TIMEOUT
The TRS could not be proven terminating. The proof attempt took 60003 ms.
The following DP Processors were used
Problem 1 was processed with processor DependencyGraph (35ms).
| – Problem 2 was processed with processor ForwardNarrowing (2ms).
| | – Problem 3 was processed with processor ForwardNarrowing (1ms).
| | | – Problem 4 was processed with processor ForwardNarrowing (2ms).
| | | | – Problem 5 was processed with processor ForwardNarrowing (7ms).
| | | | | – Problem 6 was processed with processor ForwardNarrowing (2ms).
| | | | | | – Problem 7 was processed with processor ForwardNarrowing (4ms).
| | | | | | | – Problem 8 was processed with processor ForwardNarrowing (4ms).
| | | | | | | | – Problem 9 was processed with processor ForwardNarrowing (10ms).
| | | | | | | | | – Problem 10 was processed with processor ForwardNarrowing (4ms).
| | | | | | | | | | – Problem 11 was processed with processor ForwardNarrowing (7ms).
| | | | | | | | | | | – Problem 12 was processed with processor ForwardNarrowing (4ms).
| | | | | | | | | | | | – Problem 13 was processed with processor ForwardNarrowing (2ms).
| | | | | | | | | | | | | – Problem 14 was processed with processor ForwardNarrowing (5ms).
| | | | | | | | | | | | | | – Problem 15 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | – Problem 16 was processed with processor ForwardNarrowing (3ms).
| | | | | | | | | | | | | | | | – Problem 17 was processed with processor ForwardNarrowing (7ms).
| | | | | | | | | | | | | | | | | – Problem 18 was processed with processor ForwardNarrowing (5ms).
| | | | | | | | | | | | | | | | | | – Problem 19 was processed with processor ForwardNarrowing (5ms).
| | | | | | | | | | | | | | | | | | | – Problem 20 was processed with processor ForwardNarrowing (9ms).
| | | | | | | | | | | | | | | | | | | | – Problem 21 was processed with processor ForwardNarrowing (7ms).
| | | | | | | | | | | | | | | | | | | | | – Problem 22 was processed with processor ForwardNarrowing (4ms).
| | | | | | | | | | | | | | | | | | | | | | – Problem 23 was processed with processor ForwardNarrowing (33ms).
| | | | | | | | | | | | | | | | | | | | | | | – Problem 24 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | | | | | | | | | | – Problem 25 was processed with processor ForwardNarrowing (4ms).
| | | | | | | | | | | | | | | | | | | | | | | | | – Problem 26 was processed with processor ForwardNarrowing (2ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 27 was processed with processor ForwardNarrowing (3ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 28 was processed with processor ForwardNarrowing (2ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 29 was processed with processor ForwardNarrowing (1ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 30 was processed with processor ForwardNarrowing (1ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 31 was processed with processor ForwardNarrowing (2ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 32 was processed with processor ForwardNarrowing (33ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 33 was processed with processor ForwardNarrowing (0ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 34 was processed with processor ForwardNarrowing (5ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 35 was processed with processor ForwardNarrowing (2ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 36 was processed with processor ForwardNarrowing (1ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 37 was processed with processor ForwardNarrowing (13ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 38 was processed with processor ForwardNarrowing (15ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 39 was processed with processor ForwardNarrowing (5ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 40 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 41 was processed with processor ForwardNarrowing (9ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 42 was processed with processor ForwardNarrowing (7ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 43 was processed with processor ForwardNarrowing (10ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 44 was processed with processor ForwardNarrowing (10ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 45 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 46 was processed with processor ForwardNarrowing (9ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 47 was processed with processor ForwardNarrowing (54ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 48 was processed with processor ForwardNarrowing (13ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 49 was processed with processor ForwardNarrowing (9ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 50 was processed with processor ForwardNarrowing (9ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 51 was processed with processor ForwardNarrowing (9ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 52 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 53 was processed with processor ForwardNarrowing (5ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 54 was processed with processor ForwardNarrowing (10ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 55 was processed with processor ForwardNarrowing (62ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 56 was processed with processor ForwardNarrowing (60ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 57 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 58 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 59 was processed with processor ForwardNarrowing (21ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 60 was processed with processor ForwardNarrowing (74ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 61 was processed with processor ForwardNarrowing (10ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 62 was processed with processor ForwardNarrowing (8ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 63 was processed with processor ForwardNarrowing (13ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 64 was processed with processor ForwardNarrowing (14ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 65 was processed with processor ForwardNarrowing (80ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 66 was processed with