TIMEOUT
The TRS could not be proven terminating. The proof attempt took 60001 ms.
The following DP Processors were used
Problem 1 was processed with processor ForwardNarrowing (2ms).
| – Problem 2 was processed with processor ForwardNarrowing (1ms).
| | – Problem 3 was processed with processor ForwardNarrowing (1ms).
| | | – Problem 4 was processed with processor ForwardNarrowing (1ms).
| | | | – Problem 5 was processed with processor ForwardNarrowing (4ms).
| | | | | – Problem 6 was processed with processor ForwardNarrowing (1ms).
| | | | | | – Problem 7 was processed with processor ForwardNarrowing (3ms).
| | | | | | | – Problem 8 was processed with processor ForwardNarrowing (1ms).
| | | | | | | | – Problem 9 was processed with processor ForwardNarrowing (2ms).
| | | | | | | | | – Problem 10 was processed with processor ForwardNarrowing (3ms).
| | | | | | | | | | – Problem 11 was processed with processor ForwardNarrowing (1ms).
| | | | | | | | | | | – Problem 12 was processed with processor ForwardNarrowing (2ms).
| | | | | | | | | | | | – Problem 13 was processed with processor ForwardNarrowing (4ms).
| | | | | | | | | | | | | – Problem 14 was processed with processor ForwardNarrowing (4ms).
| | | | | | | | | | | | | | – Problem 15 was processed with processor ForwardNarrowing (3ms).
| | | | | | | | | | | | | | | – Problem 16 was processed with processor ForwardNarrowing (3ms).
| | | | | | | | | | | | | | | | – Problem 17 was processed with processor ForwardNarrowing (2ms).
| | | | | | | | | | | | | | | | | – Problem 18 was processed with processor ForwardNarrowing (2ms).
| | | | | | | | | | | | | | | | | | – Problem 19 was processed with processor ForwardNarrowing (2ms).
| | | | | | | | | | | | | | | | | | | – Problem 20 was processed with processor ForwardNarrowing (2ms).
| | | | | | | | | | | | | | | | | | | | – Problem 21 was processed with processor ForwardNarrowing (4ms).
| | | | | | | | | | | | | | | | | | | | | – Problem 22 was processed with processor ForwardNarrowing (12ms).
| | | | | | | | | | | | | | | | | | | | | | – Problem 23 was processed with processor ForwardNarrowing (17ms).
| | | | | | | | | | | | | | | | | | | | | | | – Problem 24 was processed with processor ForwardNarrowing (31ms).
| | | | | | | | | | | | | | | | | | | | | | | | – Problem 25 was processed with processor ForwardNarrowing (12ms).
| | | | | | | | | | | | | | | | | | | | | | | | | – Problem 26 was processed with processor ForwardNarrowing (21ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 27 was processed with processor ForwardNarrowing (34ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 28 was processed with processor ForwardNarrowing (77ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 29 was processed with processor ForwardNarrowing (75ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 30 was processed with processor ForwardNarrowing (120ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 31 was processed with processor ForwardNarrowing (157ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 32 was processed with processor ForwardNarrowing (145ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 33 was processed with processor ForwardNarrowing (181ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 34 was processed with processor ForwardNarrowing (280ms).
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | – Problem 35 remains open; application of the following processors failed [ForwardNarrowing (221ms), ForwardNarrowing (250ms), ForwardNarrowing (280ms), ForwardNarrowing (217ms), ForwardNarrowing (242ms), ForwardNarrowing (338ms), ForwardNarrowing (222ms), ForwardNarrowing (255ms), ForwardNarrowing (333ms), ForwardNarrowing (261ms), ForwardNarrowing (304ms), ForwardNarrowing (284ms), ForwardNarrowing (217ms), ForwardNarrowing (209ms), ForwardNarrowing (245ms), ForwardNarrowing (284ms), ForwardNarrowing (253ms), ForwardNarrowing (259ms), ForwardNarrowing (297ms), ForwardNarrowing (215ms), ForwardNarrowing (294ms), ForwardNarrowing (289ms), ForwardNarrowing (223ms), ForwardNarrowing (251ms), ForwardNarrowing (291ms), ForwardNarrowing (229ms), ForwardNarrowing (308ms), ForwardNarrowing (295ms), ForwardNarrowing (223ms), ForwardNarrowing (254ms), ForwardNarrowing (295ms), ForwardNarrowing (timeout)].
