TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60017 ms.

The following DP Processors were used


Problem 1 was processed with processor DependencyGraph (54ms).
 | – Problem 2 was processed with processor ForwardNarrowing (1ms).
 | – Problem 3 was processed with processor PolynomialLinearRange4iUR (408ms).
 |    | – Problem 5 was processed with processor ForwardNarrowing (2ms).
 |    |    | – Problem 7 was processed with processor ForwardNarrowing (1ms).
 |    |    |    | – Problem 8 was processed with processor ForwardNarrowing (5ms).
 |    |    |    |    | – Problem 9 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    | – Problem 10 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    | – Problem 11 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    | – Problem 12 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    | – Problem 13 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    | – Problem 14 was processed with processor ForwardNarrowing (1ms).
 |    |    |    |    |    |    |    |    |    |    | – Problem 15 was processed with processor ForwardNarrowing (1ms).
 |    |    |    |    |    |    |    |    |    |    |    | – Problem 16 was processed with processor ForwardNarrowing (1ms).
 |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 17 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 18 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 19 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 20 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 21 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 22 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 23 was processed with processor ForwardNarrowing (2ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 24 was processed with processor ForwardNarrowing (4ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 25 was processed with processor ForwardNarrowing (3ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 26 was processed with processor ForwardNarrowing (9ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 27 was processed with processor ForwardNarrowing (22ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 28 was processed with processor ForwardNarrowing (31ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 29 was processed with processor ForwardNarrowing (6ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 30 was processed with processor ForwardNarrowing (19ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 31 was processed with processor ForwardNarrowing (34ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 32 was processed with processor ForwardNarrowing (53ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 33 was processed with processor ForwardNarrowing (66ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 34 was processed with processor ForwardNarrowing (88ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 35 was processed with processor ForwardNarrowing (132ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 36 was processed with processor ForwardNarrowing (131ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 37 was processed with processor ForwardNarrowing (13ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 38 was processed with processor ForwardNarrowing (27ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 39 was processed with processor ForwardNarrowing (70ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 40 was processed with processor ForwardNarrowing (52ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 41 was processed with processor ForwardNarrowing (116ms).
 |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    |    | – Problem 42 remains open; application of the following processors failed [ForwardNarrowing (65ms), ForwardNarrowing (82ms), ForwardNarrowing (72ms), ForwardNarrowing (81ms), ForwardNarrowing (69ms), ForwardNarrowing (66ms), ForwardNarrowing (69ms), ForwardNarrowing (61ms), ForwardNarrowing (76ms), ForwardNarrowing (81ms), ForwardNarrowing (125ms), ForwardNarrowing (82ms), ForwardNarrowing (87ms), ForwardNarrowing (77ms), ForwardNarrowing (86ms), ForwardNarrowing (78ms)].
 | – Problem 4 was processed with processor ForwardNarrowing (1ms).
 |    | – Problem 6 remains open; application of the following processors failed [ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (44ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), 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 (1ms), 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 (1ms), ForwardNarrowing (1ms), 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 (1ms), 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 (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), 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 (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 (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), 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 (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 (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (4ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), 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 (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), 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 (1ms), ForwardNarrowing (2ms), 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 (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (2ms), ForwardNarrowing (1ms), 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 (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), 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 (0ms), ForwardNarrowing (0ms), 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 (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), 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 (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), 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 (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 (1ms), 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 (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), 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 (1ms), 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 (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), 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 (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (16ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), 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 (14ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (2ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), 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 (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), 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 (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (3ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (2ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (3ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (17ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (43ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), 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 (0ms), 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 (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing 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ForwardNarrowing (0ms), ForwardNarrowing (0ms), 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 (0ms), ForwardNarrowing (1ms), 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 (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), 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 (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (39ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (2ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), 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 (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (4ms), 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 (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 (4ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (3ms), ForwardNarrowing (1ms), ForwardNarrowing (45ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (4ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (4ms), 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 (0ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (0ms), ForwardNarrowing (0ms), ForwardNarrowing (1ms), ForwardNarrowing (1ms), 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 (1ms)].

