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 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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 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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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(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 Terms	Irrelevant 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

a: 0
b: 0
c: 1
d: 1
e: 1
f(x): 0
g(x,y): 2y + x
g#(x,y): y

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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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

Relevant Terms	Irrelevant Terms

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

Relevant Terms

Irrelevant 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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

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

Relevant Terms

Irrelevant 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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

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

Relevant Terms	Irrelevant Terms

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 Terms	Irrelevant 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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
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, 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(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, d))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))	→	g^#(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(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, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, g(d, g(e, g(c, 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 Terms	Irrelevant 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 Terms	Irrelevant 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

Relevant Terms	Irrelevant Terms

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

Relevant Terms	Irrelevant Terms

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

Relevant Terms	Irrelevant Terms

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 Terms	Irrelevant 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 Terms	Irrelevant 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 Terms	Irrelevant 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)))