TIMEOUT
The TRS could not be proven terminating. The proof attempt took 60017 ms.
The following DP Processors were used
Problem 1 was processed with processor PolynomialLinearRange4iUR (342ms).
| – Problem 2 was processed with processor ForwardNarrowing (2ms).
| | – Problem 3 was processed with processor ForwardNarrowing (1ms).
| | | – Problem 4 was processed with processor ForwardNarrowing (3ms).
| | | | – Problem 5 was processed with processor ForwardNarrowing (1ms).
| | | | | – Problem 6 was processed with processor ForwardNarrowing (2ms).
| | | | | | – 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 (4ms).
| | | | | | | | | | | | – Problem 13 was processed with processor ForwardNarrowing (3ms).
| | | | | | | | | | | | | – Problem 14 was processed with processor ForwardNarrowing (10ms).
| | | | | | | | | | | | | | – Problem 15 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | – Problem 16 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | | – Problem 17 was processed with processor ForwardNarrowing (6ms).
| | | | | | | | | | | | | | | | | – Problem 18 was processed with processor ForwardNarrowing (7ms).
| | | | | | | | | | | | | | | | | | – Problem 19 was processed with processor ForwardNarrowing (7ms).
| | | | | | | | | | | | | | | | | | | – Problem 20 was processed with processor ForwardNarrowing (7ms).
| | | | | | | | | | | | | | | | | | | | – Problem 21 was processed with processor ForwardNarrowing (7ms).
| | | | | | | | | | | | | | | | | | | | | – Problem 22 was processed with processor ForwardNarrowing (25ms).
| | | | | | | | | | | | | | | | | | | | | | – Problem 23 was processed with processor ForwardNarrowing (76ms).
| | | | | | | | | | | | | | | | | | | | | | | – Problem 24 was processed with processor ForwardNarrowing (129ms).
| | | | | | | | | | | | | | | | | | | | | | | | – Problem 25 was processed with processor ForwardNarrowing (224ms).
| | | | | | | | | | | | | | | | | | | | | | | | | – Problem 26 was processed with processor ForwardNarrowing (329ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 27 was processed with processor ForwardNarrowing (504ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 28 remains open; application of the following processors failed [ForwardNarrowing (489ms), ForwardNarrowing (510ms), ForwardNarrowing (361ms)].
The following open problems remain:
Open Dependency Pair Problem 2
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, a) | | f#(a, f(x, a)) | → | f#(a, f(f(a, a), f(a, x))) |
| f#(a, f(x, a)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Problem 1: PolynomialLinearRange4iUR
Dependency Pair Problem
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, a) | | f#(a, f(x, a)) | → | f#(a, f(f(a, a), f(a, x))) |
| f#(a, f(x, a)) | → | f#(a, x) | | f#(a, f(x, a)) | → | f#(f(a, a), f(a, x)) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
Polynomial Interpretation
- a: 2
- f(x,y): 1
- f#(x,y): x
Improved Usable rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:
| f#(a, f(x, a)) | → | f#(f(a, a), f(a, x)) |
Problem 2: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, a) | | f#(a, f(x, a)) | → | f#(a, f(f(a, a), f(a, x))) |
| f#(a, f(x, a)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(
x, 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 |
|---|
Thus, the rule f
#(a, f(
x, a)) → f
#(a, a) is deleted.
Problem 3: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, f(f(a, a), f(a, x))) | | f#(a, f(x, a)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(
x, a)) → f
#(a, f(f(a, a), f(a,
x))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, a), f(a, f(f(a, a), f(a, _x51))))) | |
Thus, the rule f
#(a, f(
x, a)) → f
#(a, f(f(a, a), f(a,
x))) is replaced by the following rules:
| f#(a, f(f(_x51, a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, _x51))))) |
Problem 4: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, x) | | f#(a, f(f(_x51, a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, _x51))))) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(
_x51, a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x51))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x101))))))) | |
Thus, the rule f
#(a, f(f(
_x51, a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x51))))) is replaced by the following rules:
| f#(a, f(f(f(_x101, a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x101))))))) |
Problem 5: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, x) | | f#(a, f(f(f(_x101, a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x101))))))) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(
_x101, a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x101))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x131))))))))) | |
Thus, the rule f
#(a, f(f(f(
_x101, a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x101))))))) is replaced by the following rules:
| f#(a, f(f(f(f(_x131, a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x131))))))))) |
Problem 6: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, x) | | f#(a, f(f(f(f(_x131, a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x131))))))))) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(
_x131, a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x131))))))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x181))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(
_x131, a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x131))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(_x181, a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x181))))))))))) |
Problem 7: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(f(f(f(f(_x181, a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x181))))))))))) | | f#(a, f(x, a)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(
_x181, a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x181))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x211))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(
_x181, a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x181))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(_x211, a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x211))))))))))))) |
Problem 8: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(f(f(f(f(f(_x211, a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x211))))))))))))) | | f#(a, f(x, a)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(
_x211, a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x211))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x261))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(
_x211, a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x211))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(_x261, a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x261))))))))))))))) |
Problem 9: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, x) | | f#(a, f(f(f(f(f(f(f(_x261, a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x261))))))))))))))) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(
_x261, a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x261))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x291))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(
_x261, a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x261))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(_x291, a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x291))))))))))))))))) |
Problem 10: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, x) | | f#(a, f(f(f(f(f(f(f(f(_x291, a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x291))))))))))))))))) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(
_x291, a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x291))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x341))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(
_x291, a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x291))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(_x341, a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x341))))))))))))))))))) |
Problem 11: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(f(f(f(f(f(f(f(f(_x341, a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x341))))))))))))))))))) | | f#(a, f(x, a)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(
_x341, a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x341))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x391))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(
_x341, a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x341))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(_x391, a), a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x391))))))))))))))))))))) |
Problem 12: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, x) | | f#(a, f(f(f(f(f(f(f(f(f(f(_x391, a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x391))))))))))))))))))))) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(f(
_x391, a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x391))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x421))))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(f(
_x391, a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x391))))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(f(_x421, a), a), a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x421))))))))))))))))))))))) |
Problem 13: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(f(f(f(f(f(f(f(f(f(f(_x421, a), a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x421))))))))))))))))))))))) | | f#(a, f(x, a)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(
_x421, a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x421))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x451))))))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(
_x421, a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x421))))))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(_x451, a), a), a), a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x451))))))))))))))))))))))))) |