The following open problems remain:



Open Dependency Pair Problem 4

Dependency Pairs

f#(g(x, y))f#(x)f#(g(x, y))f#(f(x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a




Open Dependency Pair Problem 5

Dependency Pairs

g#(e, g(e, x))g#(d, g(c, x))g#(d, g(d, x))g#(c, g(e, x))
g#(c, g(c, x))g#(e, g(d, x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a


Problem 1: DependencyGraph



Dependency Pair Problem

Dependency Pairs

f#(g(x, y))g#(f(f(x)), a)g#(c, g(c, x))g#(d, x)
g#(e, g(e, x))g#(d, g(c, x))g#(d, g(d, x))g#(c, g(e, x))
g#(x, x)g#(a, b)g#(d, g(d, x))g#(e, x)
f#(g(x, y))f#(x)g#(e, g(e, x))g#(c, x)
g#(c, g(c, x))g#(e, g(d, x))f#(g(x, y))g#(y, g(f(f(x)), a))
f#(g(x, y))f#(f(x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The following SCCs where found

f#(g(x, y)) → f#(x)f#(g(x, y)) → f#(f(x))

g#(x, x) → g#(a, b)

g#(e, g(e, x)) → g#(d, g(c, x))g#(c, g(c, x)) → g#(d, x)
g#(d, g(d, x)) → g#(c, g(e, x))g#(d, g(d, x)) → g#(e, x)
g#(e, g(e, x)) → g#(c, x)g#(c, g(c, x)) → g#(e, g(d, x))

Problem 2: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(x, x)g#(a, b)

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(x, x) → g#(a, b) 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
Thus, the rule g#(x, x) → g#(a, b) is deleted.

Problem 3: PolynomialLinearRange4iUR



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, x))g#(d, g(c, x))g#(c, g(c, x))g#(d, x)
g#(d, g(d, x))g#(c, g(e, x))g#(d, g(d, x))g#(e, x)
g#(e, g(e, x))g#(c, x)g#(c, g(c, x))g#(e, g(d, x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


Polynomial Interpretation

Improved Usable rules

g(c, g(c, x))g(e, g(d, x))g(e, g(e, x))g(d, g(c, x))
g(x, x)g(a, b)g(d, g(d, x))g(c, g(e, x))

The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:

g#(c, g(c, x))g#(d, x)g#(d, g(d, x))g#(e, x)
g#(e, g(e, x))g#(c, x)

Problem 5: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, x))g#(d, g(c, x))g#(d, g(d, x))g#(c, g(e, x))
g#(c, g(c, x))g#(e, g(d, x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, x)) → g#(d, g(c, x)) 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
g#(d, g(a, b)) 
g#(d, g(e, g(d, _x31))) 
Thus, the rule g#(e, g(e, x)) → g#(d, g(c, x)) is replaced by the following rules:
g#(e, g(e, c)) → g#(d, g(a, b))g#(e, g(e, g(c, _x31))) → g#(d, g(e, g(d, _x31)))

Problem 7: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(d, g(d, x))g#(c, g(e, x))g#(e, g(e, c))g#(d, g(a, b))
g#(e, g(e, g(c, _x31)))g#(d, g(e, g(d, _x31)))g#(c, g(c, x))g#(e, g(d, x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(d, g(d, x)) → g#(c, g(e, x)) 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
g#(c, g(d, g(c, _x31))) 
g#(c, g(a, b)) 
Thus, the rule g#(d, g(d, x)) → g#(c, g(e, x)) is replaced by the following rules:
g#(d, g(d, e)) → g#(c, g(a, b))g#(d, g(d, g(e, _x31))) → g#(c, g(d, g(c, _x31)))

Problem 8: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(d, g(d, e))g#(c, g(a, b))g#(d, g(d, g(e, _x31)))g#(c, g(d, g(c, _x31)))
g#(e, g(e, c))g#(d, g(a, b))g#(e, g(e, g(c, _x31)))g#(d, g(e, g(d, _x31)))
g#(c, g(c, x))g#(e, g(d, x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(d, g(d, e)) → g#(c, g(a, b)) 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
Thus, the rule g#(d, g(d, e)) → g#(c, g(a, b)) is deleted.

