(U11(U41(U11(U31(tt)))))))
isNeList#U41#(U11(U41(U22(tt))))isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(tt)))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))isNeList#U51#(U41(U11(U51(U41(isList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(tt))))))))))isList#U21#(U21(U11(U31(isQid))))
isNeList#U41#(U11(U41(U21(U11(U31(tt))))))isList#U21#(U21(U11(U41(U11(U41(U22(U21(isList))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U21(isList)))))))))))isNeList#U51#(U42(U41(U11(U51(isNeList)))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(tt)))))))))isNeList#U51#(U41(U11(U41(U21(tt)))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))isNeList#U41#(U11(U51(U41(U11(U51(isNeList))))))
isNeList#U41#(U22(U11(U41(tt))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(U11(isNeList))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U41#(U11(U41(U22(U21(U21(U11(U41(U11(U31(isQid)))))))))) 
U41#(U11(U41(U22(U21(U21(U11(U41(U11(U41(isList)))))))))) 
U41#(U11(U41(U22(U21(U21(U11(U41(U11(U51(isNeList)))))))))) 
Thus, the rule isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(U11(isNeList))))))))) is replaced by the following rules:
isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(U11(U51(isNeList))))))))))isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(U11(U31(isQid))))))))))
isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(U11(U41(isList))))))))))

Problem 33: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isNeList#isList#isNeList#U51#(tt)
isList#isList#isList#U21#(U21(U11(U51(U51(U52(U11(tt)))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U21(isList))))))))))isNeList#U51#(U42(U51(isNeList)))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U31(isQid)))))))))))isNeList#U51#(U51(U41(U21(U11(U41(U21(isList)))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U51(isNeList)))))))))isList#U21#(U21(U21(U21(U11(U51(U51(isNeList)))))))
isList#U21#(U11(U42(U51(U41(U21(U21(U21(isList))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U31(isQid)))))))))
isList#U21#(U21(U11(U51(U51(U52(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(tt)))))))
isNeList#U41#(U11(U41(U22(U21(U21(U11(U51(U31(isQid)))))))))isList#U21#(U21(U11(U41(U21(U11(U51(U31(tt))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(isNeList)))))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(isNeList))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(tt)))))))))isNeList#U51#(U42(U41(U21(isList))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U51(U31(tt))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(isNeList)))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(isNeList)))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U51(U31(tt))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U51(U31(isQid)))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(isNeList))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U31(tt)))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(isList)))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U42(isNeList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(tt)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(U31(isQid))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(isList)))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U41(isList))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U31(isQid)))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U41(isList))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U51(U31(isQid))))))))))))))
isList#U21#(U11(U42(U51(U51(isNeList)))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(isList)))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U41(isList))))))))))isList#U21#(U21(U11(U41(U11(U51(U31(isQid)))))))
isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(isNeList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(isNeList))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(isList))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(isList)))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(tt))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U21(U21(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(tt)))))))))))isList#U21#(U21(U11(U41(U22(isList)))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U31(isQid))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U51(isNeList)))))))))
isNeList#U51#(U41(U11(U41(U21(U21(U11(isNeList)))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(isNeList))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U51(U51(isNeList)))))))))isNeList#U41#(U11(U41(U21(U21(U21(isList))))))
isList#U21#(U21(U11(U41(tt))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(isNeList)))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(isNeList)))))))))))isNeList#U51#(U41(U11(U41(U11(U51(isNeList))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U11(U51(isNeList)))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(isList))))))))))isNeList#U51#(U51(U41(U21(tt))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(tt)))))))))))isList#U21#(U11(U42(U51(U41(U21(U21(tt)))))))
U51#(tt)isList#isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U31(tt)))))))))
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isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(isNeList)))))))))))isNeList#U51#(U42(U42(isNeList)))
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isNeList#U41#(U21(U21(U11(U31(tt)))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))))))))))))
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isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(U11(isNeList)))))))))))U41#(tt)isNeList#
isNeList#U41#(U11(U41(U21(U21(U11(U42(U51(isNeList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))
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isNeList#U41#(tt)isNeList#U41#(U21(U21(tt)))
isNeList#U51#(U51(U41(U21(U11(U42(isNeList))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U11(isNeList)))))))))))
isList#U21#(U21(U22(isList)))isNeList#U41#(U22(U21(U11(U51(U41(isList))))))
isNeList#U51#(U41(U21(U11(U42(U41(tt))))))isNeList#U41#(U21(U11(U51(isNeList))))
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isNeList#U41#(U22(U11(U51(isNeList))))isNeList#U41#(U11(U51(U51(isNeList))))
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isNeList#U41#(U11(U41(U11(isNeList))))isNeList#U51#(U41(U21(U11(U42(U51(U51(isNeList)))))))
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isList#U21#(U21(U11(U51(U51(U51(U41(U21(tt))))))))isList#U21#(U21(U11(U51(U51(U51(U41(tt)))))))
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isNeList#U41#(U22(U21(U11(U31(isQid)))))isNeList#U51#(U51(U41(U21(U21(isList)))))
isNeList#U51#(U41(U11(U42(isNeList))))isNeList#U41#(U11(U41(U21(U11(U41(isList))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U31(isQid))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(tt))))))))
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isNeList#U41#(U11(U51(U41(U11(U41(U11(isNeList)))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U51(isNeList)))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(tt))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U31(tt))))))))))))
isList#U21#(U21(U21(U11(U31(tt)))))isNeList#U41#(U22(U21(U22(isList))))
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isList#U21#(U21(U21(U21(U21(tt)))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U41(isList))))))))))))))))
isList#U21#(U21(U11(U51(U51(U52(U21(isList)))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U21(U11(isNeList))))))))))))))
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isNeList#U41#(U11(U41(U21(U21(U11(U41(U21(tt))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U51(U51(isNeList)))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U22(isList))))))))isNeList#isNeList#
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U31(isQid))))))))))))))isNeList#U51#(U41(U21(U11(U42(U41(U11(U41(isList))))))))
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isNeList#U51#(U51(U41(U21(U11(U51(tt))))))isNeList#U51#(U41(U11(U51(U51(isNeList)))))
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isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U41(U21(isList)))))))))))))))))))isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(tt))))))))
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isNeList#U51#(U41(U11(U41(U11(U41(U21(tt)))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(tt))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(tt)))))))))isList#U21#(U11(U41(U11(U41(isList)))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U21(isList)))))))))))isNeList#U51#(U41(U11(U41(U11(U41(U21(U21(isList))))))))
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isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U11(isNeList)))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U51(U41(isList)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U41(U21(U21(isList)))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U21(isList)))))))))))))
isNeList#U51#(U51(U41(U11(U42(isNeList)))))isList#U21#(U21(U21(U11(U41(isList)))))
isNeList#U51#(U41(U21(U11(U41(U11(U31(isQid)))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U31(tt))))))))))
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isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U41(U21(isList))))))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(tt))))))))
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isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U31(isQid)))))))))isNeList#U41#(U21(U21(U11(U41(isList)))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U41(isList)))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U31(isQid)))))))
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isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(tt)))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U11(isNeList)))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))isNeList#U41#(U11(U41(U21(U22(isList)))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U21(isList))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U51(isNeList)))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U41(isList)))))))))isList#U21#(U21(U11(U51(U41(isList)))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(U11(isNeList)))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U41(isList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U51(isNeList)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(tt)))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U21(tt)))))))))))))isList#U21#(U21(U21(U21(U21(U21(isList))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(tt)))))))isList#U21#(U21(U11(U51(U51(U52(U11(U41(isList))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U11(isNeList)))))))))))isNeList#U51#(U51(U41(U21(U11(U41(U11(U41(isList))))))))
isNeList#U51#(U41(U21(U11(U52(U21(isList))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))
isNeList#U51#(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))isNeList#U41#(U21(U11(U41(isList))))
isNeList#U51#(U51(U41(U11(U51(U41(isList))))))isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))
isNeList#U41#(U21(U21(U21(isList))))isNeList#U51#(U41(U21(U11(U51(U51(U31(isQid)))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U41(isList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U21(isList))))))))))))
isNeList#U51#(U41(U21(U21(isList))))isList#U21#(U11(U42(U51(U41(U21(tt))))))
isNeList#U41#(U11(U51(U41(U21(isList)))))isNeList#U51#(U41(U21(U11(U41(U11(U41(isList)))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U21(isList)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(tt)))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(tt))))))))))isNeList#U51#(U51(U51(isNeList)))
isList#U21#(U21(U11(U41(U11(U41(U22(U11(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(tt))))))))
isList#U21#(U21(U11(U41(U11(U41(tt))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U31(isQid)))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U31(tt))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U51(isNeList))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U22(U21(tt))))))))
isNeList#U51#(U41(tt))isNeList#U51#(U41(U11(U41(U21(U22(isList))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(tt)))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U51(isNeList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(tt)))))))))))))isNeList#U51#(U51(U41(U11(U41(U11(U31(tt)))))))
isNeList#U41#(U11(U41(U22(tt))))isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(tt)))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))isNeList#U51#(U41(U11(U51(U41(isList)))))
isList#U21#(U11(U42(U51(U41(U11(U51(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(tt))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(tt)))))))))))))))isList#U21#(U21(U11(U31(isQid))))
isNeList#U41#(U11(U41(U21(U11(U31(tt))))))isList#U21#(U21(U11(U41(U11(U41(U22(U21(isList))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U21(isList)))))))))))isNeList#U51#(U42(U41(U11(U51(isNeList)))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(tt)))))))))isNeList#U51#(U41(U11(U41(U21(tt)))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))isNeList#U41#(U11(U51(U41(U11(U51(isNeList))))))
isNeList#U41#(U22(U11(U41(tt))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isList#U21#(U21(U11(U51(U51(U52(U11(tt))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U21#(U21(U11(U51(U51(U52(tt)))))) 
Thus, the rule isList#U21#(U21(U11(U51(U51(U52(U11(tt))))))) is replaced by the following rules:
isList#U21#(U21(U11(U51(U51(U52(tt))))))

Problem 34: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isNeList#isList#isNeList#U51#(tt)
isList#isList#isNeList#U51#(U42(U41(U21(isList))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(isNeList)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U51(U31(tt))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(isNeList)))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U51(U31(tt))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U51(U31(isQid)))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U31(tt)))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(isNeList))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(isList)))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U42(isNeList))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(tt)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U51(U31(isQid))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(isList)))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U31(isQid)))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U41(isList))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U41(isList))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U51(U31(isQid))))))))))))))isList#U21#(U11(U42(U51(U51(isNeList)))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(isList)))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U41(isList))))))))))
isList#U21#(U21(U11(U41(U11(U51(U31(isQid)))))))isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(isNeList))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(isNeList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(isList))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(isList)))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(tt))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U21(U21(isList)))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U51(U41(isList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(tt)))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U22(isList))))))))))
isList#U21#(U21(U11(U41(U22(isList)))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U31(isQid))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U51(isNeList)))))))))isNeList#U51#(U41(U11(U41(U21(U21(U11(isNeList)))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U11(U51(isNeList)))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(isNeList))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U51(U51(isNeList)))))))))isNeList#U41#(U11(U41(U21(U21(U21(isList))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(isNeList)))))))))isList#U21#(U21(U11(U41(tt))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U11(U51(isNeList)))))))))))))isNeList#U51#(U41(U11(U41(U11(U51(isNeList))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(isNeList)))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U51(isNeList))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(tt))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(isList))))))))))
isNeList#U51#(U51(U41(U21(tt))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(tt)))))))))))
isList#U21#(U11(U42(U51(U41(U21(U21(tt)))))))U51#(tt)isList#
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U31(tt)))))))))isNeList#U51#(U51(U41(U11(U41(U21(isList))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U41(U21(U11(U31(isQid)))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(tt))))))))))
isList#U21#(U21(U11(U51(U51(U41(isList))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U21(isList))))))))))
isNeList#U41#(U11(U41(U22(U11(isNeList)))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U41(U11(isNeList))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(isNeList)))))))))))isNeList#U51#(U42(U42(isNeList)))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U21(U21(isList)))))))))))))isNeList#U51#(U51(U41(U21(U11(U31(isQid))))))
isNeList#U51#(U41(U21(U11(U41(U21(tt))))))isNeList#U51#(U41(U21(U11(U52(U11(U42(U31(tt))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U31(isQid)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U41(tt))))))))))))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U11(isNeList))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U31(tt))))))))
isList#U21#(U21(U11(U41(U21(U11(U42(U41(isList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U51(isNeList)))))))))))
isList#U21#(U11(U42(U51(U41(U21(U21(U11(isNeList))))))))isNeList#U41#(U11(U51(U42(U51(U31(isQid))))))
isList#U21#(U11(U42(U31(isQid))))isList#U21#(U21(U11(U41(U21(U11(U51(U51(isNeList))))))))
isNeList#U41#(U22(U22(isList)))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(tt))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U51(isNeList)))))))isNeList#U41#(U21(U21(U11(U31(tt)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U31(isQid))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U21(isList))))))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U51(U31(isQid)))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U11(U41(tt)))))))))))))isNeList#U41#(U21(tt))
isList#U21#(U21(U21(U11(U51(U41(U11(isNeList)))))))isNeList#U51#(U41(U11(U41(U11(U41(U21(U11(U41(isList)))))))))
isList#U21#(U21(U21(U11(U51(U51(isNeList))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U41(U21(isList))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(tt)))))))isNeList#U41#(U22(U21(U21(U21(isList)))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U21(isList)))))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(isList))))))))))))
isNeList#U41#(U11(U51(U41(U11(U41(U21(isList)))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U21(isList)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U22(tt))))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(U11(isNeList)))))))))))
U41#(tt)isNeList#isNeList#U41#(U11(U41(U21(U21(U11(U42(U51(isNeList))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U41(U11(isNeList))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(isNeList))))))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(tt))))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U31(isQid)))))))))isNeList#U41#(tt)
isNeList#U41#(U21(U21(tt)))isNeList#U51#(U51(U41(U21(U11(U42(isNeList))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U11(isNeList)))))))))))isList#U21#(U21(U22(isList)))
isNeList#U41#(U22(U21(U11(U51(U41(isList))))))isNeList#U51#(U41(U21(U11(U42(U41(tt))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U41(isList))))))))))))))isNeList#U41#(U21(U11(U51(isNeList))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U31(isQid)))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U11(isNeList))))))))))
isNeList#U41#(U22(U11(U51(isNeList))))isNeList#U41#(U11(U51(U51(isNeList))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U41(isList)))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U11(U31(tt)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(isList))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U31(isQid)))))))))))))
isNeList#U51#(U41(U21(U11(U42(U51(U31(isQid)))))))isNeList#U41#(U11(U41(U11(isNeList))))
isNeList#U51#(U41(U21(U11(U42(U51(U51(isNeList)))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U41(isList))))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U11(isNeList))))))))isList#U21#(U21(U11(U51(U52(isList)))))
isNeList#U51#(U41(U21(U11(U52(U11(U42(U51(isNeList))))))))isNeList#U51#(U41(U11(U41(U11(U31(tt))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(U21(U11(isNeList)))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(tt))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(tt)))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U11(U31(isQid))))))))))))))))
isList#U21#(U21(U21(U21(U11(U31(isQid))))))isNeList#U41#(U22(U21(U11(U41(tt)))))
isList#U21#(U21(U11(U51(U51(U52(U11(U51(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(isNeList))))))))))
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isList#U21#(U21(U11(U51(U41(isList)))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(U11(isNeList)))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U51(U31(isQid))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U41(isList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U51(isNeList)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(tt)))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U21(tt)))))))))))))isList#U21#(U21(U21(U21(U21(U21(isList))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(tt)))))))isList#U21#(U21(U11(U51(U51(U52(U11(U41(isList))))))))
isList#U21#(U21(U21(U21(U11(U51(U51(U41(U11(isNeList)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U11(isNeList)))))))))))
isNeList#U51#(U51(U41(U21(U11(U41(U11(U41(isList))))))))isNeList#U51#(U41(U21(U11(U52(U21(isList))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))isNeList#U51#(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))
isNeList#U41#(U21(U11(U41(isList))))isNeList#U51#(U51(U41(U11(U51(U41(isList))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))isNeList#U41#(U21(U21(U21(isList))))
isNeList#U51#(U41(U21(U11(U51(U51(U31(isQid)))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U21(isList))))))))))))isNeList#U51#(U41(U21(U21(isList))))
isList#U21#(U11(U42(U51(U41(U21(tt))))))isNeList#U41#(U11(U51(U41(U21(isList)))))
isNeList#U51#(U41(U21(U11(U41(U11(U41(isList)))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U21(isList)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(tt)))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(tt))))))))))
isNeList#U51#(U51(U51(isNeList)))isList#U21#(U21(U11(U41(U11(U41(U22(U11(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(tt))))))))isList#U21#(U21(U11(U41(U11(U41(tt))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U31(isQid)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U31(tt))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U51(isNeList))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U22(U21(tt))))))))isList#U21#(U21(U21(U21(U11(U51(U51(U42(isNeList))))))))
isNeList#U51#(U41(tt))isNeList#U51#(U41(U11(U41(U21(U22(isList))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(tt)))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U51(isNeList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(tt)))))))))))))
isNeList#U51#(U51(U41(U11(U41(U11(U31(tt)))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U21(U11(isNeList)))))))))))
isNeList#U41#(U11(U41(U22(tt))))isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(tt)))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))isNeList#U51#(U41(U11(U51(U41(isList)))))
isList#U21#(U11(U42(U51(U41(U11(U51(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(tt))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(tt)))))))))))))))isList#U21#(U21(U11(U31(isQid))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U51(isNeList))))))))))))))isNeList#U41#(U11(U41(U21(U11(U31(tt))))))
isNeList#U51#(U42(U41(U11(U41(U11(tt))))))isList#U21#(U21(U11(U41(U11(U41(U22(U21(isList))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U21(isList)))))))))))isNeList#U51#(U42(U41(U11(U51(isNeList)))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(tt)))))))))isNeList#U51#(U41(U11(U41(U21(tt)))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))isNeList#U41#(U11(U51(U41(U11(U51(isNeList))))))
isNeList#U41#(U22(U11(U41(tt))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U51#(U42(U41(U21(isList)))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(U42(U41(U21(U11(isNeList))))) 
U51#(U42(U41(U21(tt)))) 
U51#(U42(U41(U21(U21(isList))))) 
Thus, the rule isNeList#U51#(U42(U41(U21(isList)))) is replaced by the following rules:
isNeList#U51#(U42(U41(U21(tt))))isNeList#U51#(U42(U41(U21(U21(isList)))))
isNeList#U51#(U42(U41(U21(U11(isNeList)))))