The following open problems remain:
Open Dependency Pair Problem 1
Dependency Pairs
| a#(x, g) | → | a#(g, a(f, x)) | | a#(x, g) | → | a#(f, x) |
| a#(f, a(f, x)) | → | a#(x, g) | | a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Problem 1: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(x, g) | → | a#(g, a(f, x)) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(x, g) | → | a#(f, x) | | a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(
x, g) → a
#(g, a(f,
x)) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| a#(g, a(f, a(g, a(f, f)))) | |
| a#(g, a(_x31, g)) | |
Thus, the rule a
#(
x, g) → a
#(g, a(f,
x)) is replaced by the following rules:
| a#(a(f, _x31), g) → a#(g, a(_x31, g)) | a#(g, g) → a#(g, a(f, a(g, a(f, f)))) |
Problem 2: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, _x31), g) | → | a#(g, a(_x31, g)) | | a#(x, g) | → | a#(f, x) |
| a#(f, a(f, x)) | → | a#(x, g) | | a#(g, g) | → | a#(g, a(f, a(g, a(f, f)))) |
| a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f,
_x31), g) → a
#(g, a(
_x31, g)) 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 |
|---|
| a#(g, a(f, a(g, a(f, _x41)))) | |
Thus, the rule a
#(a(f,
_x31), g) → a
#(g, a(
_x31, g)) is replaced by the following rules:
| a#(a(f, _x41), g) → a#(g, a(f, a(g, a(f, _x41)))) |
Problem 3: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, _x41), g) | → | a#(g, a(f, a(g, a(f, _x41)))) | | a#(g, g) | → | a#(g, a(f, a(g, a(f, f)))) |
| a#(f, a(f, x)) | → | a#(x, g) | | a#(x, g) | → | a#(f, x) |
| a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f,
_x41), g) → a
#(g, a(f, a(g, a(f,
_x41)))) 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 |
|---|
| a#(g, a(f, a(g, a(_x71, g)))) | |
| a#(g, a(f, a(g, a(f, a(g, a(f, f)))))) | |
Thus, the rule a
#(a(f,
_x41), g) → a
#(g, a(f, a(g, a(f,
_x41)))) is replaced by the following rules:
| a#(a(f, g), g) → a#(g, a(f, a(g, a(f, a(g, a(f, f)))))) | a#(a(f, a(f, _x71)), g) → a#(g, a(f, a(g, a(_x71, g)))) |
Problem 4: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, g), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, f)))))) | | a#(x, g) | → | a#(f, x) |
| a#(f, a(f, x)) | → | a#(x, g) | | a#(g, g) | → | a#(g, a(f, a(g, a(f, f)))) |
| a#(a(f, a(f, _x71)), g) | → | a#(g, a(f, a(g, a(_x71, g)))) | | a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, g), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, f)))))) 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 a
#(a(f, g), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, f)))))) is deleted.
Problem 5: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(g, g) | → | a#(g, a(f, a(g, a(f, f)))) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(x, g) | → | a#(f, x) | | a#(a(f, a(f, _x71)), g) | → | a#(g, a(f, a(g, a(_x71, g)))) |
| a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(g, g) → a
#(g, a(f, a(g, a(f, f)))) 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 a
#(g, g) → a
#(g, a(f, a(g, a(f, f)))) is deleted.