Problem 9: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(d, g(d, g(e, _x31)))g#(c, g(d, g(c, _x31)))g#(e, g(e, c))g#(d, g(a, b))
g#(e, g(e, g(c, _x31)))g#(d, g(e, g(d, _x31)))g#(c, g(c, x))g#(e, g(d, x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(d, g(d, g(e, _x31))) → g#(c, g(d, g(c, _x31))) 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
g#(c, g(d, g(a, b))) 
g#(c, g(d, g(e, g(d, _x61)))) 
Thus, the rule g#(d, g(d, g(e, _x31))) → g#(c, g(d, g(c, _x31))) is replaced by the following rules:
g#(d, g(d, g(e, g(c, _x61)))) → g#(c, g(d, g(e, g(d, _x61))))g#(d, g(d, g(e, c))) → g#(c, g(d, g(a, b)))

Problem 10: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(d, g(d, g(e, g(c, _x61))))g#(c, g(d, g(e, g(d, _x61))))g#(e, g(e, c))g#(d, g(a, b))
g#(e, g(e, g(c, _x31)))g#(d, g(e, g(d, _x31)))g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))
g#(c, g(c, x))g#(e, g(d, x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(d, g(d, g(e, g(c, _x61)))) → g#(c, g(d, g(e, g(d, _x61)))) 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
g#(c, g(d, g(e, g(c, g(e, _x71))))) 
g#(c, g(d, g(e, g(a, b)))) 
Thus, the rule g#(d, g(d, g(e, g(c, _x61)))) → g#(c, g(d, g(e, g(d, _x61)))) is replaced by the following rules:
g#(d, g(d, g(e, g(c, g(d, _x71))))) → g#(c, g(d, g(e, g(c, g(e, _x71)))))g#(d, g(d, g(e, g(c, d)))) → g#(c, g(d, g(e, g(a, b))))

Problem 11: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(d, g(d, g(e, g(c, g(d, _x71)))))g#(c, g(d, g(e, g(c, g(e, _x71)))))g#(d, g(d, g(e, g(c, d))))g#(c, g(d, g(e, g(a, b))))
g#(e, g(e, c))g#(d, g(a, b))g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))
g#(e, g(e, g(c, _x31)))g#(d, g(e, g(d, _x31)))g#(c, g(c, x))g#(e, g(d, x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(d, g(d, g(e, g(c, g(d, _x71))))) → g#(c, g(d, g(e, g(c, g(e, _x71))))) 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
g#(c, g(d, g(e, g(c, g(d, g(c, _x101)))))) 
g#(c, g(d, g(e, g(c, g(a, b))))) 
Thus, the rule g#(d, g(d, g(e, g(c, g(d, _x71))))) → g#(c, g(d, g(e, g(c, g(e, _x71))))) is replaced by the following rules:
g#(d, g(d, g(e, g(c, g(d, e))))) → g#(c, g(d, g(e, g(c, g(a, b)))))g#(d, g(d, g(e, g(c, g(d, g(e, _x101)))))) → g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))

Problem 12: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(d, g(d, g(e, g(c, g(d, e)))))g#(c, g(d, g(e, g(c, g(a, b)))))g#(d, g(d, g(e, g(c, d))))g#(c, g(d, g(e, g(a, b))))
g#(e, g(e, c))g#(d, g(a, b))g#(e, g(e, g(c, _x31)))g#(d, g(e, g(d, _x31)))
g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))g#(c, g(c, x))g#(e, g(d, x))
g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(d, g(d, g(e, g(c, g(d, e))))) → g#(c, g(d, g(e, g(c, g(a, b))))) 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
Thus, the rule g#(d, g(d, g(e, g(c, g(d, e))))) → g#(c, g(d, g(e, g(c, g(a, b))))) is deleted.

Problem 13: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(d, g(d, g(e, g(c, d))))g#(c, g(d, g(e, g(a, b))))g#(e, g(e, c))g#(d, g(a, b))
g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))g#(e, g(e, g(c, _x31)))g#(d, g(e, g(d, _x31)))
g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))g#(c, g(c, x))g#(e, g(d, x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(d, g(d, g(e, g(c, d)))) → g#(c, g(d, g(e, g(a, b)))) 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
Thus, the rule g#(d, g(d, g(e, g(c, d)))) → g#(c, g(d, g(e, g(a, b)))) is deleted.