processor ForwardNarrowing (9ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 67 was processed with processor ForwardNarrowing (9ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 68 was processed with processor ForwardNarrowing (83ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 69 was processed with processor ForwardNarrowing (10ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 70 was processed with processor ForwardNarrowing (15ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 71 was processed with processor ForwardNarrowing (12ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 72 was processed with processor ForwardNarrowing (12ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 73 was processed with processor ForwardNarrowing (11ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 74 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 75 was processed with processor ForwardNarrowing (12ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 76 was processed with processor ForwardNarrowing (12ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 77 was processed with processor ForwardNarrowing (13ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 78 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 79 was processed with processor ForwardNarrowing (12ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 80 was processed with processor ForwardNarrowing (13ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 81 was processed with processor ForwardNarrowing (14ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 82 was processed with processor ForwardNarrowing (11ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 83 was processed with processor ForwardNarrowing (5ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 84 was processed with processor ForwardNarrowing (12ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 85 was processed with processor ForwardNarrowing (12ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 86 was processed with processor ForwardNarrowing (12ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 87 was processed with processor ForwardNarrowing (7ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 88 was processed with processor ForwardNarrowing (13ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 89 was processed with processor ForwardNarrowing (16ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 90 was processed with processor ForwardNarrowing (135ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 91 was processed with processor ForwardNarrowing (5ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 92 was processed with processor ForwardNarrowing (11ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 93 was processed with processor ForwardNarrowing (5ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 94 was processed with processor ForwardNarrowing (5ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 95 was processed with processor ForwardNarrowing (11ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 96 was processed with processor ForwardNarrowing (13ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 97 was processed with processor ForwardNarrowing (12ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 98 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 99 was processed with processor ForwardNarrowing (15ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 100 was processed with processor ForwardNarrowing (15ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 101 was processed with processor ForwardNarrowing (4ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 102 was processed with processor ForwardNarrowing (11ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 103 was processed with processor ForwardNarrowing (8ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 104 was processed with processor ForwardNarrowing (12ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 105 was processed with processor ForwardNarrowing (5ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 106 was processed with processor ForwardNarrowing (5ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 107 remains open; application of the following processors failed [ForwardNarrowing (6ms), ForwardNarrowing (10ms), ForwardNarrowing (4ms), ForwardNarrowing (9ms), ForwardNarrowing (6ms), ForwardNarrowing (3ms), ForwardNarrowing (4ms), ForwardNarrowing (4ms), ForwardNarrowing (11ms), ForwardNarrowing (4ms), ForwardNarrowing (10ms), ForwardNarrowing (3ms), ForwardNarrowing (10ms), ForwardNarrowing (3ms), ForwardNarrowing (9ms), ForwardNarrowing (4ms), ForwardNarrowing (16ms), ForwardNarrowing (4ms), ForwardNarrowing (11ms), ForwardNarrowing (4ms), ForwardNarrowing (10ms), ForwardNarrowing (4ms), ForwardNarrowing (8ms), ForwardNarrowing (4ms), ForwardNarrowing (10ms), ForwardNarrowing (4ms), ForwardNarrowing (6ms), ForwardNarrowing (9ms), ForwardNarrowing (4ms), ForwardNarrowing (9ms), ForwardNarrowing (4ms), ForwardNarrowing (8ms), ForwardNarrowing (5ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| c#(b(a(X))) | → | c#(c(X)) | | c#(b(a(X))) | → | c#(X) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Problem 1: DependencyGraph
Dependency Pair Problem
Dependency Pairs
| c#(b(a(X))) | → | a#(b(b(c(c(X))))) | | c#(b(a(X))) | → | c#(c(X)) |
| c#(b(a(X))) | → | a#(a(b(b(c(c(X)))))) | | c#(b(a(X))) | → | b#(b(c(c(X)))) |
| c#(b(a(X))) | → | b#(c(c(X))) | | c#(b(a(X))) | → | c#(X) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The following SCCs where found
| c#(b(a(X))) → c#(c(X)) | c#(b(a(X))) → c#(X) |
Problem 2: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(X))) | → | c#(c(X)) | | c#(b(a(X))) | → | c#(X) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(
X))) → c
#(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 |
|---|
| c#(a(a(b(b(c(c(_x21))))))) | |
| c#(e) | |
Thus, the rule c
#(b(a(
X))) → c
#(c(
X)) is replaced by the following rules:
| c#(b(a(_x21))) → c#(e) | c#(b(a(b(a(_x21))))) → c#(a(a(b(b(c(c(_x21))))))) |
Problem 3: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(_x21))) | → | c#(e) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(c(c(_x21))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(
_x21))) → c
#(e) 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 c
#(b(a(
_x21))) → c
#(e) is deleted.