Problem 35: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isNeList#isList#isNeList#U51#(tt)
isList#isList#isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U11(U31(isQid))))))))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(isList)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U31(isQid))))))))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U41(isList))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U31(isQid)))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(isList))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U41(isList))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U51(U31(isQid))))))))))))))isList#U21#(U11(U42(U51(U51(isNeList)))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(isList)))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U41(isList))))))))))
isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(isNeList))))))))isList#U21#(U21(U11(U41(U11(U51(U31(isQid)))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(isNeList))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(isList)))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(isList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(tt))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U21(U21(isList)))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U51(U41(isList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(tt)))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U22(isList))))))))))
isList#U21#(U21(U11(U41(U22(isList)))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U31(isQid))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U51(isNeList)))))))))isNeList#U51#(U41(U11(U41(U21(U21(U11(isNeList)))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U11(U51(isNeList)))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U51(U41(isList)))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(isNeList))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U51(U51(isNeList)))))))))
isNeList#U41#(U11(U41(U21(U21(U21(isList))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(isNeList)))))))))
isList#U21#(U21(U11(U41(tt))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U11(U51(isNeList)))))))))))))
isNeList#U51#(U41(U11(U41(U11(U51(isNeList))))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(isNeList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(isList))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(tt))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U42(U51(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(tt)))))))))))
isNeList#U51#(U51(U41(U21(tt))))U51#(tt)isList#
isList#U21#(U11(U42(U51(U41(U21(U21(tt)))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U41(isList))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U31(tt)))))))))isNeList#U51#(U51(U41(U11(U41(U21(isList))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U41(U21(U11(U31(isQid)))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(tt))))))))))
isList#U21#(U21(U11(U51(U51(U41(isList))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U21(isList))))))))))
isNeList#U41#(U11(U41(U22(U11(isNeList)))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U41(U11(isNeList))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(U31(tt))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(isNeList)))))))))))
isNeList#U51#(U42(U42(isNeList)))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U21(U21(isList)))))))))))))
isNeList#U51#(U51(U41(U21(U11(U31(isQid))))))isNeList#U51#(U41(U21(U11(U41(U21(tt))))))
isNeList#U51#(U41(U21(U11(U52(U11(U42(U31(tt))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U31(isQid)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U41(tt))))))))))))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U11(isNeList))))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U31(tt))))))))isList#U21#(U21(U11(U41(U21(U11(U42(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U51(isNeList)))))))))))isList#U21#(U11(U42(U51(U41(U21(U21(U11(isNeList))))))))
isNeList#U41#(U11(U51(U42(U51(U31(isQid))))))isList#U21#(U11(U42(U31(isQid))))
isList#U21#(U21(U11(U41(U21(U11(U51(U51(isNeList))))))))isNeList#U41#(U22(U22(isList)))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(tt))))))))))))isList#U21#(U21(U11(U51(U51(U51(U51(isNeList)))))))
isNeList#U41#(U21(U21(U11(U31(tt)))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U31(isQid))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U21(isList))))))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U51(U31(isQid)))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U11(U41(tt)))))))))))))
isNeList#U41#(U21(tt))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(tt)))))))))
isList#U21#(U21(U21(U11(U51(U41(U11(isNeList)))))))isNeList#U51#(U41(U11(U41(U11(U41(U21(U11(U41(isList)))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U11(isNeList)))))))))))))isList#U21#(U21(U21(U11(U51(U51(isNeList))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U41(U21(isList))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(tt)))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U21(isList)))))))))))))))isNeList#U41#(U22(U21(U21(U21(isList)))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(isList))))))))))))isNeList#U41#(U11(U51(U41(U11(U41(U21(isList)))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U22(tt))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U21(isList)))))))))
U41#(tt)isNeList#isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(U11(isNeList)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U51(isNeList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(U11(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(isNeList))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(tt))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U31(isQid)))))))))
isNeList#U41#(tt)isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(isList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(U11(U51(isNeList))))))))))))))))isNeList#U41#(U21(U21(tt)))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U51(tt)))))))))isNeList#U51#(U51(U41(U21(U11(U42(isNeList))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U11(isNeList)))))))))))isList#U21#(U21(U22(isList)))
isNeList#U41#(U22(U21(U11(U51(U41(isList))))))isNeList#U51#(U41(U21(U11(U42(U41(tt))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U41(isList))))))))))))))isNeList#U41#(U21(U11(U51(isNeList))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U31(isQid)))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U11(isNeList))))))))))
isNeList#U41#(U22(U11(U51(isNeList))))isNeList#U41#(U11(U51(U51(isNeList))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U41(isList)))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U11(U31(tt)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(isList))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U31(isQid)))))))))))))
isNeList#U51#(U41(U21(U11(U42(U51(U31(isQid)))))))isNeList#U41#(U11(U41(U11(isNeList))))
isNeList#U51#(U41(U21(U11(U42(U51(U51(isNeList)))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U41(isList))))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U11(isNeList))))))))isList#U21#(U21(U11(U51(U52(isList)))))
isNeList#U51#(U41(U21(U11(U52(U11(U42(U51(isNeList))))))))isNeList#U51#(U41(U11(U41(U11(U31(tt))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(U21(U11(isNeList)))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(tt))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(tt)))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U11(U31(isQid))))))))))))))))
isList#U21#(U21(U21(U21(U11(U31(isQid))))))isNeList#U41#(U22(U21(U11(U41(tt)))))
isList#U21#(U21(U11(U51(U51(U52(U11(U51(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(isNeList))))))))))
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isNeList#U41#(U11(U51(U41(U11(U42(U51(isNeList)))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U41(isList))))))))))))
isNeList#U41#(U11(U41(U22(U21(U21(U11(U31(tt))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U21(U11(isNeList))))))))))))))))))
isNeList#U41#(U22(U11(U41(U11(isNeList)))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U51(U31(isQid)))))))))))isNeList#U41#(U11(U51(U31(isQid))))
isList#U21#(U21(U21(U21(U11(U51(U51(U31(isQid))))))))isList#U21#(U21(U11(U41(U21(U11(U51(U41(isList))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U41(U11(isNeList))))))))))))isList#U21#(U21(U21(U21(U21(U11(isNeList))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U42(U41(isList)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U31(isQid))))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(tt)))))))))isList#U21#(U21(U11(U41(U21(U21(isList))))))
isNeList#U41#(U22(U11(U41(U21(isList)))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U51(U51(isNeList))))))))))))))
isNeList#U51#(U51(U41(U11(U31(isQid)))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U21(tt)))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(tt))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U22(isList))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U11(isNeList)))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U31(isQid)))))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U31(isQid)))))))isList#U21#(U21(U21(U21(U11(U41(U11(U31(isQid))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(tt)))))))isNeList#U41#(U22(U21(U11(U51(U31(tt))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U22(U21(isList)))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U41(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U41(isList)))))))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U51(U41(isList))))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U31(tt))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U31(tt))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U51(isNeList))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U51(U51(isNeList))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U31(tt)))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U31(isQid)))))))))))
isNeList#U51#(U41(U21(U11(U42(U41(U21(isList)))))))isNeList#U51#(U42(U41(U11(U31(isQid)))))
isNeList#U51#(U41(U11(U51(U31(tt)))))isList#U21#(U21(U11(U41(U21(U11(U42(U31(isQid))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U42(U42(isNeList))))))))isNeList#U51#(U41(U21(U11(U42(U51(U41(isList)))))))
isList#U21#(U21(U11(U41(U11(U41(U11(U51(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(tt))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U41(isList))))))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U21(isList))))))))
isNeList#U51#(U51(U41(tt)))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U11(isNeList))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(tt)))))))))))))isNeList#U51#(U41(U21(U11(U42(U41(U11(U51(isNeList))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U41(tt))))))))))))))isNeList#U51#(U42(U51(U41(isList))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(tt)))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U11(isNeList)))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(U21(U11(isNeList))))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))
isNeList#U41#(U11(U41(U21(U22(isList)))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U21(isList))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U51(isNeList)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(tt))))))))))))
isNeList#U51#(U51(U41(U21(U11(U41(U21(U11(U31(isQid)))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U41(isList)))))))))
isList#U21#(U21(U11(U51(U41(isList)))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(U11(isNeList)))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U51(U31(isQid))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U41(isList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U51(isNeList)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(tt)))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U21(tt)))))))))))))isList#U21#(U21(U21(U21(U21(U21(isList))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(tt)))))))isList#U21#(U21(U11(U51(U51(U52(U11(U41(isList))))))))
isList#U21#(U21(U21(U21(U11(U51(U51(U41(U11(isNeList)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U41(U11(U41(isList))))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U11(isNeList)))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(U11(isNeList))))))))))))))
isNeList#U51#(U51(U41(U21(U11(U41(U11(U41(isList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(U21(tt)))))))))))))
isNeList#U51#(U41(U21(U11(U52(U21(isList))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))
isNeList#U51#(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(U11(isNeList)))))))))))))
isNeList#U41#(U21(U11(U41(isList))))isNeList#U51#(U51(U41(U11(U51(U41(isList))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))isNeList#U41#(U21(U21(U21(isList))))
isNeList#U51#(U41(U21(U11(U51(U51(U31(isQid)))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U21(isList))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U31(isQid))))))))))))
isNeList#U51#(U41(U21(U21(isList))))isList#U21#(U11(U42(U51(U41(U21(tt))))))
isNeList#U41#(U11(U51(U41(U21(isList)))))isNeList#U51#(U41(U21(U11(U41(U11(U41(isList)))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U21(isList)))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U51(isNeList)))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(tt)))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(tt))))))))))
isNeList#U51#(U51(U51(isNeList)))isList#U21#(U21(U11(U41(U11(U41(U22(U11(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(tt))))))))isList#U21#(U21(U11(U41(U11(U41(tt))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U31(isQid)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U31(tt))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U51(isNeList))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U22(U21(tt))))))))isList#U21#(U21(U21(U21(U11(U51(U51(U42(isNeList))))))))
isNeList#U51#(U41(tt))isNeList#U51#(U41(U11(U41(U21(U22(isList))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(tt)))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U51(isNeList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(tt)))))))))))))
isNeList#U51#(U51(U41(U11(U41(U11(U31(tt)))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U21(U11(isNeList)))))))))))
isNeList#U41#(U11(U41(U22(tt))))isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(tt)))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U51(isNeList))))))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))
isNeList#U51#(U41(U11(U51(U41(isList)))))isList#U21#(U11(U42(U51(U41(U11(U51(U51(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(tt))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(tt)))))))))))))))
isList#U21#(U21(U11(U31(isQid))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U51(isNeList))))))))))))))
isNeList#U41#(U11(U41(U21(U11(U31(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(tt))))))
isList#U21#(U21(U11(U41(U11(U41(U22(U21(isList))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U21(isList)))))))))))
isNeList#U51#(U42(U41(U11(U51(isNeList)))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(tt)))))))))
isNeList#U51#(U41(U11(U41(U21(tt)))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))
isNeList#U41#(U11(U51(U41(U11(U51(isNeList))))))isNeList#U41#(U22(U11(U41(tt))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U11(U31(isQid)))))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U11(U31(tt)))))))))))))))))) 
Thus, the rule isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U11(U31(isQid)))))))))))))))))) is replaced by the following rules:
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U11(U31(tt))))))))))))))))))