Problem 14: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, c))g#(d, g(a, b))g#(e, g(e, g(c, _x31)))g#(d, g(e, g(d, _x31)))
g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))g#(c, g(c, x))g#(e, g(d, x))
g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, c)) → g#(d, g(a, b)) 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
Thus, the rule g#(e, g(e, c)) → g#(d, g(a, b)) is deleted.

Problem 15: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))g#(e, g(e, g(c, _x31)))g#(d, g(e, g(d, _x31)))
g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))g#(c, g(c, x))g#(e, g(d, x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, g(c, _x31))) → g#(d, g(e, g(d, _x31))) 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
g#(d, g(e, g(c, g(e, _x61)))) 
g#(d, g(e, g(a, b))) 
Thus, the rule g#(e, g(e, g(c, _x31))) → g#(d, g(e, g(d, _x31))) is replaced by the following rules:
g#(e, g(e, g(c, d))) → g#(d, g(e, g(a, b)))g#(e, g(e, g(c, g(d, _x61)))) → g#(d, g(e, g(c, g(e, _x61))))

Problem 16: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, g(c, d)))g#(d, g(e, g(a, b)))g#(e, g(e, g(c, g(d, _x61))))g#(d, g(e, g(c, g(e, _x61))))
g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))g#(c, g(c, x))g#(e, g(d, x))
g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, g(c, d))) → g#(d, g(e, g(a, b))) 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
Thus, the rule g#(e, g(e, g(c, d))) → g#(d, g(e, g(a, b))) is deleted.

Problem 17: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, g(c, g(d, _x61))))g#(d, g(e, g(c, g(e, _x61))))g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))
g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))g#(c, g(c, x))g#(e, g(d, x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, g(c, g(d, _x61)))) → g#(d, g(e, g(c, g(e, _x61)))) 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
g#(d, g(e, g(c, g(d, g(c, _x71))))) 
g#(d, g(e, g(c, g(a, b)))) 
Thus, the rule g#(e, g(e, g(c, g(d, _x61)))) → g#(d, g(e, g(c, g(e, _x61)))) is replaced by the following rules:
g#(e, g(e, g(c, g(d, g(e, _x71))))) → g#(d, g(e, g(c, g(d, g(c, _x71)))))g#(e, g(e, g(c, g(d, e)))) → g#(d, g(e, g(c, g(a, b))))

Problem 18: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, g(c, g(d, g(e, _x71)))))g#(d, g(e, g(c, g(d, g(c, _x71)))))g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))
g#(e, g(e, g(c, g(d, e))))g#(d, g(e, g(c, g(a, b))))g#(c, g(c, x))g#(e, g(d, x))
g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, g(c, g(d, g(e, _x71))))) → g#(d, g(e, g(c, g(d, g(c, _x71))))) 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
g#(d, g(e, g(c, g(d, g(e, g(d, _x101)))))) 
g#(d, g(e, g(c, g(d, g(a, b))))) 
Thus, the rule g#(e, g(e, g(c, g(d, g(e, _x71))))) → g#(d, g(e, g(c, g(d, g(c, _x71))))) is replaced by the following rules:
g#(e, g(e, g(c, g(d, g(e, c))))) → g#(d, g(e, g(c, g(d, g(a, b)))))g#(e, g(e, g(c, g(d, g(e, g(c, _x101)))))) → g#(d, g(e, g(c, g(d, g(e, g(d, _x101))))))

Problem 19: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, g(c, g(d, g(e, c)))))g#(d, g(e, g(c, g(d, g(a, b)))))g#(e, g(e, g(c, g(d, g(e, g(c, _x101))))))g#(d, g(e, g(c, g(d, g(e, g(d, _x101))))))
g#(e, g(e, g(c, g(d, e))))g#(d, g(e, g(c, g(a, b))))g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))
g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))g#(c, g(c, x))g#(e, g(d, x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, g(c, g(d, g(e, c))))) → g#(d, g(e, g(c, g(d, g(a, b))))) 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
Thus, the rule g#(e, g(e, g(c, g(d, g(e, c))))) → g#(d, g(e, g(c, g(d, g(a, b))))) is deleted.