Problem 4: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(c(c(_x21))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(
_x21))))) → c
#(a(a(b(b(c(c(
_x21))))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(b(b(c(a(a(b(b(c(c(_x81)))))))))))) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(e))))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
Thus, the rule c
#(b(a(b(a(
_x21))))) → c
#(a(a(b(b(c(c(
_x21))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(_x81))))))) → c#(a(a(b(b(c(a(a(b(b(c(c(_x81)))))))))))) | c#(b(a(b(a(_x21))))) → c#(a(a(b(b(e))))) |
| c#(b(a(b(a(_x21))))) → c#(a(a(e))) | c#(b(a(b(a(_x21))))) → c#(a(e)) |
| c#(b(a(b(a(_x21))))) → c#(e) | c#(b(a(b(a(_x81))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) → c#(a(a(b(e)))) |
Problem 5: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(c(_x81)))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) | | c#(b(a(b(a(_x21))))) | → | c#(a(e)) |
| c#(b(a(b(a(_x21))))) | → | c#(e) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(
_x81))))))) → c
#(a(a(b(b(c(a(a(b(b(c(c(
_x81)))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x131))))))))))))))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(
_x81))))))) → c
#(a(a(b(b(c(a(a(b(b(c(c(
_x81)))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(_x81))))))) → c#(a(e)) | c#(b(a(b(a(b(a(_x81))))))) → c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x131))))))))))))))))) | c#(b(a(b(a(b(a(_x81))))))) → c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(_x131))))))) → c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | c#(b(a(b(a(b(a(_x81))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(_x81))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) | c#(b(a(b(a(b(a(_x81))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(_x81))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(_x81))))))) → c#(e) |
Problem 6: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x131))))))))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(
_x81))))))) → c
#(a(e)) 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 |
|---|
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(
_x81))))))) → c
#(a(e)) is replaced by the following rules:
| c#(b(a(b(a(b(a(_x81))))))) → c#(e) |
Problem 7: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x131))))))))))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(
_x81))))))) → c
#(a(a(b(b(c(a(e))))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(e))))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
Thus, the rule c
#(b(a(b(a(b(a(
_x81))))))) → c
#(a(a(b(b(c(a(e))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(_x81))))))) → c#(a(e)) | c#(b(a(b(a(b(a(_x81))))))) → c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(_x81))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(_x81))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(_x81))))))) → c#(e) |
Problem 8: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x131))))))))))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(
_x81))))))) → c
#(a(e)) 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 |
|---|
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(
_x81))))))) → c
#(a(e)) is replaced by the following rules:
| c#(b(a(b(a(b(a(_x81))))))) → c#(e) |
Problem 9: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x131))))))))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(
_x131))))))))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(
_x131))))))))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(e)))))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(e)))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
Problem 10: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(e))))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(e))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(e)) |
Problem 11: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(e))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(e))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(e)))))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(e)))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(e)) |
Problem 12: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(e))))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(e))))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(e))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(e)) |
Problem 13: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(e)))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(e)))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(e)) |
Problem 14: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(e)))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(e)) |
Problem 15: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(e))))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(e))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(e)) |
Problem 16: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(e)))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(e)))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(e)) |
Problem 17: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
Problem 18: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(c(a(e))))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(c(a(e))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(e)))) |
Problem 19: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(e)) 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 |
|---|
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(e)) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(e) |
Problem 20: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(e)))))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(e)))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
Problem 21: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(c(a(e))))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(c(a(e))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(e)))) |
Problem 22: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(e)) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(e)))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(e))))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(e))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(e)) |
Problem 23: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(e)) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(e)))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(e)))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(e)))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(e)))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(e)))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(e)))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(e))))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(e))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(e)) |
Problem 24: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(e)) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(e)))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(e)))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(e))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(e))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(e)))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(e)) |
Problem 25: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(e)))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(e)))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(e))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(e))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(e)))) |
Problem 26: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(e)))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(_x21))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(e)))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(e))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(e))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(e)))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x131))))))))) → c
#(a(a(b(b(c(e)))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) → c#(a(e)) |
Problem 27: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(e)))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(e)))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(_x21))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(e))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(e)))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(e))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(e)))))))) → c
#(e) 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 c
#(b(a(b(a(b(a(b(e)))))))) → c
#(e) is deleted.