Problem 36: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isNeList#isList#isNeList#U51#(tt)
isList#isList#isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(isList))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U41(isList))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(isList))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(isList)))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(tt))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(tt))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U21(U21(isList)))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U51(U41(isList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(tt)))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U22(isList))))))))))isList#U21#(U21(U11(U41(U22(isList)))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U31(isQid))))))))))isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U51(U51(isNeList))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U11(U51(isNeList)))))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U51(isNeList)))))))))
isNeList#U51#(U41(U11(U41(U21(U21(U11(isNeList)))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(tt)))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U51(U41(isList)))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U51(U51(isNeList)))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(isNeList))))))))))))isNeList#U41#(U11(U41(U21(U21(U21(isList))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(isNeList)))))))))isList#U21#(U21(U11(U41(tt))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U11(U51(isNeList)))))))))))))isNeList#U51#(U41(U11(U41(U11(U51(isNeList))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(isNeList)))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(tt)))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(isList))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(tt))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U42(U51(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(tt)))))))))))
isNeList#U51#(U51(U41(U21(tt))))U51#(tt)isList#
isList#U21#(U11(U42(U51(U41(U21(U21(tt)))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U41(isList))))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U41(U11(isNeList)))))))))))))isList#U21#(U21(U11(U41(U11(U51(U31(tt)))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U31(tt)))))))))isNeList#U51#(U51(U41(U11(U41(U21(isList))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U41(U21(U11(U31(isQid)))))))))))))isList#U21#(U21(U11(U51(U51(U41(isList))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(tt))))))))))isNeList#U41#(U11(U41(U22(U11(isNeList)))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U21(isList))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U41(U11(isNeList))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(U31(tt))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(isNeList)))))))))))
isNeList#U51#(U42(U42(isNeList)))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U41(isList)))))))))))
isList#U21#(U11(U42(U51(U51(U51(U41(isList)))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U21(U21(isList)))))))))))))
isNeList#U51#(U51(U41(U21(U11(U31(isQid))))))isNeList#U51#(U41(U21(U11(U41(U21(tt))))))
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isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(U11(isNeList)))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U51(U31(isQid))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U41(isList)))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U51(isNeList)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(tt)))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U21(tt)))))))))))))
isList#U21#(U21(U21(U21(U21(U21(isList))))))isNeList#U41#(U22(U21(U11(U51(U51(U41(tt)))))))
isList#U21#(U21(U11(U51(U51(U52(U11(U41(isList))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U31(isQid)))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U51(U41(U11(isNeList)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U41(U11(U41(isList))))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U11(isNeList)))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(U11(isNeList))))))))))))))
isNeList#U51#(U51(U41(U21(U11(U41(U11(U41(isList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(U21(tt)))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U41(U11(isNeList)))))))))))))isNeList#U51#(U41(U21(U11(U52(U21(isList))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))isNeList#U51#(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(U11(isNeList)))))))))))))isNeList#U41#(U21(U11(U41(isList))))
isNeList#U51#(U51(U41(U11(U51(U41(isList))))))isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))
isNeList#U41#(U21(U21(U21(isList))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U31(isQid)))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U21(isList))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U31(isQid))))))))))))
isNeList#U51#(U41(U21(U21(isList))))isList#U21#(U11(U42(U51(U41(U21(tt))))))
isNeList#U41#(U11(U51(U41(U21(isList)))))isNeList#U51#(U41(U21(U11(U41(U11(U41(isList)))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U21(isList)))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U51(isNeList)))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(tt)))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(tt))))))))))
isNeList#U51#(U51(U51(isNeList)))isList#U21#(U21(U11(U41(U11(U41(U22(U11(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(tt))))))))isList#U21#(U21(U11(U41(U11(U41(tt))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U31(isQid)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U31(tt))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U51(isNeList))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U22(U21(tt))))))))isList#U21#(U21(U21(U21(U11(U51(U51(U42(isNeList))))))))
isNeList#U51#(U41(tt))isNeList#U51#(U41(U11(U41(U21(U22(isList))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(tt)))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U51(isNeList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(tt)))))))))))))
isNeList#U51#(U51(U41(U11(U41(U11(U31(tt)))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U21(U11(isNeList)))))))))))
isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U51(tt)))))))))isNeList#U41#(U11(U41(U22(tt))))
isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(tt)))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(U11(isNeList))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U51(isNeList))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))isNeList#U51#(U41(U11(U51(U41(isList)))))
isList#U21#(U11(U42(U51(U41(U11(U51(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(tt))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(tt)))))))))))))))isList#U21#(U21(U11(U31(isQid))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U51(isNeList))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U31(tt)))))))))
isNeList#U41#(U11(U41(U21(U11(U31(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(tt))))))
isList#U21#(U21(U11(U41(U11(U41(U22(U21(isList))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U21(isList)))))))))))
isNeList#U51#(U42(U41(U11(U51(isNeList)))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(tt)))))))))
isNeList#U51#(U41(U11(U41(U21(tt)))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U11(tt)))))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))isNeList#U41#(U11(U51(U41(U11(U51(isNeList))))))
isNeList#U41#(U22(U11(U41(tt))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U41(U21(isList)))))))))))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(isList)))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(U11(isNeList))))))))))))))) 
U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(U21(isList))))))))))))))) 
U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(tt)))))))))))))) 
Thus, the rule isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(isList)))))))))))))) is replaced by the following rules:
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(U21(isList)))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(tt))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(U11(isNeList)))))))))))))))

Problem 37: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(isList))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(tt)))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U41(isList))))))))))isList#U21#(U21(U11(U41(U11(U51(U31(tt)))))))
isList#U21#(U21(U11(U51(U51(U41(isList))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U21(isList))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U41(U11(isNeList))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U51(U31(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(isNeList)))))))))))isNeList#U51#(U42(U42(isNeList)))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U41(isList)))))))))))isNeList#U51#(U41(U21(U11(U52(U11(U42(U31(tt))))))))
isNeList#U51#(U51(U41(U21(U11(U31(isQid))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U41(tt))))))))))))))))))
isList#U21#(U21(U11(U41(U21(U11(U42(U41(isList))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U31(tt))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U51(isNeList)))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(U11(isNeList)))))))))
isList#U21#(U11(U42(U51(U41(U21(U21(U11(isNeList))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U51(U31(isQid)))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(tt))))))))))))isList#U21#(U21(U11(U41(U21(U11(U51(U51(isNeList))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(tt))))))))))))isNeList#U41#(U21(U21(U11(U31(tt)))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U21(isList))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))))))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U51(U31(isQid)))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U21(U11(U31(isQid)))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U22(isList)))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(tt)))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U22(isList))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U21(isList))))))))))))
isList#U21#(U21(U21(U11(U51(U51(isNeList))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(tt)))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U41(U21(isList))))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U21(isList)))))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(isList))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U21(isList)))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(isNeList))))))))isNeList#U41#(tt)
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(isList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(U11(U51(isNeList))))))))))))))))
isNeList#U41#(U21(U21(tt)))isList#U21#(U21(U22(isList)))
isNeList#U41#(U22(U21(U11(U51(U41(isList))))))isNeList#U51#(U41(U21(U11(U42(U41(tt))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U41(isList))))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U31(tt))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U31(isQid)))))))))))isNeList#U41#(U22(U11(U51(isNeList))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U41(isList)))))))))))isNeList#U41#(U11(U51(U51(isNeList))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(isList))))))))))))isNeList#U51#(U41(U21(U11(U42(U51(U31(isQid)))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U11(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U41(isList))))))))))))))
isList#U21#(U21(U11(U51(U52(isList)))))isNeList#U51#(U41(U11(U41(U11(U31(tt))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U41(U11(isNeList)))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(tt)))))))
isList#U21#(U21(U21(U21(U11(U31(isQid))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(isNeList))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(isNeList))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U31(isQid))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U21(isList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U31(isQid))))))))))))))))
isNeList#U51#(U41(U21(U11(U52(U11(U31(isQid)))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U31(tt)))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(isList)))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U51(U41(tt)))))))))))))))
isList#U21#(U21(U21(U21(U11(U41(U11(U51(isNeList))))))))isNeList#U41#(U11(U51(U42(U51(U51(isNeList))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(tt)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(tt))))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(U11(isNeList))))))))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U51(U51(U51(U41(U21(isList)))))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U21(U11(U51(isNeList)))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(U21(isList)))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(U51(isNeList)))))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U31(isQid))))))))
isNeList#U41#(U11(U41(U21(U11(U41(isList))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U31(tt)))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U21(isList)))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(tt))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U51(isNeList)))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U11(isNeList))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(isList))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U51(U51(isNeList))))))))))
isList#U21#(U11(U42(U51(U41(U21(U21(U21(U21(U11(isNeList))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U41(U21(isList)))))))))))))))
isNeList#U51#(U42(U41(U21(U11(isNeList)))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U11(U51(isNeList))))))))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(tt))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U31(tt)))))))))))
isList#U21#(U21(tt))isList#U21#(U21(U11(U41(U21(U11(U31(isQid)))))))
isNeList#U41#(U11(U51(U42(U41(isList)))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U51(isNeList))))))))))
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isNeList#U51#(U41(U11(U41(U11(U41(U21(U11(U51(U51(isNeList))))))))))isNeList#U41#(U11(U41(U22(U21(U21(U11(U31(tt))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U51(U31(isQid))))))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))))
isNeList#U41#(U22(U11(U41(U11(isNeList)))))isList#U21#(U21(U21(U21(U11(U51(U51(U31(isQid))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(U21(isList)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U51(U31(isQid)))))))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U42(U41(isList)))))))))isList#U21#(U21(U21(U21(U21(U11(isNeList))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U41(U11(isNeList))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U31(isQid))))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(tt)))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U21(tt)))))))))
isNeList#U51#(U51(U41(U11(U31(isQid)))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U51(U51(isNeList))))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U31(isQid)))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(tt)))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U41(U21(isList))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U22(U21(isList)))))))))))))
isList#U21#(U21(U11(U42(isNeList))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U51(U41(isList))))))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U31(tt))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U31(tt))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U51(isNeList))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U51(U51(isNeList))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U31(tt)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U42(isNeList))))))))
isList#U21#(U21(U11(U41(U21(U11(U42(U31(isQid))))))))isList#U21#(U21(U11(U41(U11(U41(U11(U51(isNeList))))))))
isNeList#U51#(U41(U21(U11(U42(U51(U41(isList)))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U11(isNeList))))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U21(isList))))))))
isNeList#U51#(U41(U21(U11(U42(U41(U11(U51(isNeList))))))))isNeList#U51#(U42(U51(U41(isList))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(tt)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U51(U51(isNeList))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(U21(U11(isNeList))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U11(isNeList)))))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U11(U51(U31(isQid))))))))))))))isList#U21#(U11(U42(U51(U51(U41(U11(isNeList)))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U21(isList))))))))isNeList#U41#(U11(U41(U21(U22(isList)))))
isNeList#U51#(U41(U11(U41(U21(U21(U11(U51(isNeList))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U51(isNeList)))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(tt))))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U41(U21(isList)))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U41(isList)))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U41(isList)))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U51(U31(isQid))))))))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U41(isList))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U21(tt)))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(tt)))))))))))))
isList#U21#(U21(U21(U21(U21(U21(isList))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U41(U21(isList)))))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U41(U11(isNeList)))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(U21(tt)))))))))))))
isNeList#U51#(U51(U41(U21(U11(U41(U11(U41(isList))))))))isNeList#U51#(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))
isNeList#U51#(U41(U21(U11(U52(U21(isList))))))isNeList#U41#(U21(U21(U21(isList))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U21(isList))))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U41(isList))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U31(isQid)))))))isNeList#U51#(U41(U21(U21(isList))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U22(U21(isList)))))))))))isNeList#U41#(U11(U51(U41(U21(isList)))))
isNeList#U51#(U41(U21(U11(U41(U11(U41(isList)))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U21(isList)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(tt)))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U31(isQid)))))))))))))
isNeList#U51#(U51(U51(isNeList)))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(tt))))))))
isList#U21#(U21(U11(U41(U11(U41(U22(U11(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U31(tt))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U31(isQid)))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U51(isNeList))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U22(U21(tt))))))))isNeList#U51#(U41(U11(U41(U21(U21(U11(U31(isQid))))))))
isNeList#U51#(U41(tt))isNeList#U41#(U22(U21(U11(U41(U11(U41(tt)))))))
isNeList#U51#(U41(U11(U41(U21(U22(isList))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U51(isNeList))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U21(U11(isNeList)))))))))))isNeList#U51#(U51(U41(U11(U41(U11(U31(tt)))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(tt)))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U51(isNeList))))))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(tt))))))))))
isList#U21#(U21(U11(U31(isQid))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U31(tt)))))))))
isList#U21#(U21(U11(U41(U11(U41(U22(U21(isList))))))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(tt)))))))))
isNeList#U51#(U41(U11(U41(U21(tt)))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U11(tt)))))))))))))))))
isNeList#U41#(U11(U51(U41(U11(U51(isNeList))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U51(U51(isNeList)))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U51(U41(isList))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U51(U41(isList)))))))))
isNeList#isList#isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U11(U51(U41(isList))))))))))))))
isNeList#U51#(tt)isList#isList#
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U51(U41(U11(isNeList))))))))))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U51(U31(isQid))))))))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U51(U51(U41(isList)))))))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U11(U51(U51(isNeList))))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U51(U51(isNeList)))))))))isNeList#U41#(U11(U41(U21(U21(U21(isList))))))
isNeList#U51#(U41(U11(U41(U11(U51(isNeList))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U11(U51(isNeList)))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(tt)))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(tt))))))))
isNeList#U51#(U51(U41(U21(tt))))isList#U21#(U11(U42(U51(U41(U21(U21(tt)))))))
U51#(tt)isList#isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U41(U11(isNeList)))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U31(tt)))))))))isNeList#U51#(U51(U41(U11(U41(U21(isList))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U41(U21(U11(U31(isQid)))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(tt))))))))))
isNeList#U41#(U11(U41(U22(U11(isNeList)))))isList#U21#(U11(U42(U51(U51(U51(U41(isList)))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U21(U21(isList)))))))))))))isNeList#U51#(U41(U21(U11(U41(U21(tt))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U11(isNeList))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U31(isQid)))))))))))
isNeList#U41#(U11(U51(U42(U51(U31(isQid))))))isList#U21#(U11(U42(U31(isQid))))
isNeList#U41#(U22(U22(isList)))isList#U21#(U21(U11(U51(U51(U51(U51(isNeList)))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U31(isQid))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U31(isQid))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U51(U51(isNeList)))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U11(U41(tt)))))))))))))
isNeList#U41#(U21(tt))isList#U21#(U21(U21(U11(U51(U41(U11(isNeList)))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U51(isNeList)))))))))isNeList#U51#(U41(U11(U41(U11(U41(U21(U11(U41(isList)))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U11(isNeList)))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U41(U21(isList)))))))))))))
isNeList#U41#(U22(U21(U21(U21(isList)))))isList#U21#(U21(U11(U41(U22(U11(isNeList))))))
isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U41(U21(isList))))))))))isNeList#U41#(U11(U51(U41(U11(U41(U21(isList)))))))
U41#(tt)isNeList#isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(U11(isNeList)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U22(tt))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U51(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U11(U41(U11(isNeList))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(tt))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U31(isQid)))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U51(tt)))))))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U51(U51(U51(U41(U11(isNeList)))))))))))))))))
isNeList#U51#(U51(U41(U21(U11(U42(isNeList))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U11(isNeList)))))))))))
isNeList#U41#(U21(U11(U51(isNeList))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U11(isNeList))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U11(U31(tt)))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U31(isQid)))))))))))))
isNeList#U41#(U11(U41(U11(isNeList))))isNeList#U51#(U41(U21(U11(U42(U51(U51(isNeList)))))))
isNeList#U51#(U41(U21(U11(U52(U11(U42(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(U21(U11(isNeList)))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(tt))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U11(U31(isQid))))))))))))))))
isNeList#U41#(U22(U21(U11(U41(tt)))))isList#U21#(U21(U11(U51(U51(U52(U11(U51(isNeList))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U21(U11(U41(isList)))))))))))))))isNeList#U51#(U41(U21(U11(U41(U11(U51(isNeList)))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U21(isList)))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U51(U41(isList))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U51(U51(isNeList)))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U22(isList))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U41(U21(tt)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U51(isNeList))))))))))))))
isNeList#U41#(U22(U21(U21(U11(isNeList)))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U41(isList))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U11(isNeList))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(U21(isList))))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U31(isQid)))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U51(U51(isNeList))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U11(U31(isQid)))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U41(U11(isNeList)))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U21(U21(isList))))))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U31(tt))))))))))))))
isNeList#U51#(U51(U41(U21(U11(U51(U51(U41(isList))))))))isList#U21#(U21(U11(U51(tt))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U51(U31(tt))))))))))))isNeList#U41#(U22(U21(U11(U31(isQid)))))
isNeList#U51#(U51(U41(U21(U21(isList)))))isNeList#U51#(U41(U11(U42(isNeList))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U11(isNeList)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U11(isNeList))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U51(U41(tt))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U51(U51(isNeList))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U31(isQid))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U41(U11(isNeList)))))))))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U41(isList))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U21(U21(isList))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U31(isQid))))))))))))))isList#U21#(U11(U42(U51(U41(U21(U21(U21(tt))))))))
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isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U51(U51(isNeList))))))))))))))isNeList#U41#(U11(U41(U22(U21(U22(U21(isList)))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U51(isNeList)))))))))))isList#U21#(U11(U41(U11(U31(isQid)))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U51(U51(isNeList))))))))))isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U31(tt)))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U31(isQid))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U22(isList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U42(isNeList)))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U11(isNeList)))))))))
isNeList#U51#(U41(U11(U41(U11(U41(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))
isList#U21#(U11(U42(U51(U41(U21(U11(isNeList)))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U51(U51(isNeList))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U41(isList)))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U21(isList))))))))
isList#U21#(U21(U11(U41(U21(U11(U42(U51(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U11(U41(U21(isList))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U41(isList))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U21(isList)))))))))
isNeList#U51#(U41(U11(U41(U21(U21(U21(isList)))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U21(isList))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U42(U31(isQid))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U41(isList))))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U11(U41(isList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(U21(isList)))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(U21(isList)))))))))))))))isNeList#U51#(U51(U41(U11(U41(U11(U41(isList)))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U41(isList))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U41(isList))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U21(U11(isNeList))))))))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U51(U31(isQid)))))))))))
isNeList#U41#(U11(U51(U31(isQid))))isList#U21#(U21(U11(U41(U21(U11(U51(U41(isList))))))))
isList#U21#(U21(U11(U41(U21(U21(isList))))))isNeList#U41#(U22(U11(U41(U21(isList)))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(tt))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U22(isList))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U11(isNeList)))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U31(isQid)))))))))))))))
isList#U21#(U21(U21(U21(U11(U41(U11(U31(isQid))))))))isNeList#U41#(U22(U21(U11(U51(U31(tt))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U41(isList)))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U41(isList)))))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U31(tt)))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U31(isQid)))))))))))
isNeList#U51#(U41(U21(U11(U42(U41(U21(isList)))))))isNeList#U51#(U42(U41(U11(U31(isQid)))))
isNeList#U51#(U41(U11(U51(U31(tt)))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U41(isList))))))))))))
isNeList#U51#(U51(U41(tt)))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(tt)))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U41(tt))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U41(isList))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(U21(isList))))))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U41(isList))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U51(U41(isList)))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U21(isList))))))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U42(isNeList)))))))))))
isNeList#U51#(U51(U41(U21(U11(U41(U21(U11(U31(isQid)))))))))isList#U21#(U21(U11(U51(U41(isList)))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(U11(isNeList)))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U51(isNeList)))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(tt)))))))isList#U21#(U21(U11(U51(U51(U52(U11(U41(isList))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U31(isQid)))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U51(U41(U11(isNeList)))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U41(U11(U41(isList))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U11(isNeList)))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(U11(isNeList))))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(U11(isNeList)))))))))))))isNeList#U41#(U21(U11(U41(isList))))
isNeList#U51#(U51(U41(U11(U51(U41(isList))))))isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U31(isQid))))))))))))
isList#U21#(U11(U42(U51(U41(U21(tt))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U51(isNeList)))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(tt))))))))))isList#U21#(U21(U11(U41(U11(U41(tt))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))isList#U21#(U21(U21(U21(U11(U51(U51(U42(isNeList))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(tt)))))))))))))
isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U51(tt)))))))))isNeList#U41#(U11(U41(U22(tt))))
isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(U11(isNeList))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))isNeList#U51#(U41(U11(U51(U41(isList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(tt)))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U51(isNeList))))))))))))))
isNeList#U41#(U11(U41(U21(U11(U31(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(tt))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U21(isList)))))))))))isNeList#U51#(U42(U41(U11(U51(isNeList)))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))isNeList#U41#(U22(U11(U41(tt))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U41(U21(isList)))))))))))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(isList)))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(U21(isList))))))))))) 
U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(tt)))))))))) 
U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(U11(isNeList))))))))))) 
Thus, the rule isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(isList)))))))))) is replaced by the following rules:
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(tt))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(U11(isNeList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(U21(isList)))))))))))