Problem 20: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, g(c, g(d, g(e, g(c, _x101))))))g#(d, g(e, g(c, g(d, g(e, g(d, _x101))))))g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))
g#(e, g(e, g(c, g(d, e))))g#(d, g(e, g(c, g(a, b))))g#(c, g(c, x))g#(e, g(d, x))
g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, g(c, g(d, g(e, g(c, _x101)))))) → g#(d, g(e, g(c, g(d, g(e, g(d, _x101)))))) 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
g#(d, g(e, g(c, g(d, g(e, g(a, b)))))) 
g#(d, g(e, g(c, g(d, g(e, g(c, g(e, _x111))))))) 
Thus, the rule g#(e, g(e, g(c, g(d, g(e, g(c, _x101)))))) → g#(d, g(e, g(c, g(d, g(e, g(d, _x101)))))) is replaced by the following rules:
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, _x111))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(e, _x111)))))))g#(e, g(e, g(c, g(d, g(e, g(c, d)))))) → g#(d, g(e, g(c, g(d, g(e, g(a, b))))))

Problem 21: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, g(c, g(d, g(e, g(c, g(d, _x111)))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(e, _x111)))))))g#(e, g(e, g(c, g(d, g(e, g(c, d))))))g#(d, g(e, g(c, g(d, g(e, g(a, b))))))
g#(e, g(e, g(c, g(d, e))))g#(d, g(e, g(c, g(a, b))))g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))
g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))g#(c, g(c, x))g#(e, g(d, x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, g(c, g(d, g(e, g(c, g(d, _x111))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(e, _x111))))))) 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
g#(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))) 
g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x141)))))))) 
Thus, the rule g#(e, g(e, g(c, g(d, g(e, g(c, g(d, _x111))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(e, _x111))))))) is replaced by the following rules:
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, e))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x141)))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x141))))))))

Problem 22: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))g#(e, g(e, g(c, g(d, g(e, g(c, d))))))g#(d, g(e, g(c, g(d, g(e, g(a, b))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x141))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x141))))))))g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))
g#(e, g(e, g(c, g(d, e))))g#(d, g(e, g(c, g(a, b))))g#(c, g(c, x))g#(e, g(d, x))
g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, g(c, g(d, g(e, g(c, g(d, e))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))) 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
Thus, the rule g#(e, g(e, g(c, g(d, g(e, g(c, g(d, e))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))) is deleted.

Problem 23: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x141))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x141))))))))g#(e, g(e, g(c, g(d, g(e, g(c, d))))))g#(d, g(e, g(c, g(d, g(e, g(a, b))))))
g#(e, g(e, g(c, g(d, e))))g#(d, g(e, g(c, g(a, b))))g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))
g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))g#(c, g(c, x))g#(e, g(d, x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, g(c, g(d, g(e, g(c, d)))))) → g#(d, g(e, g(c, g(d, g(e, g(a, b)))))) 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
Thus, the rule g#(e, g(e, g(c, g(d, g(e, g(c, d)))))) → g#(d, g(e, g(c, g(d, g(e, g(a, b)))))) is deleted.

Problem 24: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x141))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x141))))))))g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))
g#(e, g(e, g(c, g(d, e))))g#(d, g(e, g(c, g(a, b))))g#(c, g(c, x))g#(e, g(d, x))
g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x141)))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x141)))))))) 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
g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))) 
g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x151))))))))) 
Thus, the rule g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x141)))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x141)))))))) is replaced by the following rules:
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x151))))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x151)))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))

Problem 25: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x151)))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x151)))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))
g#(e, g(e, g(c, g(d, e))))g#(d, g(e, g(c, g(a, b))))g#(d, g(d, g(e, c)))g#(c, g(d, g(a, b)))
g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))g#(c, g(c, x))g#(e, g(d, x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x151))))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x151))))))))) 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
g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b))))))))) 
g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x181)))))))))) 
Thus, the rule g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x151))))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x151))))))))) is replaced by the following rules:
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d))))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x181)))))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x181))))))))))

