YES
The TRS could be proven terminating. The proof took 679 ms.
The following DP Processors were used
Problem 1 was processed with processor PolynomialLinearRange4iUR (224ms).
| – Problem 2 was processed with processor PolynomialLinearRange4iUR (142ms).
Problem 1: PolynomialLinearRange4iUR
Dependency Pair Problem
Dependency Pairs
| *#(x, *(minus(y), y)) | → | *#(minus(*(y, y)), x) | | *#(x, *(minus(y), y)) | → | *#(y, y) |
Rewrite Rules
| *(x, *(minus(y), y)) | → | *(minus(*(y, y)), x) |
Original Signature
Termination of terms over the following signature is verified: minus, *
Strategy
Polynomial Interpretation
- *(x,y): 2y + 1
- *#(x,y): y + x + 1
- minus(x): 1
Improved Usable rules
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:
| *#(x, *(minus(y), y)) | → | *#(y, y) |
Problem 2: PolynomialLinearRange4iUR
Dependency Pair Problem
Dependency Pairs
| *#(x, *(minus(y), y)) | → | *#(minus(*(y, y)), x) |
Rewrite Rules
| *(x, *(minus(y), y)) | → | *(minus(*(y, y)), x) |
Original Signature
Termination of terms over the following signature is verified: minus, *
Strategy
Polynomial Interpretation
- *(x,y): 2
- *#(x,y): y + 2x
- minus(x): 0
Improved Usable rules
The following dependency pairs are strictly oriented by an ordering on the given polynomial interpretation, thus they are removed:
| *#(x, *(minus(y), y)) | → | *#(minus(*(y, y)), x) |