Problem 38: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(isNeList)))))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U21(U11(U31(isQid)))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U22(isList)))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(tt)))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U22(isList))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U21(isList))))))))))))
isList#U21#(U21(U21(U11(U51(U51(isNeList))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(tt)))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U41(U21(isList))))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U21(isList)))))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(isList))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U21(isList)))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(isList))))))))))
isNeList#U41#(tt)isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(U11(U51(isNeList))))))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U41(tt))))))))))isNeList#U41#(U21(U21(tt)))
isList#U21#(U21(U22(isList)))isNeList#U41#(U22(U21(U11(U51(U41(isList))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U41(isList))))))))))))))isNeList#U51#(U41(U21(U11(U42(U41(tt))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U31(tt))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U31(isQid)))))))))))
isNeList#U41#(U22(U11(U51(isNeList))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U41(isList)))))))))))
isNeList#U41#(U11(U51(U51(isNeList))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(isList))))))))))))
isNeList#U51#(U41(U21(U11(U42(U51(U31(isQid)))))))isList#U21#(U21(U11(U51(U51(U51(U41(U11(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U41(isList))))))))))))))isList#U21#(U21(U11(U51(U52(isList)))))
isNeList#U51#(U41(U11(U41(U11(U31(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U41(U11(isNeList)))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(tt)))))))isList#U21#(U21(U21(U21(U11(U31(isQid))))))
isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(isNeList))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(isNeList))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U31(isQid))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U21(isList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U31(isQid))))))))))))))))isNeList#U51#(U41(U21(U11(U52(U11(U31(isQid)))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U31(tt)))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(isList)))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U51(U41(tt)))))))))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U51(isNeList))))))))
isNeList#U41#(U11(U51(U42(U51(U51(isNeList))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(tt)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(tt))))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(U11(isNeList))))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U51(U51(U51(U41(U21(isList)))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U21(U11(U51(isNeList)))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(U21(isList)))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(U51(isNeList)))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U31(isQid))))))))isNeList#U41#(U11(U41(U21(U11(U41(isList))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U31(tt)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U21(isList)))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(tt))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U51(isNeList)))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(isNeList))))))))isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U11(isNeList))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(isList))))))))))
isList#U21#(U21(U11(U41(U21(U11(U42(U41(U21(U11(isNeList))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U51(U51(isNeList))))))))))
isList#U21#(U11(U42(U51(U41(U21(U21(U21(U21(U11(isNeList))))))))))isList#U21#(U21(U11(U41(U21(U11(U51(U51(U41(U11(isNeList))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U41(U21(isList)))))))))))))))isNeList#U51#(U42(U41(U21(U11(isNeList)))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U11(U51(isNeList))))))))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(tt))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U31(tt)))))))))))isList#U21#(U21(tt))
isNeList#U41#(U11(U51(U42(U41(isList)))))isList#U21#(U21(U11(U41(U21(U11(U31(isQid)))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U51(isNeList))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U51(U51(isNeList))))))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U21(isList))))))))isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(U11(U41(isList))))))))))
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isList#isList#isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(U41(isList))))))))))))
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U51#(tt)isList#isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U41(U11(isNeList)))))))))))))
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isList#U21#(U21(U11(U41(U11(U41(U21(U11(U31(tt)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U42(U51(isNeList))))))))))))
isNeList#U51#(U51(U41(U21(U11(U51(U51(U31(isQid))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(U11(U31(isQid))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U51(U41(U11(isNeList))))))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U22(isList))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U21(U11(isNeList))))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U21(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U41(U11(U41(isList)))))))))))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U42(U31(tt)))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U41(isList))))))))isNeList#U51#(U41(U21(U11(U51(U51(U41(isList)))))))
isNeList#U41#(U21(U21(U11(U51(isNeList)))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U41(tt))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U42(isNeList)))))))))))isList#U21#(U11(U42(U51(U41(U11(U41(isList)))))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(tt)))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(tt))))))))))
isList#U21#(U21(U11(U51(U51(U41(U21(isList)))))))isNeList#U51#(U51(U41(U11(U51(U31(tt))))))
isNeList#U41#(U22(U21(U11(U41(U21(U22(U21(U21(isList)))))))))isList#U21#(U21(U21(U21(U11(U51(U51(U41(U21(isList)))))))))
isNeList#U51#(U51(U41(U21(U11(U41(U21(U21(U11(U41(U11(isNeList)))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U21(U21(isList)))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U21(U21(U11(U51(U41(isList))))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U51(U41(isList))))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U51(U51(U51(U41(tt))))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U31(tt))))))))))))))
isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(U21(isList)))))))))isList#U21#(U21(U21(U11(U51(U41(tt))))))
isNeList#U51#(U41(U21(U11(U52(U11(U41(U21(U11(isNeList)))))))))isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(U11(U51(isNeList))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(tt))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(tt))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U21(U11(isNeList)))))))))))isList#U21#(U21(U21(U21(U11(U41(U21(tt)))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U41(isList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U41(U11(U31(isQid)))))))))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U41(isList))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U31(isQid))))))))))
isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U41(U11(isNeList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U51(U51(U51(isNeList)))))))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U51(U41(isList))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U41(U11(isNeList)))))))))))))))
isNeList#U51#(U41(U11(U41(U11(U41(U11(isNeList)))))))isNeList#U41#(U11(U41(U21(U11(U51(U52(isList)))))))
isList#U21#(U21(U11(U41(U11(tt)))))isNeList#U51#(U41(U11(U41(U21(U21(U11(U41(isList))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U22(U21(U11(isNeList)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U41(isList))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U21(U11(isNeList))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U31(isQid))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(U31(isQid)))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U52(U21(U21(isList)))))))))))))))
isNeList#U41#(U11(U51(U41(U11(U31(tt))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U31(isQid)))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U11(U31(isQid)))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(U21(isList))))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(tt))))))))))))
isList#U21#(U11(U42(U51(U51(U42(isNeList))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U52(U22(isList))))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U51(U31(tt)))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U22(U11(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U31(isQid)))))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U51(U51(U31(isQid)))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(U11(U51(U31(isQid)))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U51(isNeList))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U51(U51(isNeList))))))))))))))isNeList#U41#(U11(U41(U22(U21(U22(U21(isList)))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U51(isNeList)))))))))))isList#U21#(U11(U41(U11(U31(isQid)))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U51(U51(isNeList))))))))))isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U31(tt)))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(U51(U31(isQid)))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U31(isQid))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U22(isList)))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U42(isNeList)))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U11(isNeList)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(U11(U51(U51(isNeList)))))))))))
isNeList#U51#(U41(U11(U41(U11(U41(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))
isList#U21#(U11(U42(U51(U41(U21(U11(isNeList)))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U51(U51(isNeList))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U41(isList)))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U21(isList))))))))
isList#U21#(U21(U11(U41(U21(U11(U42(U51(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U11(U41(U21(isList))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U41(isList))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U21(isList)))))))))
isNeList#U51#(U41(U11(U41(U21(U21(U21(isList)))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U21(isList))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U42(U31(isQid))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U41(isList))))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U11(U41(isList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(U21(isList)))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(U21(isList)))))))))))))))isNeList#U51#(U51(U41(U11(U41(U11(U41(isList)))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U41(isList))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U41(isList))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U21(U11(isNeList))))))))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U51(U31(isQid)))))))))))
isNeList#U41#(U11(U51(U31(isQid))))isList#U21#(U21(U11(U41(U21(U11(U51(U41(isList))))))))
isList#U21#(U21(U11(U41(U21(U21(isList))))))isNeList#U41#(U22(U11(U41(U21(isList)))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(tt))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U22(isList))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U31(isQid)))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U11(isNeList)))))))))))))
isList#U21#(U21(U21(U21(U11(U41(U11(U31(isQid))))))))isNeList#U41#(U22(U21(U11(U51(U31(tt))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U41(isList)))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U41(isList)))))))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U42(isNeList))))))))))))isNeList#U51#(U42(U42(U41(isList))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U31(tt)))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U31(isQid)))))))))))
isNeList#U51#(U41(U21(U11(U42(U41(U21(isList)))))))isNeList#U51#(U41(U11(U51(U31(tt)))))
isNeList#U51#(U42(U41(U11(U31(isQid)))))isList#U21#(U21(U11(U51(U51(U42(U31(isQid)))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U41(isList))))))))))))isNeList#U51#(U51(U41(tt)))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(tt)))))))))))))isNeList#U51#(U42(U42(U31(isQid))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U41(tt))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U41(isList))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(U21(isList))))))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U41(isList))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U51(U41(isList)))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U21(isList))))))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(U31(tt))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U42(isNeList)))))))))))isNeList#U51#(U51(U41(U21(U11(U41(U21(U11(U31(isQid)))))))))
isList#U21#(U21(U11(U51(U41(isList)))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(U11(isNeList)))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U51(isNeList)))))))))isNeList#U41#(U22(U21(U11(U51(U51(U41(tt)))))))
isList#U21#(U21(U11(U51(U51(U52(U11(U41(isList))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U31(isQid)))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U51(U41(U11(isNeList)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U41(U11(U41(isList))))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U11(isNeList)))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(U11(isNeList))))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(U11(isNeList)))))))))))))
isNeList#U41#(U21(U11(U41(isList))))isNeList#U51#(U51(U41(U11(U51(U41(isList))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U41(U21(tt))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U31(isQid))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(tt)))))))isList#U21#(U11(U42(U51(U41(U21(tt))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U51(isNeList)))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(tt))))))))))
isList#U21#(U21(U11(U41(U11(U41(tt))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))
isList#U21#(U21(U21(U21(U11(U51(U51(U42(isNeList))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U41(U11(U41(isList)))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(tt)))))))))))))
isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U51(tt)))))))))isNeList#U41#(U11(U41(U22(tt))))
isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(U11(isNeList))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))isNeList#U51#(U41(U11(U51(U41(isList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(tt)))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U51(isNeList))))))))))))))
isNeList#U41#(U11(U41(U21(U11(U31(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(tt))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U21(isList)))))))))))isNeList#U51#(U42(U41(U11(U51(isNeList)))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))isNeList#U41#(U22(U11(U41(tt))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U41(U21(isList)))))))))))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(isNeList))))))))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(U41(isList)))))))))))))))))))) 
U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(U51(isNeList)))))))))))))))))))) 
U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(U31(isQid)))))))))))))))))))) 
Thus, the rule isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(isNeList))))))))))))))))))) is replaced by the following rules:
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(U41(isList))))))))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(U51(isNeList))))))))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(U31(isQid))))))))))))))))))))