Problem 28: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(e))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(c(e)))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(c(e)))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(e)))) |
Problem 29: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(e))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(b(e))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(b(e))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) → c#(a(e)) |
Problem 30: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(e))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(e)) 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 |
|---|
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(e)) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(e) |
Problem 31: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(e)) 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 |
|---|
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(e)) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(e) |
Problem 32: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(e)))))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(e)))) |
Problem 33: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(_x21))))) | → | c#(a(e)) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(_x21))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x181)))))))))))))))))))))) | | c#(b(a(b(a(_x21))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(a(b(b(e)))))))) | → | c#(e) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(
_x21))))) → c
#(a(e)) 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 |
|---|
| c#(e) | |
Thus, the rule c
#(b(a(b(a(
_x21))))) → c
#(a(e)) is replaced by the following rules:
| c#(b(a(b(a(e))))) → c#(e) |
Problem 34: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(e)) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x231))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(a(b(b(e)))))))) | → | c#(e) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(
_x181))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(
_x181))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) → c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
Problem 35: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x231))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(a(b(b(e)))))))) | → | c#(e) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c
#(a(a(b(b(e))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c
#(a(a(b(b(e))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(a(a(b(e)))) |
Problem 36: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(e)) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x231))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(a(b(b(e)))))))) | → | c#(e) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(
_x181))))))))))) → c
#(a(e)) 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 |
|---|
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(
_x181))))))))))) → c
#(a(e)) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) → c#(e) |
Problem 37: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x231))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(a(b(b(e)))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x231))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(
_x231))))))))))))))))))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x231))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(
_x231))))))))))))))))))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
Problem 38: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(a(b(b(e)))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x291))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x291))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(e)))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
Problem 39: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(a(b(b(e)))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x291))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x291))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(e) |
Problem 40: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(a(b(b(e)))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(
_x181))))))))))) → c
#(a(e)) 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 |
|---|
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(
_x181))))))))))) → c
#(a(e)) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) → c#(e) |
Problem 41: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(a(b(b(e)))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(e)))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(c(e)))))) |
Problem 42: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(a(b(b(e)))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c
#(a(a(b(e)))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c
#(a(a(b(e)))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c#(e) |
Problem 43: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(a(b(b(e)))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
Problem 44: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(a(b(b(e)))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(c(a(a(b(e))))))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(
_x181))))))))) → c
#(a(a(b(b(c(a(a(b(e))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(_x181))))))))) → c#(a(a(b(e)))) |
Problem 45: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(e)) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c
#(a(e)) 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 |
|---|
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c
#(a(e)) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(e) |
Problem 46: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(a(a(b(e)))) |
Problem 47: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(e)))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(e)))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) → c#(a(a(b(b(e))))) |
Problem 48: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(e)))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(e)) |
Problem 49: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(e)) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x291))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(e))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x291))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(e))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(e))))) |
Problem 50: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) → c#(a(e)) |
Problem 51: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x291))))))))))))) → c
#(a(a(b(b(c(a(e))))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x291))))))))))))) → c
#(a(a(b(b(c(a(e))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(e))))) |
Problem 52: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c
#(a(a(b(b(e))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c
#(a(a(b(b(e))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(a(a(b(e)))) | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) → c#(e) |
Problem 53: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(e)) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x291))))))))))))) → c
#(e) 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 c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x291))))))))))))) → c
#(e) is deleted.
Problem 54: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x291))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x291))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
Problem 55: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(e)) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(
_x181))))))))))) → c
#(a(e)) 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 |
|---|
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(
_x181))))))))))) → c
#(a(e)) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) → c#(e) |
Problem 56: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(e)) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c
#(e) 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 c
#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) → c
#(e) is deleted.
