TIMEOUT
The TRS could not be proven terminating. The proof attempt took 60000 ms.
The following DP Processors were used
Problem 1 was processed with processor PolynomialLinearRange4iUR (420ms).
| – Problem 2 was processed with processor ForwardNarrowing (2ms).
| | – Problem 3 was processed with processor ForwardNarrowing (1ms).
| | | – Problem 4 was processed with processor ForwardNarrowing (1ms).
| | | | – Problem 5 was processed with processor ForwardNarrowing (2ms).
| | | | | – Problem 6 was processed with processor ForwardNarrowing (4ms).
| | | | | | – Problem 7 was processed with processor ForwardNarrowing (2ms).
| | | | | | | – Problem 8 was processed with processor ForwardNarrowing (3ms).
| | | | | | | | – Problem 9 was processed with processor ForwardNarrowing (4ms).
| | | | | | | | | – Problem 10 was processed with processor ForwardNarrowing (3ms).
| | | | | | | | | | – Problem 11 was processed with processor ForwardNarrowing (4ms).
| | | | | | | | | | | – Problem 12 was processed with processor ForwardNarrowing (5ms).
| | | | | | | | | | | | – Problem 13 was processed with processor ForwardNarrowing (5ms).
| | | | | | | | | | | | | – Problem 14 was processed with processor ForwardNarrowing (9ms).
| | | | | | | | | | | | | | – Problem 15 was processed with processor ForwardNarrowing (4ms).
| | | | | | | | | | | | | | | – Problem 16 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | | – Problem 17 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | | | – Problem 18 was processed with processor ForwardNarrowing (11ms).
| | | | | | | | | | | | | | | | | | – Problem 19 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | | | | | – Problem 20 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | | | | | | – Problem 21 was processed with processor ForwardNarrowing (7ms).
| | | | | | | | | | | | | | | | | | | | | – Problem 22 was processed with processor ForwardNarrowing (26ms).
| | | | | | | | | | | | | | | | | | | | | | – Problem 23 was processed with processor ForwardNarrowing (79ms).
| | | | | | | | | | | | | | | | | | | | | | | – Problem 24 was processed with processor ForwardNarrowing (135ms).
| | | | | | | | | | | | | | | | | | | | | | | | – Problem 25 was processed with processor ForwardNarrowing (227ms).
| | | | | | | | | | | | | | | | | | | | | | | | | – Problem 26 was processed with processor ForwardNarrowing (382ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 27 was processed with processor ForwardNarrowing (493ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 28 remains open; application of the following processors failed [ForwardNarrowing (512ms), ForwardNarrowing (480ms), ForwardNarrowing (timeout)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| f#(a, f(a, x)) | → | f#(a, f(f(a, x), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, a) |
| f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Problem 1: PolynomialLinearRange4iUR
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, x)) | → | f#(a, f(f(a, x), f(a, a))) | | f#(a, f(a, x)) | → | f#(f(a, x), f(a, a)) |
| f#(a, f(a, x)) | → | f#(a, a) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
Polynomial Interpretation
- a: 1
- f(x,y): 0
- f#(x,y): x
Improved Usable rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:
| f#(a, f(a, x)) | → | f#(f(a, x), f(a, a)) |
Problem 2: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, x)) | → | f#(a, f(f(a, x), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, a) |
| f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a,
x)) → f
#(a, f(f(a,
x), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, _x41), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a,
x)) → f
#(a, f(f(a,
x), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, _x41))) → f#(a, f(f(a, f(f(a, _x41), f(a, a))), f(a, a))) |
Problem 3: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, _x41))) | → | f#(a, f(f(a, f(f(a, _x41), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, a) |
| f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a,
_x41))) → f
#(a, f(f(a, f(f(a,
_x41), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, _x81), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a,
_x41))) → f
#(a, f(f(a, f(f(a,
_x41), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, _x81)))) → f#(a, f(f(a, f(f(a, f(f(a, _x81), f(a, a))), f(a, a))), f(a, a))) |
Problem 4: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, x)) | → | f#(a, a) | | f#(a, f(a, x)) | → | f#(a, x) |
| f#(a, f(a, f(a, f(a, _x81)))) | → | f#(a, f(f(a, f(f(a, f(f(a, _x81), f(a, a))), f(a, a))), f(a, a))) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a,
x)) → f
#(a, a) 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 f
#(a, f(a,
x)) → f
#(a, a) is deleted.