Problem 39: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isNeList#U41#(tt)isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(isList))))))))))))
isNeList#U51#(U41(U21(U11(U42(U51(U31(isQid)))))))isList#U21#(U21(U11(U51(U51(U51(U41(U11(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U41(isList))))))))))))))isList#U21#(U21(U11(U51(U52(isList)))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U41(U11(isNeList)))))))))))))isNeList#U51#(U41(U11(U41(U11(U31(tt))))))
isList#U21#(U21(U11(U51(U51(U51(U41(tt)))))))isList#U21#(U21(U21(U21(U11(U31(isQid))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(isNeList))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(isNeList))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U31(isQid))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U21(isList))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U31(isQid))))))))))))))))isNeList#U51#(U41(U21(U11(U52(U11(U31(isQid)))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(U11(U51(U31(isQid)))))))))))))))))isList#U21#(U21(U22(U11(U51(U31(tt))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U31(tt)))))))))))))isNeList#U51#(U41(U21(U11(U42(U42(isNeList))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(isList)))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U51(U41(tt)))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U41(isList)))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U51(isNeList))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(tt)))))))))isNeList#U41#(U11(U51(U42(U51(U51(isNeList))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(U11(isNeList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(tt))))))))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U51(U51(U51(U41(U21(isList)))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U21(U11(U51(isNeList)))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(U21(isList)))))))))))isNeList#U41#(U11(U41(U21(U11(U41(isList))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U31(tt)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U21(isList)))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U31(isQid))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(U51(isNeList)))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(tt))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U51(isNeList)))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(isNeList))))))))isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U11(isNeList))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(isList))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U51(U51(isNeList))))))))))isList#U21#(U21(U11(U41(U21(U11(U42(U41(U21(U11(isNeList))))))))))
isList#U21#(U11(U42(U51(U41(U21(U21(U21(U21(U11(isNeList))))))))))isList#U21#(U21(U11(U41(U21(U11(U51(U51(U41(U11(isNeList))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U41(U21(isList)))))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(isList))))))))))))
isNeList#U51#(U42(U41(U21(U11(isNeList)))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U11(U51(isNeList))))))))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(tt))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U31(tt)))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U21(U21(isList))))))))))isList#U21#(U21(tt))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U31(isQid)))))))))isNeList#U41#(U11(U51(U42(U41(isList)))))
isList#U21#(U21(U11(U41(U21(U11(U31(isQid)))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U51(isNeList))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U51(U51(isNeList))))))))))))isList#U21#(U21(U21(U21(U11(U41(U21(U21(isList))))))))
isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(U11(U41(isList))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U31(tt))))))))))))
isList#U21#(U11(U51(isNeList)))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(U11(isNeList)))))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U41(U22(isList)))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(isNeList)))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U51(U41(U21(isList))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U51(U31(isQid)))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U21(U11(isNeList))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U41(U11(U31(isQid))))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U51(isNeList)))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U21(U21(isList))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(U51(isNeList))))))))))))))))))))isList#U21#(U21(U21(U11(U51(U51(U51(U31(isQid))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U41(U11(isNeList)))))))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U31(isQid)))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(U21(isList)))))))))isList#U21#(U21(U21(U21(U21(tt)))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U52(U21(U11(isNeList)))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U31(isQid))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(tt))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U22(U11(isNeList))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U41(isList))))))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U21(U11(isNeList))))))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U21(U11(isNeList))))))))))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U42(isNeList))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U51(U41(isList))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U31(isQid)))))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U41(U21(isList))))))))))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U21(tt)))))))))))))
isList#U21#(U21(U11(U41(U22(U21(isList))))))isList#U21#(U21(U22(U11(U41(isList)))))
isList#U21#(U21(U21(U21(U11(U41(tt))))))isNeList#U51#(U42(U41(U21(U21(isList)))))
isList#U21#(U21(U21(U11(U51(U51(U31(tt)))))))isNeList#U41#(U21(U22(U21(isList))))
isNeList#U41#(U11(U41(U21(U21(U11(U41(U21(tt))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U41(U11(U31(tt)))))))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U41(tt)))))))))))))isNeList#U51#(U51(U41(U21(U11(U41(U21(tt)))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U22(isList))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(tt)))))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U31(isQid)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U21(isList))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U51(U41(U11(isNeList))))))))))))))))isList#U21#(U21(U11(U41(U11(U51(tt))))))
isNeList#U51#(U42(U51(U51(isNeList))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U51(U41(isList))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U51(U51(isNeList)))))))))))))isNeList#U51#(U41(U11(U51(U51(isNeList)))))
isNeList#U51#(U51(U41(U21(U11(U51(tt))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U51(U51(isNeList)))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U21(U21(isList)))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(tt))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(tt))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(U11(U41(isList))))))))))))))))
isNeList#U51#(U41(U21(U11(U52(U11(U41(U21(tt))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(tt))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U41(U11(U51(isNeList))))))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U21(U21(isList)))))))))))))
isList#U21#(U21(U22(U11(U51(U51(isNeList))))))isList#U21#(U11(U42(U51(U51(U51(U51(isNeList)))))))
isNeList#U41#(U22(U11(U51(U41(isList)))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U31(isQid)))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U21(U21(U11(U51(U51(isNeList))))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U21(U21(U11(U51(U31(isQid))))))))))))))))
isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(tt))))))))isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U51(U51(U31(isQid)))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U22(U11(isNeList)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U51(U31(isQid))))))))))))))))))
isList#U21#(tt)isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(U11(isNeList))))))))))))))
isNeList#U41#(U22(U11(U31(tt))))isList#U21#(U21(U22(tt)))
isNeList#U51#(U41(U11(U41(U11(U41(U21(tt)))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(tt))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(tt))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U31(isQid)))))))))))
isList#U21#(U21(U11(U51(U51(U42(U51(U51(isNeList))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U21(U22(U11(isNeList))))))))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U21(isList)))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U51(U41(U11(isNeList)))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U41(U11(isNeList)))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U42(isNeList)))))))))))
isNeList#U51#(U51(U41(U21(U11(U41(U21(U21(tt))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U21(tt))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U11(U41(isList))))))))))))))))))isNeList#U51#(U41(U21(U11(U52(U11(tt))))))
isNeList#U41#(U11(U41(U21(U21(U11(U41(U21(U21(isList)))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U31(isQid))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U21(U11(isNeList)))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U21(isList)))))))))))))
isNeList#U51#(U51(U41(U11(U42(isNeList)))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U31(tt))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U21(isList)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U41(U21(U21(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U51(U31(isQid)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U51(U41(tt)))))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U41(U11(isNeList))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U51(U31(tt)))))))))
isNeList#U51#(U41(U21(U11(U52(tt)))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U41(isList)))))))))))))isNeList#U41#(U21(U21(U11(U41(isList)))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U31(isQid)))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U51(U31(tt))))))))))
isNeList#U41#(U11(U41(U22(U21(U21(U21(isList)))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U41(tt)))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U51(U41(isList))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U22(U21(isList))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U41(U21(isList))))))))isList#U21#(U21(U21(U21(U11(U51(U51(U51(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U31(tt)))))))))))isList#U21#(U11(U42(U51(U41(tt)))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(tt))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(U21(isList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(tt))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U42(isNeList)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U31(tt))))))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U22(isList))))))))))
isList#U21#(U21(U21(U11(U51(U51(U51(U41(U11(isNeList)))))))))isList#U21#(U21(U11(U41(U11(U41(U11(U31(isQid))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U21(isList)))))))))))))))isNeList#U51#(U51(U41(U21(U11(U51(U41(isList)))))))
isNeList#U41#(U11(U51(tt)))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U31(isQid))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U21(U11(isNeList)))))))))))))isNeList#U51#(U51(tt))
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U51#(tt)isList#isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U41(U11(isNeList)))))))))))))
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isNeList#U41#(U22(U21(U11(U41(U21(U22(U21(U11(isNeList)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U41(isList))))))))))
isList#U21#(U21(U21(U11(U51(U51(U41(isList)))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U21(U11(isNeList))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U31(isQid))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(U31(isQid)))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U52(U21(U21(isList)))))))))))))))isNeList#U41#(U11(U51(U41(U11(U31(tt))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U31(isQid)))))))))))isNeList#U41#(U11(U51(U41(U11(U42(tt))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U11(U31(isQid)))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(U21(isList))))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(tt))))))))))))isList#U21#(U11(U42(U51(U51(U42(isNeList))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U52(U22(isList))))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U22(U11(isNeList))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U51(U31(tt)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U31(isQid)))))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U51(U51(U31(isQid)))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(U11(U51(U31(isQid)))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U51(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U51(U51(isNeList))))))))))))))
isNeList#U41#(U11(U41(U22(U21(U22(U21(isList)))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U51(isNeList)))))))))))
isList#U21#(U11(U41(U11(U31(isQid)))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U51(U51(isNeList))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(tt)))))))))isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U31(tt)))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(U51(U31(isQid)))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U31(isQid))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U22(isList)))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U42(isNeList)))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U11(isNeList)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(U11(U51(U51(isNeList)))))))))))
isNeList#U51#(U41(U11(U41(U11(U41(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))
isList#U21#(U11(U42(U51(U41(U21(U11(isNeList)))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U51(U51(isNeList))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U41(U21(tt)))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U41(isList)))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U21(isList))))))))isList#U21#(U21(U11(U41(U21(U11(U42(U51(isNeList))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(U21(isList))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U41(isList))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U21(isList)))))))))isNeList#U51#(U41(U11(U41(U21(U21(U21(isList)))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U21(isList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U42(U31(isQid))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U41(isList))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U11(U41(isList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(U21(isList)))))))))))))))isNeList#U51#(U51(U41(U11(U41(U11(U41(isList)))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(U21(isList)))))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U41(isList))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U41(isList))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U21(U11(isNeList))))))))))))))))))
isNeList#U41#(U11(U51(U31(isQid))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U51(U31(isQid)))))))))))
isList#U21#(U21(U11(U41(U21(U11(U51(U41(isList))))))))isList#U21#(U21(U11(U41(U21(U21(isList))))))
isNeList#U41#(U22(U11(U41(U21(isList)))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(tt))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U22(isList))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U31(isQid)))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U11(isNeList)))))))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U31(isQid))))))))
isNeList#U41#(U22(U21(U11(U51(U31(tt))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U41(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U41(isList)))))))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U42(isNeList))))))))))))
isNeList#U51#(U42(U42(U41(isList))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U31(tt)))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U31(isQid)))))))))))isNeList#U51#(U41(U21(U11(U42(U41(U21(isList)))))))
isNeList#U51#(U41(U11(U51(U31(tt)))))isNeList#U51#(U42(U41(U11(U31(isQid)))))
isList#U21#(U21(U11(U51(U51(U42(U31(isQid)))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U41(isList))))))))))))
isNeList#U51#(U51(U41(tt)))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(tt)))))))))))))
isNeList#U51#(U42(U42(U31(isQid))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U41(tt))))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U41(isList))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(U21(isList))))))))))))
isList#U21#(U21(U21(U21(U11(U41(U11(U41(isList))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U41(U21(U11(U51(isNeList))))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U51(U41(isList)))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U21(isList))))))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(U31(tt))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U42(isNeList)))))))))))isNeList#U41#(U21(U22(U11(isNeList))))
isNeList#U51#(U51(U41(U21(U11(U41(U21(U11(U31(isQid)))))))))isList#U21#(U21(U11(U51(U41(isList)))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(U11(isNeList)))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U51(isNeList)))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(tt)))))))isList#U21#(U21(U11(U51(U51(U52(U11(U41(isList))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U31(isQid)))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U51(U41(U11(isNeList)))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U41(U11(U41(isList))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U11(isNeList)))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(U11(isNeList))))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(U11(isNeList)))))))))))))isNeList#U41#(U21(U11(U41(isList))))
isNeList#U51#(U51(U41(U11(U51(U41(isList))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U41(U21(tt))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U31(isQid))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U51(tt)))))))
isList#U21#(U11(U42(U51(U41(U21(tt))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U51(isNeList)))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(tt))))))))))isList#U21#(U21(U11(U41(U11(U41(tt))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))isList#U21#(U21(U21(U21(U11(U51(U51(U42(isNeList))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U41(U11(U41(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(tt)))))))))))))isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U51(tt)))))))))
isNeList#U41#(U11(U41(U22(tt))))isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(U11(isNeList))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))
isNeList#U51#(U41(U11(U51(U41(isList)))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(tt)))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U51(isNeList))))))))))))))isNeList#U41#(U11(U41(U21(U11(U31(tt))))))
isNeList#U51#(U42(U41(U11(U41(U11(tt))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U21(isList)))))))))))
isNeList#U51#(U42(U41(U11(U51(isNeList)))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))
isNeList#U41#(U22(U11(U41(tt))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U41(U21(isList)))))))))))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(isList)))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(U21(isList))))))))))))) 
U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(tt)))))))))))) 
U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(U11(isNeList))))))))))))) 
Thus, the rule isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(isList)))))))))))) is replaced by the following rules:
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(U11(isNeList)))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(U21(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(tt))))))))))))