Problem 26: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x461))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x461))))))))))))))))))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))
g#(c, g(c, x))g#(e, g(d, x))g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x461)))))))))))))))))))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x461)))))))))))))))))))))))) 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
g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))) 
g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x471))))))))))))))))))))))))) 
Thus, the rule g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x461)))))))))))))))))))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x461)))))))))))))))))))))))) is replaced by the following rules:
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x471))))))))))))))))))))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x471)))))))))))))))))))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b))))))))))))))))))))))))

Problem 27: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x981))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x981))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, x))g#(e, g(d, x))
g#(d, g(d, g(e, g(c, g(d, g(e, _x101))))))g#(c, g(d, g(e, g(c, g(d, g(c, _x101))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))))))))))))))))))))))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))))))))))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x981)))))))))))))))))))))))))))))))))))))))))))))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x981)))))))))))))))))))))))))))))))))))))))))))))))))) 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
g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1011))))))))))))))))))))))))))))))))))))))))))))))))))) 
g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))) 
Thus, the rule g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x981)))))))))))))))))))))))))))))))))))))))))))))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x981)))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1011))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1011)))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))

Problem 28: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1371)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1371)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, _x31)))g#(e, g(c, g(e, _x31)))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x221))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x221))))))))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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
Thus, the rule g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is deleted.

Problem 29: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x221))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x221))))))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x331)))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x331)))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x331))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x331))))))))))))))))) 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
g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x341)))))))))))))))))) 
g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b))))))))))))))))) 
Thus, the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x331))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x331))))))))))))))))) is replaced by the following rules:
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x341)))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x341))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))

Problem 30: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x221))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x221))))))))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x901))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x901))))))))))))))))))))))))))))))))))))))))))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))))))) 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
Thus, the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))))))) is deleted.

Problem 31: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1341))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1341))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x221))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x221))))))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1341)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1341)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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
g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 
g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x1371))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 
Thus, the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1341)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1341)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x1371))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x1371)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Problem 32: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x1831)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x1831)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x221))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x221))))))))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x1831))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x1831))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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
g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 
g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x1861)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 
Thus, the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x1831))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x1831))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x1861)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x1861))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Problem 33: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x2301))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x2301))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x271)))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x271)))))))))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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
Thus, the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is deleted.

Problem 34: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x2781))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x2781))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x271)))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x271)))))))))))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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
Thus, the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is deleted.

Problem 35: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x3331)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x3331)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
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g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x271)))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x271)))))))))))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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
Thus, the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is deleted.

Problem 36: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, _x271)))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(c, _x271)))))))))))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x3771)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x3771)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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
Thus, the rule g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is deleted.

Problem 37: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x811)))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x811)))))))))))))))))))))))))))))))))))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x3771)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x3771)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b))))))))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))))))))))))))))))))))))))))))) → g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))) 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
Thus, the rule g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))))))))))))))))))))))))))))))) → g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))) is deleted.

Problem 38: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1541))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x3771)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x3771)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1331)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1331)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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
Thus, the rule g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is deleted.

Problem 39: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1431)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1431)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x1931)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x1931)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x3771)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x3771)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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
Thus, the rule g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is deleted.

Problem 40: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, _x1981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(d, _x1981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x1931)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x1931)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x3771)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x3771)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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
Thus, the rule g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is deleted.

Problem 41: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x2471)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x2471)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, d)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, e))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(c, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x3771)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x3771)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(e, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, _x1931)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(e, _x1931)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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
Thus, the rule g#(d, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, c))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → g#(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(a, b))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is deleted.

Problem 4: ForwardNarrowing



Dependency Pair Problem

Dependency Pairs

f#(g(x, y))f#(x)f#(g(x, y))f#(f(x))

Rewrite Rules

g(x, x)g(a, b)g(c, g(c, x))g(e, g(d, x))
g(d, g(d, x))g(c, g(e, x))g(e, g(e, x))g(d, g(c, x))
f(g(x, y))g(y, g(f(f(x)), a))

Original Signature

Termination of terms over the following signature is verified: f, g, d, e, b, c, a

Strategy


The right-hand side of the rule f#(g(x, y)) → f#(f(x)) 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
f#(g(_x21, g(f(f(_x22)), a))) 
Thus, the rule f#(g(x, y)) → f#(f(x)) is replaced by the following rules:
f#(g(g(_x22, _x21), y)) → f#(g(_x21, g(f(f(_x22)), a)))