Problem 5: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, x)) | → | f#(a, x) | | f#(a, f(a, f(a, f(a, _x81)))) | → | f#(a, f(f(a, f(f(a, f(f(a, _x81), f(a, a))), f(a, a))), f(a, a))) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a,
_x81)))) → f
#(a, f(f(a, f(f(a, f(f(a,
_x81), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, _x101), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a,
_x81)))) → f
#(a, f(f(a, f(f(a, f(f(a,
_x81), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, _x101))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, _x101), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 6: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, _x101))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, _x101), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a,
_x101))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x101), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x141), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a,
_x101))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x101), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, _x141)))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x141), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 7: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, _x141)))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x141), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a,
_x141)))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x141), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x161), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a,
_x141)))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x141), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, _x161))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x161), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 8: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, _x161))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x161), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x161))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x161), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x201), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x161))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x161), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x201)))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x201), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 9: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x201)))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x201), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x201)))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x201), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x221), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x201)))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x201), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x221))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x221), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 10: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, x)) | → | f#(a, x) | | f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x221))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x221), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x221))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x221), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x261), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x221))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x221), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x261)))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x261), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 11: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x261)))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x261), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x261)))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x261), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x281), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x261)))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x261), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x281))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x281), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 12: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, x)) | → | f#(a, x) | | f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x281))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x281), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x281))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x281), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x321), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x281))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x281), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x321)))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x321), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 13: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x321)))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x321), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x321)))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x321), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x361), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x321)))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x321), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x361))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x361), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 14: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x361))))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x361), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x361))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x361), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x381), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x361))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x361), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x381)))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x381), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 15: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x381)))))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x381), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x381)))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x381), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x421), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x381)))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x381), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x421))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x421), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 16: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x421))))))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x421), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x421))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x421), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x441), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x421))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x421), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x441)))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x441), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 17: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, x)) | → | f#(a, x) | | f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x441)))))))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x441), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x441)))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x441), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x441)))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x441), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x481))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 18: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, x)) | → | f#(a, x) | | f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x481))))))))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x481))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x481))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x501)))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 19: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x501)))))))))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x501)))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x501)))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x521))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 20: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x521))))))))))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x521))))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x561), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x521))))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x561)))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x561), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 21: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x561)))))))))))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x561), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x561)))))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x561), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x581), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x561)))))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x561), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x581))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x581), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 22: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x1481))))))))))))))))))))))))))))))))))))))))))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x1481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x1481))))))))))))))))))))))))))))))))))))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x1481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x1521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x1481))))))))))))))))))))))))))))))))))))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x1481), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x1521)))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x1521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 23: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x2981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x2981), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x2981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x2981), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x3021), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x2981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x2981), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x3021)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x3021), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 24: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x4501))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x4501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x4501))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x4501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x4521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x4501))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x4501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x4521)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x4521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 25: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x5981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x5981), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x5981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x5981), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x6021), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x5981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x5981), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x6021)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x6021), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 26: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x7501))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, 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a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x7501))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x7501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, _x7521), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x7501))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x7501), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is replaced by the following rules:
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x7521)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, 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f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) |
Problem 27: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, _x8981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | → | f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, 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a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | | f#(a, f(a, x)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(a, x)) | → | f(a, f(f(a, x), f(a, a))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x8981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f
#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a,
_x8981), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, f(f(a, 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f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))), f(a, a))) | |
Thus, the rule f
#(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a, f(a,
_x8981))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) → f
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