Problem 40: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isNeList#U41#(tt)isNeList#U51#(U41(U21(U11(U42(U42(U51(U51(U31(isQid)))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(U51(isNeList)))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(isList)))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U51(U41(tt)))))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U41(isList)))))))))
isList#U21#(U21(U21(U21(U11(U41(U11(U51(isNeList))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(tt)))))))))
isNeList#U41#(U11(U51(U42(U51(U51(isNeList))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(tt))))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(U11(isNeList))))))))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U51(U51(U51(U41(U21(isList)))))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U21(U11(U51(isNeList)))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(U21(isList)))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U31(isQid))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U31(tt)))))))))
isNeList#U41#(U11(U41(U21(U11(U41(isList))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U21(isList)))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(U51(isNeList)))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(tt))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U51(isNeList)))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U51#(U41(U11(U41(U21(U11(isNeList))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U21(U11(isNeList))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(isList))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U51(U51(isNeList))))))))))
isList#U21#(U21(U11(U41(U21(U11(U42(U41(U21(U11(isNeList))))))))))isList#U21#(U11(U42(U51(U41(U21(U21(U21(U21(U11(isNeList))))))))))
isList#U21#(U21(U11(U41(U21(U11(U51(U51(U41(U11(isNeList))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U41(U21(isList)))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(isList))))))))))))isNeList#U51#(U42(U41(U21(U11(isNeList)))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U11(U51(isNeList))))))))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(tt))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U31(tt)))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U21(U21(isList))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U31(isQid)))))))))isList#U21#(U21(tt))
isList#U21#(U21(U11(U51(U51(U51(U41(U11(U51(U41(isList))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(U41(U21(U21(U21(isList))))))))))))))
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isList#U21#(U21(U22(U21(isList))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(U11(U51(U41(U11(isNeList))))))))))))
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isNeList#U51#(U42(U42(U51(isNeList))))isNeList#isList#
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U22(U21(isList)))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U22(isList)))))))))
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isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U42(isNeList))))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U21(tt))))))))))))
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isNeList#U51#(tt)isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(tt)))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U41(U11(U41(U11(isNeList)))))))))))))))isList#isList#
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isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U51(U41(U11(isNeList))))))))))))isList#U21#(U21(U11(U41(U21(U11(U42(U41(U11(isNeList)))))))))
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isList#U21#(U21(U21(U11(U51(U51(U51(U41(U21(isList)))))))))isNeList#U41#(U11(U51(U51(U51(U41(U21(isList)))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U42(isNeList))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U11(U41(isList)))))))))
isList#U21#(U21(U11(U51(U52(U21(isList))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U41(tt))))))))))))))
isNeList#U41#(U11(U51(U51(U51(U41(U11(isNeList)))))))isNeList#U51#(U41(U21(U11(U42(U42(U51(U51(U51(U51(isNeList))))))))))
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isNeList#U41#(U11(U41(U21(U21(U21(isList))))))isNeList#U51#(U41(U11(U41(U11(U51(isNeList))))))
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U51#(tt)isList#isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U41(U11(isNeList)))))))))))))
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isList#U21#(U11(U42(U31(isQid))))isNeList#U41#(U22(U22(isList)))
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isNeList#U41#(U21(tt))isList#U21#(U21(U21(U11(U51(U41(U11(isNeList)))))))
isList#U21#(U21(U11(U51(U51(U51(U42(U51(U41(U11(isNeList))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U51(isNeList)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(tt))))))isNeList#U51#(U41(U11(U41(U11(U41(U21(U11(U41(isList)))))))))
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isNeList#U41#(U22(U21(U21(U21(isList)))))isNeList#U41#(U22(U21(U11(U41(U11(U51(tt)))))))
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U41#(tt)isNeList#isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(U11(isNeList)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U22(tt))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))
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isNeList#U41#(U21(U11(U51(isNeList))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U11(isNeList))))))))))
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isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U41(U21(U11(isNeList))))))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U51(isNeList)))))))))
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isList#U21#(U21(U21(U21(U11(U51(U42(U41(isList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U41(U11(U31(isQid)))))))))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U41(isList))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U31(isQid))))))))))
isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U41(U11(isNeList))))))))))isList#U21#(U21(U11(U51(U51(U51(U42(U51(U41(tt)))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U51(U51(U51(isNeList)))))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U51(U41(isList))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U41(U11(isNeList)))))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(U41(U11(U31(isQid)))))))))))))
isNeList#U51#(U41(U11(U41(U11(U41(U11(isNeList)))))))isNeList#U41#(U11(U41(U21(U11(U51(U52(isList)))))))
isList#U21#(U21(U11(U41(U11(tt)))))isNeList#U51#(U41(U11(U41(U21(U21(U11(U41(isList))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U22(U21(U11(isNeList)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U41(isList))))))))))
isList#U21#(U21(U21(U11(U51(U51(U41(isList)))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U21(U11(isNeList))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U31(isQid))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(U31(isQid)))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U52(U21(U21(isList)))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U41(U11(U51(U41(isList)))))))))))))))
isNeList#U41#(U11(U51(U41(U11(U31(tt))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U31(isQid)))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U11(U31(isQid)))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U41(U21(U21(isList))))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(tt))))))))))))
isList#U21#(U11(U42(U51(U51(U42(isNeList))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U52(U22(isList))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U22(U11(isNeList))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U51(U31(tt)))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U31(isQid)))))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U51(U51(U31(isQid)))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(U11(U51(U31(isQid)))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U51(isNeList))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U51(U51(isNeList))))))))))))))isNeList#U41#(U11(U41(U22(U21(U22(U21(isList)))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U51(isNeList)))))))))))isList#U21#(U11(U41(U11(U31(isQid)))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U51(U51(isNeList))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(tt)))))))))
isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U31(tt)))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(U51(U31(isQid)))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U31(isQid))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U22(isList)))))))))))
isList#U21#(U21(U11(U51(U51(U51(U42(U51(U51(U41(isList))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U41(U21(isList)))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U42(isNeList)))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U11(isNeList)))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(U11(U51(U51(isNeList)))))))))))isNeList#U51#(U41(U11(U41(U11(U41(tt))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))isList#U21#(U11(U42(U51(U41(U21(U11(isNeList)))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U51(U51(isNeList))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U41(U21(tt)))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U41(isList)))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U21(isList))))))))
isList#U21#(U21(U11(U41(U21(U11(U42(U51(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U11(U41(U21(isList))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U41(isList))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U21(isList)))))))))
isNeList#U51#(U41(U11(U41(U21(U21(U21(isList)))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U21(isList))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U42(U31(isQid))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U41(isList))))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U11(U41(isList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(U21(isList)))))))))))))))
isNeList#U51#(U51(U41(U11(U41(U11(U41(isList)))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(U21(isList)))))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U41(isList))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U41(isList))))))))))))
isNeList#U51#(U41(U21(U11(U42(U42(U51(U41(U11(isNeList)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U21(U11(isNeList))))))))))))))))))
isNeList#U41#(U11(U51(U31(isQid))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U51(U31(isQid)))))))))))
isList#U21#(U21(U11(U41(U21(U11(U51(U41(isList))))))))isList#U21#(U21(U11(U41(U21(U21(isList))))))
isNeList#U41#(U22(U11(U41(U21(isList)))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(tt))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U22(isList))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U31(isQid)))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U11(isNeList)))))))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U31(isQid))))))))
isNeList#U41#(U22(U21(U11(U51(U31(tt))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U41(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U41(isList)))))))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U42(isNeList))))))))))))
isNeList#U51#(U42(U42(U41(isList))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(U11(isNeList)))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U31(tt)))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U31(isQid)))))))))))
isNeList#U51#(U41(U21(U11(U42(U41(U21(isList)))))))isNeList#U51#(U41(U11(U51(U31(tt)))))
isNeList#U51#(U42(U41(U11(U31(isQid)))))isList#U21#(U21(U11(U51(U51(U42(U31(isQid)))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U41(isList))))))))))))isNeList#U51#(U51(U41(tt)))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(tt)))))))))))))isNeList#U51#(U42(U42(U31(isQid))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U41(tt))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U41(isList))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(U21(isList))))))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U41(isList))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U41(U21(U11(U51(isNeList))))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U21(tt))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U51(U41(isList)))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U21(isList))))))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(U31(tt))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U42(isNeList)))))))))))isNeList#U41#(U21(U22(U11(isNeList))))
isNeList#U51#(U51(U41(U21(U11(U41(U21(U11(U31(isQid)))))))))isList#U21#(U21(U11(U51(U41(isList)))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(U51(isNeList)))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(U11(isNeList)))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U51(isNeList)))))))))isNeList#U41#(U22(U21(U11(U51(U51(U41(tt)))))))
isList#U21#(U21(U11(U51(U51(U52(U11(U41(isList))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U31(isQid)))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U51(U41(U11(isNeList)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U41(U11(U41(isList))))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U11(isNeList)))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(U11(isNeList))))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(U11(isNeList)))))))))))))
isNeList#U41#(U21(U11(U41(isList))))isNeList#U51#(U51(U41(U11(U51(U41(isList))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U41(U21(tt))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U31(isQid))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(tt)))))))isList#U21#(U11(U42(U51(U41(U21(tt))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U51(isNeList)))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(tt))))))))))
isList#U21#(U21(U11(U41(U11(U41(tt))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))
isList#U21#(U21(U21(U21(U11(U51(U51(U42(isNeList))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U41(U11(U41(isList)))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(tt)))))))))))))
isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U51(tt)))))))))isNeList#U41#(U11(U41(U22(tt))))
isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(U11(isNeList))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))isNeList#U51#(U41(U11(U51(U41(isList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(tt)))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U51(isNeList))))))))))))))
isNeList#U41#(U11(U41(U21(U11(U31(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(tt))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U21(isList)))))))))))isNeList#U51#(U42(U41(U11(U51(isNeList)))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))isNeList#U41#(U22(U11(U41(tt))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U41(U21(isList)))))))))))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U51#(U41(U21(U11(U42(U42(U51(U51(U31(isQid))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(U41(U21(U11(U42(U42(U51(U51(U31(tt))))))))) 
Thus, the rule isNeList#U51#(U41(U21(U11(U42(U42(U51(U51(U31(isQid))))))))) is replaced by the following rules:
isNeList#U51#(U41(U21(U11(U42(U42(U51(U51(U31(tt)))))))))

Problem 41: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(U21(U11(isNeList))))))))))))isNeList#U41#(tt)
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(U21(U21(isList))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(U11(U51(isNeList)))))))))))
isList#U21#(U21(U11(U41(U21(U11(U42(U41(U21(U11(isNeList))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U51(U51(isNeList))))))))))
isList#U21#(U11(U42(U51(U41(U21(U21(U21(U21(U11(isNeList))))))))))isList#U21#(U21(U11(U41(U21(U11(U51(U51(U41(U11(isNeList))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U41(U21(isList)))))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(isList))))))))))))
isNeList#U51#(U42(U41(U21(U11(isNeList)))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U11(U51(isNeList))))))))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(tt))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U41(U11(U41(isList)))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U31(tt)))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U21(U21(isList))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U11(U51(U41(isList))))))))))isList#U21#(U21(tt))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U31(isQid)))))))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(U11(U51(isNeList)))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(U41(U21(U21(U21(isList))))))))))))))isNeList#U41#(U11(U51(U42(U41(isList)))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U51(isNeList))))))))))isList#U21#(U21(U11(U41(U21(U11(U31(isQid)))))))
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isList#isList#isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(U21(tt)))))))))))
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isList#U21#(U11(U42(U51(U41(U21(U21(tt)))))))U51#(tt)isList#
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isNeList#U41#(U22(U22(isList)))isList#U21#(U21(U11(U51(U51(U51(U51(isNeList)))))))
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U41#(tt)isNeList#isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(U11(isNeList)))))))))))
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isList#U21#(U21(U11(U51(U51(U52(U11(U41(isList))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U51(U31(isQid))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U31(isQid)))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U51(U41(U11(isNeList)))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U41(U11(U41(isList))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U11(isNeList)))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(U11(isNeList))))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(U21(isList))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(U11(isNeList)))))))))))))
isNeList#U41#(U21(U11(U41(isList))))isNeList#U51#(U51(U41(U11(U51(U41(isList))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U41(U21(tt))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U31(isQid))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(tt)))))))isList#U21#(U11(U42(U51(U41(U21(tt))))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(tt)))))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(U41(U11(U51(isNeList)))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U51(isNeList)))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(tt))))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U51(U51(isNeList)))))))))
isList#U21#(U21(U11(U41(U11(U41(tt))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))
isList#U21#(U21(U21(U21(U11(U51(U51(U42(isNeList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U21(U21(U11(U41(U21(isList)))))))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U41(U11(U41(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(tt)))))))))))))isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U51(tt)))))))))
isNeList#U41#(U11(U41(U22(tt))))isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(U11(isNeList))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U42(isNeList))))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))isNeList#U51#(U41(U11(U51(U41(isList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(tt)))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U51(isNeList))))))))))))))
isNeList#U41#(U11(U41(U21(U11(U31(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(tt))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U21(isList)))))))))))isNeList#U51#(U42(U41(U11(U51(isNeList)))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))isNeList#U41#(U22(U11(U41(tt))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U41(U21(isList)))))))))))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(U21(U11(isNeList)))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(U21(U11(U51(isNeList))))))))))))) 
U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(U21(U11(U31(isQid))))))))))))) 
U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(U21(U11(U41(isList))))))))))))) 
Thus, the rule isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(U21(U11(isNeList)))))))))))) is replaced by the following rules:
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(U21(U11(U31(isQid)))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(U21(U11(U41(isList)))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(U21(U11(U51(isNeList)))))))))))))