Problem 6: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(x, g) | → | a#(f, x) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(a(f, a(f, _x71)), g) | → | a#(g, a(f, a(g, a(_x71, g)))) | | a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f,
_x71)), g) → a
#(g, a(f, a(g, a(
_x71, g)))) 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 |
|---|
| a#(g, a(f, a(g, a(f, a(g, a(f, _x81)))))) | |
Thus, the rule a
#(a(f, a(f,
_x71)), g) → a
#(g, a(f, a(g, a(
_x71, g)))) is replaced by the following rules:
| a#(a(f, a(f, _x81)), g) → a#(g, a(f, a(g, a(f, a(g, a(f, _x81)))))) |
Problem 7: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, a(f, _x81)), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, _x81)))))) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(x, g) | → | a#(f, x) | | a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f,
_x81)), g) → a
#(g, a(f, a(g, a(f, a(g, a(f,
_x81)))))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))) | |
| a#(g, a(f, a(g, a(f, a(g, a(_x111, g)))))) | |
Thus, the rule a
#(a(f, a(f,
_x81)), g) → a
#(g, a(f, a(g, a(f, a(g, a(f,
_x81)))))) is replaced by the following rules:
| a#(a(f, a(f, g)), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))) | a#(a(f, a(f, a(f, _x111))), g) → a#(g, a(f, a(g, a(f, a(g, a(_x111, g)))))) |
Problem 8: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, a(f, g)), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))) | | a#(a(f, a(f, a(f, _x111))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(_x111, g)))))) |
| a#(x, g) | → | a#(f, x) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f,
_x111))), g) → a
#(g, a(f, a(g, a(f, a(g, a(
_x111, g)))))) 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 |
|---|
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x121)))))))) | |
Thus, the rule a
#(a(f, a(f, a(f,
_x111))), g) → a
#(g, a(f, a(g, a(f, a(g, a(
_x111, g)))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, _x121))), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x121)))))))) |
Problem 9: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, a(f, g)), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(x, g) | → | a#(f, x) | | a#(a(f, a(f, a(f, _x121))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x121)))))))) |
| a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, g)), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))) 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 a
#(a(f, a(f, g)), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))) is deleted.
Problem 10: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(x, g) | → | a#(f, x) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(a(f, a(f, a(f, _x121))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x121)))))))) | | a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f,
_x121))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x121)))))))) 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 |
|---|
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x151, g)))))))) | |
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f,
_x121))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x121)))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, _x151)))), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x151, g)))))))) | a#(a(f, a(f, a(f, g))), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))) |
Problem 11: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, a(f, a(f, a(f, _x151)))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x151, g)))))))) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(x, g) | → | a#(f, x) | | a#(a(f, a(f, a(f, g))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))) |
| a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f,
_x151)))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x151, g)))))))) 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 |
|---|
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x161)))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f,
_x151)))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x151, g)))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, _x161)))), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x161)))))))))) |
Problem 12: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, a(f, a(f, a(f, _x161)))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x161)))))))))) | | a#(a(f, a(f, a(f, g))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))) |
| a#(x, g) | → | a#(f, x) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f,
_x161)))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x161)))))))))) 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 |
|---|
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x191, g)))))))))) | |
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f,
_x161)))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x161)))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, _x191))))), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x191, g)))))))))) | a#(a(f, a(f, a(f, a(f, g)))), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))) |
Problem 13: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, a(f, a(f, a(f, a(f, _x191))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x191, g)))))))))) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(x, g) | → | a#(f, x) | | a#(a(f, a(f, a(f, g))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))) |
| a#(a(f, a(f, a(f, a(f, g)))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))) | | a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f,
_x191))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x191, g)))))))))) 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 |
|---|
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x201)))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f, a(f,
_x191))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x191, g)))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, _x201))))), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x201)))))))))))) |
Problem 14: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, a(f, a(f, a(f, a(f, _x201))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x201)))))))))))) | | a#(a(f, a(f, a(f, g))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))) |
| a#(x, g) | → | a#(f, x) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(a(f, a(f, a(f, a(f, g)))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))) | | a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f,
_x201))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x201)))))))))))) 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 |
|---|
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))))) | |
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x231, g)))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f, a(f,
_x201))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x201)))))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, g))))), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))))) | a#(a(f, a(f, a(f, a(f, a(f, a(f, _x231)))))), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x231, g)))))))))))) |
Problem 15: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, a(f, a(f, a(f, a(f, g))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))))) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(x, g) | → | a#(f, x) | | a#(a(f, a(f, a(f, g))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, _x231)))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x231, g)))))))))))) | | a#(a(f, a(f, a(f, a(f, g)))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))) |
| a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, g))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))))) 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 a
#(a(f, a(f, a(f, a(f, a(f, g))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))))) is deleted.