Problem 57: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(e)) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x231))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x231))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(e)) |
Problem 58: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(e)) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x291)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x231))))))))))))) → c
#(a(a(b(b(c(a(a(e)))))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(e))))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(
_x231))))))))))))) → c
#(a(a(b(b(c(a(a(e)))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) → c#(a(e)) |
Problem 59: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x341))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
Problem 60: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(e)) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x341))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(e)) |
Problem 61: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(e) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x341))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(
_x231))))))))))) → c
#(a(a(b(e)))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(
_x231))))))))))) → c
#(a(a(b(e)))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) → c#(a(e)) |
Problem 62: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x341))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(e)) 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 |
|---|
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(e)) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(e) |
Problem 63: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x341))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x291))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(e))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(e)))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x291))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(e))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) → c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) → c#(a(a(b(e)))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
Problem 64: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x341))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(b(b(c(a(a(b(e))))))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(b(b(c(a(a(b(e))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(e)))) |
Problem 65: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(e)) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x341))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(e)) |
Problem 66: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(e)) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x341))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(e)) |
Problem 67: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x341))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(e)) |
Problem 68: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x341))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(e))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(e))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(e)))) |
Problem 69: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x341))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(b(b(c(e)))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(b(b(c(e)))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(e)))) |
Problem 70: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x341))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) → c#(a(a(b(e)))) |
Problem 71: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(e)))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 72: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 73: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 74: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 75: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 76: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 77: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 78: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(e)) 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 |
|---|
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(e)) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) |
Problem 79: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(e))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(e))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 80: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(e))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(e))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 81: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(e))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(e))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 82: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 83: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 84: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 85: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(e) 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 c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(e) is deleted.
Problem 86: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 87: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 88: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(e) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 89: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(e)))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(e)))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 90: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(e)))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(e)))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 91: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(e)))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(e)))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 92: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(e))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(e))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 93: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 94: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 95: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 96: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 97: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 98: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(e))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(e))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 99: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(e))))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
| c#(a(a(b(e)))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 100: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 101: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(e)) 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 |
|---|
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(e)) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) |
Problem 102: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(e))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(e))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 103: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) 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 |
|---|
| c#(a(a(b(b(c(a(a(b(e))))))))) | |
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(c(e)))))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(b(c(a(e))))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
| c#(a(a(b(b(c(a(a(e)))))))) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(a(a(b(b(e)))))))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(e))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(e)))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(b(e))))))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 104: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(e)))))) 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 |
|---|
| c#(a(e)) | |
| c#(a(a(e))) | |
| c#(a(a(b(b(e))))) | |
| c#(a(a(b(e)))) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(b(b(c(e)))))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(b(e))))) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(a(b(e)))) |
Problem 105: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(X))) | → | c#(X) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) | | c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |
Problem 106: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(X))) | → | c#(X) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(_x131))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(b(e))))))))) | → | c#(a(e)) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e)))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(e) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(e))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(e))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(e)))) |
| c#(b(a(b(a(b(a(_x81))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(c(_x391)))))))))))))))))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(b(e))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(e))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))) | → | c#(a(a(e))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(e))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(_x81))))) | → | c#(a(a(e))) |
| c#(b(a(b(a(b(a(b(a(_x181))))))))) | → | c#(a(a(b(e)))) | | c#(b(a(b(a(b(a(b(a(b(a(e))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(_x231))))))))))))) | → | c#(a(e)) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(e)))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(b(e))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(e)))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(e))))))))))))))))))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(e) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(e)))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(e))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(e)))))))))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(_x291))))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) |
| c#(b(a(b(a(_x81))))) | → | c#(a(a(b(b(e))))) | | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x391))))))))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(e)))))))))))))))))))))))))))))))))))) |
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(e)))))))))))))) | → | c#(a(a(b(b(c(e)))))) | | c#(b(a(b(a(b(a(b(a(b(e)))))))))) | → | c#(a(a(b(b(e))))) |
| c#(b(a(b(a(b(a(b(a(b(a(_x181))))))))))) | → | c#(a(a(b(b(c(a(a(e)))))))) | | c#(b(a(b(a(b(a(b(a(b(a(_x231))))))))))) | → | c#(a(a(b(b(c(a(a(b(b(c(a(a(b(b(c(a(a(b(b(e)))))))))))))))))))) |
| c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(e))))))) | | c#(b(a(b(a(b(a(_x131))))))) | → | c#(a(a(b(b(c(a(a(b(e))))))))) |
Rewrite Rules
| c(b(a(X))) | → | a(a(b(b(c(c(X)))))) | | a(X) | → | e |
| b(X) | → | e | | c(X) | → | e |
Original Signature
Termination of terms over the following signature is verified: e, b, c, a
Strategy
The right-hand side of the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) 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 |
|---|
| c#(a(e)) | |
| c#(e) | |
Thus, the rule c
#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(
_x341))))))))))))))))) → c
#(a(a(e))) is replaced by the following rules:
| c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(e) | c#(b(a(b(a(b(a(b(a(b(a(b(a(b(a(b(a(_x341))))))))))))))))) → c#(a(e)) |