Problem 42: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isNeList#U41#(tt)isNeList#U51#(U42(U41(U21(U11(isNeList)))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U11(U51(isNeList))))))))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U41(U11(U41(isList)))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U31(tt)))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U21(U21(isList))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U31(isQid)))))))))
isList#U21#(U21(tt))isList#U21#(U21(U11(U51(U51(U51(U41(U11(U51(U41(isList))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(U11(U51(isNeList)))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(U41(U21(U21(U21(isList))))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U51(isNeList))))))))))isList#U21#(U21(U11(U41(U21(U11(U31(isQid)))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U51(U51(isNeList))))))))))))isNeList#U41#(U11(U51(U42(U41(isList)))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(U51(U51(isNeList))))))))))))))isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(U11(U41(isList))))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U21(isList))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U31(tt))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(U11(isNeList)))))))))))))))isList#U21#(U11(U51(isNeList)))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U41(U22(isList)))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U51(U41(U21(isList))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(isNeList)))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U51(U31(isQid)))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U51(isNeList)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U41(U11(U31(isQid))))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U21(U11(isNeList))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U21(U21(isList))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(U51(isNeList))))))))))))))))))))isList#U21#(U21(U21(U11(U51(U51(U51(U31(isQid))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U41(U11(isNeList)))))))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U31(isQid)))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(U21(isList)))))))))isList#U21#(U21(U21(U21(U21(tt)))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U31(isQid))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U52(U21(U11(isNeList)))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(U41(U11(U51(U51(isNeList))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U22(U11(isNeList))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(tt))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U41(isList))))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U22(U21(U11(isNeList)))))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U21(U11(isNeList))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U11(U41(U11(U51(U41(U21(U21(U21(U11(U51(U31(tt))))))))))))))))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U21(U11(isNeList))))))))))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U42(isNeList))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U22(U21(U21(isList)))))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U51(U41(isList))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U31(isQid)))))))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(U41(tt)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U41(U21(isList))))))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U41(U21(isList))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U21(tt)))))))))))))
isList#U21#(U21(U11(U41(U22(U21(isList))))))isList#U21#(U21(U22(U11(U41(isList)))))
isList#U21#(U21(U21(U21(U11(U41(tt))))))isNeList#U51#(U42(U41(U21(U21(isList)))))
isList#U21#(U21(U21(U11(U51(U51(U31(tt)))))))isNeList#U41#(U21(U22(U21(isList))))
isNeList#U41#(U11(U41(U21(U21(U11(U41(U21(tt))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U41(U11(U31(tt)))))))))))))
isNeList#U51#(U51(U41(U21(U11(U41(U21(tt)))))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U41(tt)))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U22(isList))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(U11(U51(U41(U11(U41(isList))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U11(U41(U11(U51(U41(U11(isNeList)))))))))))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(tt)))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U51(U41(U11(isNeList))))))))))))))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U31(isQid)))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U21(isList))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U21(tt))))))))))))))
isNeList#U51#(U42(U51(U51(isNeList))))isList#U21#(U21(U11(U41(U11(U51(tt))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U51(U41(isList))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U51(U51(isNeList)))))))))))))
isNeList#U51#(U51(U41(U21(U11(U51(tt))))))isNeList#U51#(U41(U11(U51(U51(isNeList)))))
isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(U41(U21(U21(U11(U41(isList)))))))))))))))isList#U21#(U21(U22(U11(U52(isList)))))
isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(U11(U31(isQid)))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U21(U11(U51(tt)))))))))))))))
isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U51(U51(isNeList)))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U21(U21(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(tt))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(tt))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(U11(U41(isList))))))))))))))))isNeList#U51#(U41(U21(U11(U52(U11(U41(U21(tt))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(tt))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U11(U41(U11(U51(U41(tt))))))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U21(U21(isList)))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U41(U11(U51(isNeList))))))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(U21(U11(U31(isQid)))))))))))))isList#U21#(U21(U22(U11(U51(U51(isNeList))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U41(U11(U31(isQid))))))))))))))))isList#U21#(U11(U42(U51(U51(U51(U51(isNeList)))))))
isNeList#U41#(U22(U11(U51(U41(isList)))))isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U31(isQid)))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U21(U21(U11(U51(U51(isNeList))))))))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U51(U42(isNeList)))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U21(U21(U11(U51(U31(isQid))))))))))))))))isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(tt))))))))
isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U51(U51(U31(isQid)))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U22(U11(isNeList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(U41(U11(U41(tt)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U51(U31(isQid))))))))))))))))))
isList#U21#(tt)isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(U11(isNeList))))))))))))))
isNeList#U41#(U22(U11(U31(tt))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(U41(U21(U11(isNeList)))))))))))))
isList#U21#(U21(U22(tt)))isNeList#U51#(U42(U41(U11(U41(U11(U51(U31(tt))))))))
isNeList#U51#(U41(U11(U41(U11(U41(U21(tt)))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(tt))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(tt))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U31(isQid)))))))))))
isList#U21#(U21(U11(U51(U51(U42(U51(U51(isNeList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(U51(U51(isNeList))))))))))))
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isList#U21#(U11(U42(U51(U41(U21(U21(tt)))))))U51#(tt)isList#
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U41#(tt)isNeList#isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(U11(isNeList)))))))))))
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isList#U21#(U21(U21(U21(U11(U41(U11(U41(isList))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U41(U21(U11(U51(isNeList))))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U21(tt))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U51(U41(isList)))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U21(isList))))))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(U31(tt))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U42(isNeList)))))))))))
isNeList#U41#(U21(U22(U11(isNeList))))isNeList#U51#(U51(U41(U21(U11(U41(U21(U11(U31(isQid)))))))))
isList#U21#(U21(U11(U51(U41(isList)))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(U51(isNeList)))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(U11(isNeList)))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U51(isNeList)))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(tt)))))))isList#U21#(U21(U11(U51(U51(U52(U11(U41(isList))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U51(U31(isQid))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U31(isQid)))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U51(U41(U11(isNeList)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U41(U11(U41(isList))))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U11(isNeList)))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U11(U41(U11(U51(U41(U21(U21(U21(U11(U41(U11(U41(tt)))))))))))))))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(U11(isNeList))))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(U21(isList))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(U11(isNeList)))))))))))))
isNeList#U41#(U21(U11(U41(isList))))isNeList#U51#(U51(U41(U11(U51(U41(isList))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U41(U21(tt))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U31(isQid))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(tt)))))))isList#U21#(U11(U42(U51(U41(U21(tt))))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(tt)))))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(U41(U11(U51(isNeList)))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U51(isNeList)))))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(U11(U51(U31(isQid))))))))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(tt))))))))))
isList#U21#(U21(U21(U21(U11(U41(U11(U51(U51(isNeList)))))))))isList#U21#(U21(U11(U41(U11(U41(tt))))))
isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))isList#U21#(U21(U21(U21(U11(U51(U51(U42(isNeList))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U21(U21(U11(U41(U21(isList)))))))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U41(U11(U41(isList)))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U21(U21(isList)))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(tt)))))))))))))isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U51(tt)))))))))
isNeList#U41#(U11(U41(U22(tt))))isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(U11(isNeList))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U42(isNeList))))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))isNeList#U51#(U41(U11(U51(U41(isList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(tt)))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U51(isNeList))))))))))))))
isNeList#U41#(U11(U41(U21(U11(U31(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(tt))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U21(isList)))))))))))isNeList#U51#(U42(U41(U11(U51(isNeList)))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))isNeList#U41#(U22(U11(U41(tt))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U41(U21(isList)))))))))))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNeList#U51#(U42(U41(U21(U11(isNeList))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U51#(U42(U41(U21(U11(U41(isList)))))) 
U51#(U42(U41(U21(U11(U51(isNeList)))))) 
U51#(U42(U41(U21(U11(U31(isQid)))))) 
Thus, the rule isNeList#U51#(U42(U41(U21(U11(isNeList))))) is replaced by the following rules:
isNeList#U51#(U42(U41(U21(U11(U51(isNeList))))))isNeList#U51#(U42(U41(U21(U11(U31(isQid))))))
isNeList#U51#(U42(U41(U21(U11(U41(isList))))))

Problem 43: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(U41(isList))))))))))))))isNeList#U41#(tt)
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U51(U31(isQid)))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U51(U41(U21(isList))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U41(U11(U31(isQid))))))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U21(U11(isNeList))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U51(isNeList)))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U21(U21(isList))))))))))))))
isList#U21#(U21(U21(U11(U51(U51(U51(U31(isQid))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(U51(isNeList))))))))))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(U51(U51(U51(isNeList)))))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U41(U11(isNeList)))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U11(U51(U31(isQid)))))))))))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U31(isQid)))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(U21(isList)))))))))isList#U21#(U21(U21(U21(U21(tt)))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U31(isQid))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U52(U21(U11(isNeList)))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(U41(U11(U51(U51(isNeList))))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(tt))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U22(U11(isNeList))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U41(isList))))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U22(U21(U11(isNeList)))))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U41(U22(U21(U21(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U21(U11(isNeList))))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U41(U11(U41(U21(U11(U41(tt))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U11(U41(U11(U51(U41(U21(U21(U21(U11(U51(U31(tt))))))))))))))))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U21(U11(isNeList))))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U22(U21(U21(isList)))))))))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U42(isNeList))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U51(U41(isList))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U31(isQid)))))))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(U41(tt)))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(U31(isQid))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U41(U21(isList))))))))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U41(U21(isList))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U21(tt)))))))))))))isList#U21#(U21(U11(U41(U22(U21(isList))))))
isNeList#U51#(U42(U41(U21(U21(isList)))))isList#U21#(U21(U21(U21(U11(U41(tt))))))
isList#U21#(U21(U22(U11(U41(isList)))))isList#U21#(U21(U21(U11(U51(U51(U31(tt)))))))
isNeList#U41#(U21(U22(U21(isList))))isNeList#U41#(U11(U41(U21(U21(U11(U41(U21(tt))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U41(U11(U31(tt)))))))))))))isNeList#U51#(U51(U41(U21(U11(U41(U21(tt)))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U41(tt)))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U22(isList))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(U11(U51(U41(U11(U41(isList))))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U11(U41(U11(U51(U41(U11(isNeList)))))))))))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(tt)))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U51(U41(U11(isNeList))))))))))))))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U31(isQid)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U21(isList))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U21(tt))))))))))))))isNeList#U51#(U42(U51(U51(isNeList))))
isList#U21#(U21(U11(U41(U11(U51(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U51(U41(isList))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U51(U51(isNeList)))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U11(U51(U41(U11(isNeList)))))))))))
isNeList#U51#(U51(U41(U21(U11(U51(tt))))))isNeList#U51#(U41(U11(U51(U51(isNeList)))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(U51(U51(U41(U22(isList))))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(U41(U21(U21(U11(U41(isList)))))))))))))))
isList#U21#(U21(U22(U11(U52(isList)))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(U11(U31(isQid)))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U21(U11(U51(tt)))))))))))))))isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U51(U51(isNeList)))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U21(U21(isList)))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(tt))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(tt))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(U51(U51(U41(tt)))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(U11(U41(isList))))))))))))))))isNeList#U51#(U41(U21(U11(U52(U11(U41(U21(tt))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(tt))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U11(U41(U11(U51(U41(tt))))))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U21(U21(isList)))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U41(U11(U51(isNeList))))))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U41(U21(U11(U31(isQid)))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U41(U11(U31(isQid))))))))))))))))
isList#U21#(U11(U42(U51(U51(U51(U51(isNeList)))))))isList#U21#(U21(U22(U11(U51(U51(isNeList))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U41(U11(U41(U21(U11(U31(isQid))))))))))))))isNeList#U41#(U22(U11(U51(U41(isList)))))
isList#U21#(U21(U21(U21(U11(U41(U21(U11(U41(U21(U11(U51(U31(isQid)))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U21(U21(U11(U51(U51(isNeList))))))))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U51(U42(isNeList)))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U41(U21(U21(U11(U51(U31(isQid))))))))))))))))
isNeList#U41#(U11(U41(U22(U21(U21(U11(U41(tt))))))))isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U51(U51(U31(isQid)))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U21(U21(U21(isList)))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U41(U22(U11(isNeList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(U41(U11(U41(tt)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U51(U31(isQid))))))))))))))))))
isList#U21#(tt)isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(U11(isNeList))))))))))))))
isNeList#U41#(U22(U11(U31(tt))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(U41(U21(U11(isNeList)))))))))))))
isList#U21#(U21(U22(tt)))isNeList#U51#(U42(U41(U11(U41(U11(U51(U31(tt))))))))
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isNeList#U41#(U11(U51(U42(U51(U51(U41(tt)))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U51(U51(U51(U41(U11(U51(isNeList))))))))))))))))
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U51#(tt)isList#isList#U21#(U21(U11(U41(U21(U11(U41(U11(U41(U21(U11(U41(U11(isNeList)))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U31(tt)))))))))isNeList#U51#(U51(U41(U11(U41(U21(isList))))))
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isNeList#U51#(U42(U41(U21(U11(U41(isList))))))isList#U21#(U21(U21(U21(U11(U51(U42(U51(tt))))))))
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isNeList#U41#(U11(U51(U42(U51(U51(U31(isQid)))))))isNeList#U51#(U41(U21(U11(U41(U21(tt))))))
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isList#U21#(U11(U42(U31(isQid))))isNeList#U41#(U22(U22(isList)))
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isNeList#U41#(U22(U21(U11(U51(U41(U21(isList)))))))isNeList#U41#(U21(tt))
isList#U21#(U21(U21(U11(U51(U41(U11(isNeList)))))))isList#U21#(U21(U11(U51(U51(U51(U42(U51(U41(U11(isNeList))))))))))
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isNeList#U41#(U22(U21(U21(U21(isList)))))isNeList#U41#(U22(U21(U11(U41(U11(U51(tt)))))))
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U41#(tt)isNeList#isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(U11(isNeList)))))))))))
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isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U11(U41(U11(U51(U31(isQid))))))))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U22(U11(isNeList))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U51(U31(tt)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U51(U31(isQid)))))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U51(U51(U31(isQid)))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U22(U21(tt))))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(U11(U51(U31(isQid)))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U51(isNeList))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U41(U11(U51(U51(isNeList))))))))))))))isNeList#U41#(U11(U41(U22(U21(U22(U21(isList)))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U51(U51(U51(isNeList)))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U11(U51(U41(tt))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(U11(U51(U51(U41(U21(isList))))))))))))))isList#U21#(U11(U41(U11(U31(isQid)))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U41(U11(U41(U11(tt))))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U51(U51(isNeList))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(tt)))))))))isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U31(tt)))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U41(U11(U41(U21(U11(U41(U11(isNeList)))))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(U51(U31(isQid)))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U31(isQid))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(U11(U51(U41(U21(isList)))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(U21(U11(U31(isQid)))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U22(isList)))))))))))
isList#U21#(U21(U11(U51(U51(U51(U42(U51(U51(U41(isList))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U41(U11(U51(U31(isQid))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U41(U21(isList)))))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U42(isNeList)))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U11(isNeList)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(U11(U51(U51(isNeList)))))))))))
isNeList#U51#(U41(U11(U41(U11(U41(tt))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))
isList#U21#(U11(U42(U51(U41(U21(U11(isNeList)))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U51(U51(isNeList))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(U41(U21(U21(U21(U21(isList)))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U41(U21(tt)))))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U41(isList)))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U21(isList))))))))
isList#U21#(U21(U11(U41(U21(U11(U42(U51(isNeList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U21(tt)))))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(U21(isList))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U41(isList))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U21(isList)))))))))isNeList#U51#(U41(U11(U41(U21(U21(U21(isList)))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U21(isList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U42(U31(isQid))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U51(U51(U51(U41(U11(U42(isNeList))))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U41(isList))))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U11(U41(isList))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(U21(isList)))))))))))))))
isNeList#U51#(U51(U41(U11(U41(U11(U41(isList)))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(U21(isList)))))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U41(isList))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U41(isList))))))))))))
isNeList#U51#(U41(U21(U11(U42(U42(U51(U41(U11(isNeList)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U21(U11(isNeList))))))))))))))))))
isNeList#U41#(U11(U51(U31(isQid))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U51(U31(isQid)))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U51(U41(isList))))))))))))))isList#U21#(U21(U11(U41(U21(U11(U51(U41(isList))))))))
isList#U21#(U21(U11(U41(U21(U21(isList))))))isNeList#U41#(U22(U11(U41(U21(isList)))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U11(U41(U11(U51(U41(U21(U11(isNeList))))))))))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(tt))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U22(isList))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U31(isQid)))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U11(isNeList)))))))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U31(isQid))))))))
isNeList#U41#(U22(U21(U11(U51(U31(tt))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U42(U41(isList)))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(tt)))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U41(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U41(isList)))))))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U42(isNeList))))))))))))
isNeList#U51#(U42(U42(U41(isList))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(U11(isNeList)))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U31(tt)))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U31(isQid)))))))))))
isNeList#U51#(U41(U21(U11(U42(U41(U21(isList)))))))isNeList#U51#(U41(U11(U51(U31(tt)))))
isNeList#U51#(U42(U41(U11(U31(isQid)))))isList#U21#(U21(U11(U51(U51(U42(U31(isQid)))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U41(isList))))))))))))isNeList#U51#(U51(U41(tt)))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(tt)))))))))))))isNeList#U51#(U42(U42(U31(isQid))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U41(tt))))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U41(isList))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(U21(isList))))))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U41(isList))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U41(U21(U11(U51(isNeList))))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U51(U31(isQid)))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U21(tt))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U51(U41(isList)))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U21(isList))))))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(U31(tt))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U42(isNeList)))))))))))
isNeList#U41#(U21(U22(U11(isNeList))))isNeList#U51#(U51(U41(U21(U11(U41(U21(U11(U31(isQid)))))))))
isList#U21#(U21(U11(U51(U41(isList)))))isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(U51(isNeList)))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(U11(isNeList)))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U51(isNeList)))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U41(tt)))))))isList#U21#(U21(U11(U51(U51(U52(U11(U41(isList))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U51(U31(isQid))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U31(isQid)))))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U41(U22(U21(U11(isNeList)))))))))))))isList#U21#(U21(U21(U21(U11(U51(U51(U41(U11(isNeList)))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U41(U11(U41(isList))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U11(isNeList)))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U11(U41(U11(U51(U41(U21(U21(U21(U11(U41(U11(U41(tt)))))))))))))))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(U11(isNeList))))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(U21(isList))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(U11(isNeList)))))))))))))isNeList#U41#(U21(U11(U41(isList))))
isNeList#U51#(U51(U41(U11(U51(U41(isList))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U41(U21(tt))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U31(isQid))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U51(tt)))))))
isList#U21#(U11(U42(U51(U41(U21(tt))))))isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(tt)))))))isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(U41(U11(U51(isNeList)))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U51(isNeList)))))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(U11(U51(U31(isQid))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(tt))))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U51(U51(isNeList)))))))))
isList#U21#(U21(U11(U41(U11(U41(tt))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))
isList#U21#(U21(U21(U21(U11(U51(U51(U42(isNeList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U21(U21(U11(U41(U21(isList)))))))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U51(U51(U51(U51(isNeList))))))))))))))isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U41(U11(U41(isList)))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U21(U21(isList)))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(tt)))))))))))))isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U51(tt)))))))))
isNeList#U41#(U11(U41(U22(tt))))isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(U11(isNeList))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U42(isNeList))))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))isNeList#U51#(U41(U11(U51(U41(isList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(tt)))))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(U11(U51(U51(U41(U11(isNeList))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U51(isNeList))))))))))))))isNeList#U41#(U11(U41(U21(U11(U31(tt))))))
isNeList#U51#(U42(U41(U11(U41(U11(tt))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U21(isList)))))))))))
isNeList#U51#(U42(U41(U11(U51(isNeList)))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))
isNeList#U41#(U22(U11(U41(tt))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U41(U21(isList)))))))))))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(U41(isList)))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(U41(tt)))))))))))))) 
U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(U41(U21(isList))))))))))))))) 
U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))))))) 
Thus, the rule isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(U41(isList)))))))))))))) is replaced by the following rules:
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(U41(U21(isList)))))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(U41(U11(isNeList)))))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(U41(tt))))))))))))))