Problem 16: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, a(f, a(f, g))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))) | | a#(x, g) | → | a#(f, x) |
| a#(f, a(f, x)) | → | a#(x, g) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, _x231)))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x231, g)))))))))))) |
| a#(a(f, a(f, a(f, a(f, g)))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))) | | a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, g))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))) 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 a
#(a(f, a(f, a(f, g))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))) is deleted.
Problem 17: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(f, a(f, x)) | → | a#(x, g) | | a#(x, g) | → | a#(f, x) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, _x231)))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x231, g)))))))))))) | | a#(a(f, a(f, a(f, a(f, g)))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))) |
| a#(x, g) | → | a#(f, a(g, a(f, x))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f,
_x231)))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x231, g)))))))))))) 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 |
|---|
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x241)))))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f,
_x231)))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x231, g)))))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, a(f, _x241)))))), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x241)))))))))))))) |
Problem 18: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(x, g) | → | a#(f, x) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(a(f, a(f, a(f, a(f, g)))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))) | | a#(x, g) | → | a#(f, a(g, a(f, x))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, _x241)))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x241)))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, g)))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))) 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 a
#(a(f, a(f, a(f, a(f, g)))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))) is deleted.
Problem 19: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(f, a(f, x)) | → | a#(x, g) | | a#(x, g) | → | a#(f, x) |
| a#(x, g) | → | a#(f, a(g, a(f, x))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, _x241)))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x241)))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(
x, g) → a
#(f, a(g, a(f,
x))) is narrowed to the following relevant and irrelevant terms (a narrowing is irrelevant if by dropping it the correctness (and completeness) of the processor is not influenced).
| Relevant Terms | Irrelevant Terms |
|---|
| a#(f, a(g, a(f, a(g, a(f, f))))) | |
| a#(f, a(g, a(_x51, g))) | |
Thus, the rule a
#(
x, g) → a
#(f, a(g, a(f,
x))) is replaced by the following rules:
| a#(g, g) → a#(f, a(g, a(f, a(g, a(f, f))))) | a#(a(f, _x51), g) → a#(f, a(g, a(_x51, g))) |
Problem 20: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(g, g) | → | a#(f, a(g, a(f, a(g, a(f, f))))) | | a#(x, g) | → | a#(f, x) |
| a#(f, a(f, x)) | → | a#(x, g) | | a#(a(f, _x51), g) | → | a#(f, a(g, a(_x51, g))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, _x241)))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x241)))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(g, g) → a
#(f, a(g, a(f, a(g, a(f, f))))) 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 a
#(g, g) → a
#(f, a(g, a(f, a(g, a(f, f))))) is deleted.