Problem 14: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, x) | | f#(a, f(f(f(f(f(f(f(f(f(f(f(f(_x451, a), a), a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x451))))))))))))))))))))))))) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(
_x451, a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x451))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x501))))))))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(
_x451, a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x451))))))))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(_x501, a), a), a), a), a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x501))))))))))))))))))))))))))) |
Problem 15: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, x) | | f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(_x501, a), a), a), a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x501))))))))))))))))))))))))))) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(
_x501, a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x501))))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x551))))))))))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(
_x501, a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x501))))))))))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x551, a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x551))))))))))))))))))))))))))))) |
Problem 16: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x551, a), a), a), a), a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x551))))))))))))))))))))))))))))) | | f#(a, f(x, a)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x551, a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x551))))))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x581))))))))))))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x551, a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x551))))))))))))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x581, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x581))))))))))))))))))))))))))))))) |
Problem 17: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, x) | | f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x581, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x581))))))))))))))))))))))))))))))) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x581, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x581))))))))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x631))))))))))))))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x581, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x581))))))))))))))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x631, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x631))))))))))))))))))))))))))))))))) |
Problem 18: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x631, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x631))))))))))))))))))))))))))))))))) | | f#(a, f(x, a)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x631, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x631))))))))))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x661))))))))))))))))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x631, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x631))))))))))))))))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x661, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x661))))))))))))))))))))))))))))))))))) |
Problem 19: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, x) | | f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x661, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x661))))))))))))))))))))))))))))))))))) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x661, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x661))))))))))))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x691))))))))))))))))))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x661, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x661))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x691, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x691))))))))))))))))))))))))))))))))))))) |
Problem 20: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, x) | | f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x691, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x691))))))))))))))))))))))))))))))))))))) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x691, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x691))))))))))))))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x741))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x691, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x691))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x741, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x741))))))))))))))))))))))))))))))))))))))) |
Problem 21: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x741, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x741))))))))))))))))))))))))))))))))))))))) | | f#(a, f(x, a)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x741, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x741))))))))))))))))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x791))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x741, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x741))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x791, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x791))))))))))))))))))))))))))))))))))))))))) |
Problem 22: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x1991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x1991))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | f#(a, f(x, a)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x1991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x1991))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x2021))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x1991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x1991))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x2021, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x2021))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Problem 23: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x3991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x3991))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | f#(a, f(x, a)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x3991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x3991))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x4021))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x3991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x3991))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x4021, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x4021))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Problem 24: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x5991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x5991))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | f#(a, f(x, a)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x5991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x5991))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x6021))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x5991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x5991))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x6021, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x6021))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Problem 25: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x7991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x7991))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | f#(a, f(x, a)) | → | f#(a, x) |
Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x7991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x7991))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x8021))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x7991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x7991))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x8021, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x8021))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Problem 26: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x9991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, 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Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
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#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x9991))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x10021))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule f
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_x9991))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x10021, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), 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_x10021))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Problem 27: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| f#(a, f(x, a)) | → | f#(a, x) | | f#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(_x11991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) | → | f#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, 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f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, 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Rewrite Rules
| f(a, f(x, a)) | → | f(a, f(f(a, a), f(a, x))) |
Original Signature
Termination of terms over the following signature is verified: f, a
Strategy
The right-hand side of the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x11991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
#(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a,
_x11991))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, 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a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, f(f(a, a), f(a, _x12021))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule f
#(a, f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(
_x11991, a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a), a)) → f
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