Problem 44: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

U21#(tt)isList#isList#isNeList#
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U42(U41(isList)))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U42(U31(isQid)))))))))))))
isNeList#U41#(tt)isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(U41(isList))))))))))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U22(U21(U11(isNeList)))))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U41(U22(U21(U21(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U11(U41(U21(U11(isNeList))))))))))))))isList#U21#(U21(U21(U21(U22(tt)))))
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U41#(tt)isNeList#isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U41(U11(isNeList)))))))))))
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isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U51(U41(U21(U11(isNeList)))))))))))))isList#U21#(U11(U41(U11(U31(isQid)))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U41(U11(U41(U11(tt))))))))))))isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U51(U51(isNeList))))))))))
isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(tt)))))))))isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U31(tt)))))))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U41(U11(U41(U21(U11(U41(U11(isNeList)))))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(U51(U31(isQid)))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U31(isQid))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(U11(U51(U41(U21(isList)))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(U21(U11(U31(isQid)))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U22(isList)))))))))))
isList#U21#(U21(U11(U51(U51(U51(U42(U51(U51(U41(isList))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U41(U11(U51(U31(isQid))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U51(U41(U21(U11(U41(U21(isList)))))))))))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U42(isNeList)))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U11(isNeList)))))))))isNeList#U51#(U42(U41(U11(U41(U11(U51(U52(U11(U51(U51(isNeList)))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(U41(U22(U11(isNeList))))))))))))))))isNeList#U51#(U41(U11(U41(U11(U41(tt))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))isList#U21#(U11(U42(U51(U41(U21(U11(isNeList)))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U51(U51(isNeList))))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U42(U41(U11(U51(U41(U21(U21(U21(U21(isList)))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U41(U21(tt)))))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U41(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(U51(U51(U51(U51(isNeList)))))))))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U21(isList))))))))
isList#U21#(U21(U11(U41(U21(U11(U42(U51(isNeList))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U21(tt)))))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U41(U21(isList))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U41(isList))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U21(isList)))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(U51(U51(U42(U41(U21(isList))))))))))))))))))))))))
isNeList#U51#(U41(U11(U41(U21(U21(U21(isList)))))))isNeList#U41#(U22(U21(U11(U41(U21(U21(U21(isList))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U42(U31(isQid))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U51(U51(U51(U41(U11(U42(isNeList))))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U41(isList))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U11(U41(isList))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U31(isQid))))))))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U41(U21(isList)))))))))))))))
isNeList#U51#(U51(U41(U11(U41(U11(U41(isList)))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U22(U11(U41(U21(isList)))))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U41(isList))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U41(isList))))))))))))
isNeList#U51#(U41(U21(U11(U42(U42(U51(U41(U11(isNeList)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U41(U21(U21(U11(isNeList))))))))))))))))))
isNeList#U41#(U11(U51(U31(isQid))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U51(U31(isQid)))))))))))
isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U51(U41(isList))))))))))))))isList#U21#(U21(U11(U41(U21(U11(U51(U41(isList))))))))
isList#U21#(U21(U11(U41(U21(U21(isList))))))isNeList#U41#(U22(U11(U41(U21(isList)))))
isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U11(U41(U11(U51(U41(U21(U11(isNeList))))))))))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(tt))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U21(U21(U22(isList))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U31(isQid)))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U11(isNeList)))))))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U31(isQid))))))))
isNeList#U41#(U22(U21(U11(U51(U31(tt))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U42(U41(isList)))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(U41(U22(tt)))))))))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(tt)))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U51(U41(isList)))))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U41(isList)))))))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U42(isNeList))))))))))))isNeList#U51#(U42(U42(U41(isList))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U41(U11(isNeList)))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U31(tt)))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U31(isQid)))))))))))isNeList#U51#(U41(U21(U11(U42(U41(U21(isList)))))))
isNeList#U51#(U41(U11(U51(U31(tt)))))isNeList#U51#(U42(U41(U11(U31(isQid)))))
isList#U21#(U21(U11(U51(U51(U42(U31(isQid)))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U41(isList))))))))))))
isNeList#U51#(U51(U41(tt)))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(tt)))))))))))))
isNeList#U51#(U42(U42(U31(isQid))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U41(U11(U41(tt))))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U11(U41(isList))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(U21(isList))))))))))))
isList#U21#(U21(U21(U21(U11(U41(U11(U41(isList))))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U41(U21(U11(U51(isNeList))))))))))))))
isNeList#U41#(U22(U21(U11(U51(U51(U51(U51(U42(U51(U31(isQid)))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U21(tt))))))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U42(U51(U41(isList)))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U51(U51(U41(isList))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U21(isList))))))))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U41(U11(isNeList))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U41(U11(U42(U31(tt))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U21(U11(U41(isList)))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U42(isNeList)))))))))))isNeList#U41#(U21(U22(U11(isNeList))))
isNeList#U51#(U51(U41(U21(U11(U41(U21(U11(U31(isQid)))))))))isList#U21#(U21(U11(U51(U41(isList)))))
isNeList#U41#(U22(U21(U11(U41(U22(U21(U11(U51(U51(U51(isNeList)))))))))))isNeList#U41#(U22(U21(U11(U51(U51(U51(U52(U11(isNeList)))))))))
isNeList#U41#(U22(U21(U11(U41(U21(U21(U11(U51(isNeList)))))))))isNeList#U41#(U22(U21(U11(U51(U51(U41(tt)))))))
isList#U21#(U21(U11(U51(U51(U52(U11(U41(isList))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U21(U21(U11(U51(U31(isQid))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U31(isQid)))))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U41(U11(U41(U22(U21(U11(isNeList)))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U51(U41(U11(isNeList)))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U41(U11(U41(isList))))))))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U51(U41(U11(isNeList)))))))))))isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(U51(U51(U42(U42(U41(isList))))))))))))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U21(U11(U51(U51(U42(U51(U51(U41(tt)))))))))))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U11(U41(U11(U51(U41(U21(U21(U21(U11(U41(U11(U41(tt)))))))))))))))))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U51(U52(U21(U11(isNeList))))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(U21(isList))))))))))
isNeList#U51#(U41(U21(U11(U51(U51(U51(U41(U11(U51(U42(isNeList)))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U51(U41(U11(isNeList)))))))))))))
isNeList#U41#(U21(U11(U41(isList))))isNeList#U51#(U51(U41(U11(U51(U41(isList))))))
isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U41(U21(tt))))))))))))isList#U21#(U21(U21(U21(U11(U51(U41(U21(isList))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U21(U11(U51(U41(U11(isNeList))))))))))))))))isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U51(U31(isQid))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U51(tt)))))))isNeList#U51#(U41(U21(U11(U51(U51(U51(U51(U51(U51(U42(U51(U51(U51(U51(U41(isList))))))))))))))))
isList#U21#(U11(U42(U51(U41(U21(tt))))))isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(tt)))))))isNeList#U41#(U22(U21(U11(U41(U21(U11(U51(U41(U11(U51(isNeList)))))))))))
isList#U21#(U21(U11(U41(U11(U41(U21(U11(U52(U11(U41(U11(U51(U42(U51(isNeList)))))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U22(U11(U51(U31(isQid))))))))))))
isList#U21#(U21(U21(U21(U11(U51(U42(U51(U41(U21(tt))))))))))isList#U21#(U21(U21(U21(U11(U41(U11(U51(U51(isNeList)))))))))
isList#U21#(U21(U11(U41(U11(U41(tt))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U41(U11(U41(U21(isList)))))))))))
isList#U21#(U21(U21(U21(U11(U51(U51(U42(isNeList))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(U41(U21(U21(U22(U11(isNeList))))))))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U21(U21(U11(U41(U21(isList)))))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U41(U11(U41(U11(U51(U51(U51(U51(isNeList))))))))))))))
isList#U21#(U11(U42(U51(U41(U11(U51(U41(U11(U51(U41(U21(U11(U41(U11(U51(isNeList))))))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U41(U11(U41(U22(U21(isList))))))))))))))))
isNeList#U51#(U42(U41(U11(U41(U11(U51(U51(U42(U51(U41(U11(U41(isList)))))))))))))isNeList#U41#(U22(U21(U11(U41(U22(U11(U41(U21(U21(U11(U41(U21(U21(U21(isList)))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U21(U21(tt)))))))))))))isNeList#U51#(U51(U41(U21(U11(U51(U51(U51(U51(tt)))))))))
isNeList#U41#(U11(U41(U22(tt))))isList#U21#(U21(U21(U21(U11(U51(U31(isQid)))))))
isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U51(U41(isList)))))))))))))isNeList#U51#(U41(U21(U11(U41(U21(U11(U51(isNeList))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U11(U31(isQid))))))))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U21(U21(U11(U41(U11(isNeList))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U21(U11(U52(U11(U42(isNeList))))))))))))))isNeList#U41#(U11(U51(U41(U11(U42(U42(U31(tt))))))))
isNeList#U41#(U22(U21(U11(U41(U11(U51(U51(U41(U11(U51(isNeList)))))))))))isNeList#U51#(U41(U11(U51(U41(isList)))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U41(U22(U21(U11(U51(tt)))))))))))))))isNeList#U41#(U11(U41(U21(U11(U51(U51(U41(U21(U11(U51(U51(U41(U11(isNeList))))))))))))))
isNeList#U41#(U11(U41(U21(U21(U11(U42(U41(U21(U11(U51(U51(U51(U51(isNeList))))))))))))))isNeList#U41#(U11(U41(U21(U11(U31(tt))))))
isNeList#U51#(U42(U41(U11(U41(U11(tt))))))isNeList#U41#(U11(U41(U21(U11(U51(U42(U41(U11(U41(U21(isList)))))))))))
isNeList#U51#(U42(U41(U11(U51(isNeList)))))isList#U21#(U21(U21(U21(U11(U51(U41(U11(U41(U11(isNeList))))))))))
isNeList#U41#(U22(U11(U41(tt))))isNeList#U51#(U42(U41(U11(U41(U11(U41(U11(U41(U21(U11(U41(U21(isList)))))))))))))

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U42(U41(isList))))))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U42(U41(tt))))))))))))) 
U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U42(U41(U11(isNeList)))))))))))))) 
U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U42(U41(U21(isList)))))))))))))) 
Thus, the rule isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U42(U41(isList))))))))))))) is replaced by the following rules:
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U42(U41(tt)))))))))))))isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U42(U41(U21(isList))))))))))))))
isList#U21#(U21(U11(U51(U51(U51(U41(U21(U21(U11(U51(U42(U41(U11(isNeList))))))))))))))

Problem 4: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

isPal#isNePal#U71#(tt)isPal#
isNePal#U71#(isQid)

Rewrite Rules

__(__(X, Y), Z)__(X, __(Y, Z))__(X, nil)X
__(nil, X)XU11(tt)tt
U21(tt)U22(isList)U22(tt)tt
U31(tt)ttU41(tt)U42(isNeList)
U42(tt)ttU51(tt)U52(isList)
U52(tt)ttU61(tt)tt
U71(tt)U72(isPal)U72(tt)tt
U81(tt)ttisListU11(isNeList)
isListttisListU21(isList)
isNeListU31(isQid)isNeListU41(isList)
isNeListU51(isNeList)isNePalU61(isQid)
isNePalU71(isQid)isPalU81(isNePal)
isPalttisQidtt
isQidttisQidtt
isQidttisQidtt

Original Signature

Termination of terms over the following signature is verified: isList, isNeList, __, isPal, U71, U72, U61, U42, U51, tt, U41, isNePal, U52, U81, U11, U31, isQid, U21, U22, nil

Strategy


The right-hand side of the rule isNePal#U71#(isQid) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
Relevant TermsIrrelevant Terms
U71#(tt) 
Thus, the rule isNePal#U71#(isQid) is replaced by the following rules:
isNePal#U71#(tt)