Problem 21: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(f, a(f, x)) | → | a#(x, g) | | a#(x, g) | → | a#(f, x) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x411)))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x411, g)))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x351)))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x351, g))))))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x411)))))))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x411, g)))))))))))))))))))) 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 |
|---|
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x391)))))))))))))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x411)))))))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x411, g)))))))))))))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x391)))))))))), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x391)))))))))))))))))))))) |
Problem 22: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(f, a(f, x)) | → | a#(x, g) | | a#(x, g) | → | a#(f, x) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x1031)))))))))))))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x1031)))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x351)))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x351, g))))))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x1031)))))))))))))))))))))))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x1031)))))))))))))))))))))))))))))))))))))))))))))))))))))) 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 |
|---|
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x1081, g)))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x1031)))))))))))))))))))))))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x1031)))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))))))))))))))))))))))))))))))))))))))))))))))) | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x1081))))))))))))))))))))))))))), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x1081, g)))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Problem 23: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(f, a(f, x)) | → | a#(x, g) | | a#(x, g) | → | a#(f, x) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x1441)))))))))))))))))))))))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x1441, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x621))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x621, g))))))))))))))))))))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x1441)))))))))))))))))))))))))))))))))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x1441, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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 |
|---|
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x1431)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x1441)))))))))))))))))))))))))))))))))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x1441, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x1431)))))))))))))))))))))))))))))))))))), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x1431)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Problem 24: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x2121))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x2121, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(f, a(f, x)) | → | a#(x, g) | | a#(x, g) | → | a#(f, x) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x621))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x621, g))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x2121))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x2121, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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 |
|---|
| a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x2131)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x2121))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x2121, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x2131))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x2131)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Problem 25: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x1011))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x1011))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(x, g) | → | a#(f, x) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x2361))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x2361, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x1011))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x1011))))))))))))))))))))))))))))))))))))))))))))))))))))) 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 |
|---|
| a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x1061, g))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
| a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x1011))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x1011))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))), g) → a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))) | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x1061)))))))))))))))))))))))))), g) → a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x1061, g))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Problem 26: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(f, a(f, x)) | → | a#(x, g) | | a#(x, g) | → | a#(f, x) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x1701)))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x1701, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x2361))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x2361, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x1701)))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x1701, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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 |
|---|
| a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x1711))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x1701)))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x1701, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x1711)))))))))))))))))))))))))))))))))))))))))), g) → a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x1711))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Problem 27: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(f, a(f, x)) | → | a#(x, g) | | a#(x, g) | → | a#(f, x) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x2391))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x2391))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x2361))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x2361, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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 a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is deleted.
Problem 28: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x3071)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x3071))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(x, g) | → | a#(f, x) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x2361))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x2361, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x3071)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x3071))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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 |
|---|
| a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
| a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x3121, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x3071)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x3071))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x3121))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x3121, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Problem 29: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(f, a(f, x)) | → | a#(x, g) | | a#(x, g) | → | a#(f, x) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x3701)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x3701))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x2361))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x2361, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x3701)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x3701))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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 |
|---|
| a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
| a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x3751, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x3701)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x3701))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x3751))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x3751, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Problem 30: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(f, a(f, x)) | → | a#(x, g) | | a#(x, g) | → | a#(f, x) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x4251)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x4251))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x2521))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x2521, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x4251)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x4251))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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 |
|---|
| a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
| a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x4301, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x4251)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x4251))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x4301))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x4301, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Problem 31: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(f, a(f, x)) | → | a#(x, g) | | a#(x, g) | → | a#(f, x) |
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| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x2521))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x2521, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x4951))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x4951))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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 |
|---|
| a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
| a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x4981, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x4951))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x4951))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x4981)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x4981, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Problem 32: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(x, g) | → | a#(f, x) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x5631)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x5631, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
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| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x2521))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x2521, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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 a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is deleted.
Problem 33: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x6141))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x6141, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(f, a(f, x)) | → | a#(x, g) |
| a#(x, g) | → | a#(f, x) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x2641)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x2641, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x6141))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x6141, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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 |
|---|
| a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x6151))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x6141))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(
_x6141, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x6151))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, _x6151))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Problem 34: ForwardNarrowing
Dependency Pair Problem
Dependency Pairs
| a#(f, a(f, x)) | → | a#(x, g) | | a#(x, g) | → | a#(f, x) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, 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| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, 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| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | | a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, _x2641)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) | → | a#(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x2641, g)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) |
Rewrite Rules
| a(f, a(f, x)) | → | a(x, g) | | a(x, g) | → | a(f, a(g, a(f, x))) |
Original Signature
Termination of terms over the following signature is verified: f, g, a
Strategy
The right-hand side of the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x6811)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x6811))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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 |
|---|
| a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, f))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
| a#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(_x6861, g))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) | |
Thus, the rule a
#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f,
_x6811)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), g) → a
#(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f, a(g, a(f,
_x6811))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) is replaced by the following rules:
| a#(a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, a(f, 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