The TRS could be proven terminating. The proof took 25 ms.
Problem 1 was processed with processor SubtermCriterion (1ms). | – Problem 2 was processed with processor SubtermCriterion (1ms).
| *#(x, +(y, z)) | → | *#(x, z) | *#(+(x, y), z) | → | *#(x, z) | |
| *#(x, +(y, z)) | → | *#(x, y) | *#(+(x, y), z) | → | *#(y, z) |
| *(x, +(y, z)) | → | +(*(x, y), *(x, z)) | *(+(x, y), z) | → | +(*(x, z), *(y, z)) | |
| *(x, 1) | → | x | *(1, y) | → | y |
Termination of terms over the following signature is verified: 1, *, +
The following projection was used:
Thus, the following dependency pairs are removed:
| *#(+(x, y), z) | → | *#(x, z) | *#(+(x, y), z) | → | *#(y, z) |
| *#(x, +(y, z)) | → | *#(x, z) | *#(x, +(y, z)) | → | *#(x, y) |
| *(x, +(y, z)) | → | +(*(x, y), *(x, z)) | *(+(x, y), z) | → | +(*(x, z), *(y, z)) | |
| *(x, 1) | → | x | *(1, y) | → | y |
Termination of terms over the following signature is verified: 1, *, +
The following projection was used:
Thus, the following dependency pairs are removed:
| *#(x, +(y, z)) | → | *#(x, z) | *#(x, +(y, z)) | → | *#(x, y) |