The rewrite relation of the following TRS is considered.
0(0(0(0(0(1(2(1(0(1(0(1(2(2(2(0(1(2(2(0(1(1(1(x1))))))))))))))))))))))) | → | 0(0(0(1(2(2(1(1(0(2(1(1(2(2(2(2(1(2(0(0(1(1(2(2(1(1(1(x1))))))))))))))))))))))))))) | (1) |
0(0(0(2(0(1(1(1(1(2(1(1(2(1(2(1(2(1(2(1(1(1(0(x1))))))))))))))))))))))) | → | 0(1(1(1(1(1(2(1(2(1(2(1(1(1(0(0(2(2(1(1(0(1(0(0(2(1(1(x1))))))))))))))))))))))))))) | (2) |
0(0(0(2(1(2(1(2(1(2(1(1(1(0(2(0(1(1(2(2(0(1(2(x1))))))))))))))))))))))) | → | 0(1(1(2(0(1(1(1(1(1(1(0(2(0(1(0(1(1(0(1(0(1(2(2(0(2(1(x1))))))))))))))))))))))))))) | (3) |
0(0(1(1(1(0(2(1(2(2(1(1(1(2(0(2(0(1(2(0(1(1(2(x1))))))))))))))))))))))) | → | 0(1(1(1(1(1(1(1(2(0(1(0(1(0(2(2(2(0(1(2(2(2(1(0(0(1(1(x1))))))))))))))))))))))))))) | (4) |
0(0(1(1(1(1(2(2(0(0(1(1(0(2(2(1(0(1(1(2(0(1(0(x1))))))))))))))))))))))) | → | 2(2(1(1(2(2(2(0(1(1(1(2(0(1(1(1(2(1(2(1(0(1(2(2(1(1(0(x1))))))))))))))))))))))))))) | (5) |
0(1(0(1(1(2(0(1(1(2(2(0(0(2(1(0(2(0(2(2(2(0(2(x1))))))))))))))))))))))) | → | 2(1(2(1(1(2(1(1(0(1(0(1(0(1(2(1(0(0(2(1(1(1(2(1(1(1(2(x1))))))))))))))))))))))))))) | (6) |
0(1(1(0(2(1(0(2(1(0(2(0(2(2(0(1(1(0(1(2(2(1(1(x1))))))))))))))))))))))) | → | 2(1(0(1(0(0(1(1(1(2(0(0(2(2(2(1(1(2(1(1(0(1(1(0(1(1(1(x1))))))))))))))))))))))))))) | (7) |
0(1(1(2(1(1(2(2(2(1(1(2(0(0(1(2(0(0(1(0(0(2(0(x1))))))))))))))))))))))) | → | 0(0(2(2(1(0(2(1(2(1(1(2(1(2(2(1(1(1(1(1(0(0(1(2(1(2(0(x1))))))))))))))))))))))))))) | (8) |
0(1(2(1(2(0(0(1(0(1(1(2(1(1(2(2(1(1(1(2(2(0(2(x1))))))))))))))))))))))) | → | 0(1(2(0(1(1(0(1(2(1(1(1(2(0(1(0(1(1(0(1(2(2(1(2(1(2(1(x1))))))))))))))))))))))))))) | (9) |
0(2(0(2(1(2(0(0(2(0(0(1(0(0(2(2(0(1(1(0(1(0(1(x1))))))))))))))))))))))) | → | 0(1(0(2(0(0(2(1(1(1(0(0(2(1(0(2(2(2(1(1(0(1(1(1(1(0(1(x1))))))))))))))))))))))))))) | (10) |
0(2(0(2(1(2(1(0(0(1(1(2(1(1(0(1(0(1(0(2(2(2(1(x1))))))))))))))))))))))) | → | 1(2(1(2(2(1(1(1(1(1(1(0(2(2(2(1(1(2(1(2(1(0(2(1(1(0(1(x1))))))))))))))))))))))))))) | (11) |
0(2(1(0(2(0(0(2(0(1(1(1(2(0(1(1(2(1(1(0(1(0(0(x1))))))))))))))))))))))) | → | 1(2(2(2(0(1(1(2(0(0(1(1(0(1(0(1(1(1(0(1(1(1(1(2(2(1(1(x1))))))))))))))))))))))))))) | (12) |
0(2(1(2(1(1(0(0(1(1(0(2(2(0(1(2(0(2(0(1(1(0(0(x1))))))))))))))))))))))) | → | 2(1(1(1(2(2(0(1(1(1(1(2(2(2(2(1(0(0(2(0(2(1(2(1(1(2(2(x1))))))))))))))))))))))))))) | (13) |
0(2(1(2(2(0(1(0(1(0(1(0(2(1(0(0(1(1(1(2(1(0(0(x1))))))))))))))))))))))) | → | 2(2(2(2(2(1(1(2(2(1(0(1(1(1(1(0(1(1(2(2(1(1(1(2(0(1(2(x1))))))))))))))))))))))))))) | (14) |
0(2(2(1(1(1(1(2(2(1(2(1(2(0(0(1(2(1(0(0(2(0(0(x1))))))))))))))))))))))) | → | 2(2(2(1(1(2(2(2(0(2(0(1(0(1(1(2(2(2(0(1(2(1(1(0(0(2(2(x1))))))))))))))))))))))))))) | (15) |
0(2(2(2(0(1(2(2(1(2(1(0(1(0(2(2(1(2(1(0(2(1(2(x1))))))))))))))))))))))) | → | 1(0(2(2(1(2(2(2(1(2(0(2(1(0(1(0(1(2(2(1(1(0(1(1(1(1(2(x1))))))))))))))))))))))))))) | (16) |
0(2(2(2(1(2(2(0(0(2(1(2(2(1(0(1(1(1(1(1(2(0(0(x1))))))))))))))))))))))) | → | 0(1(1(1(2(0(0(0(1(1(2(2(0(1(1(2(1(1(1(1(1(1(1(2(2(2(2(x1))))))))))))))))))))))))))) | (17) |
0(2(2(2(2(0(1(1(2(1(0(1(2(2(1(1(2(2(0(2(1(0(0(x1))))))))))))))))))))))) | → | 1(2(1(1(1(2(2(1(1(1(0(1(1(0(1(2(2(1(2(1(2(0(0(1(1(1(1(x1))))))))))))))))))))))))))) | (18) |
1(0(0(0(0(2(1(1(1(2(2(2(1(2(1(0(0(1(0(0(2(1(0(x1))))))))))))))))))))))) | → | 1(1(2(1(1(2(2(0(2(0(1(1(0(1(1(0(0(1(0(1(1(1(2(1(2(1(0(x1))))))))))))))))))))))))))) | (19) |
1(0(0(1(1(1(1(0(1(0(0(1(0(2(0(2(1(1(2(0(2(1(1(x1))))))))))))))))))))))) | → | 1(2(2(1(1(2(2(1(0(2(2(2(1(2(2(1(2(0(2(1(2(1(1(1(1(0(1(x1))))))))))))))))))))))))))) | (20) |
1(0(2(2(0(2(2(2(1(0(2(2(2(1(0(0(2(0(2(0(2(1(1(x1))))))))))))))))))))))) | → | 1(0(0(1(1(1(0(2(0(0(0(1(2(1(2(1(1(1(1(1(1(0(0(0(2(1(1(x1))))))))))))))))))))))))))) | (21) |
1(0(2(2(1(1(0(0(2(1(2(1(0(2(1(0(0(2(2(0(1(2(1(x1))))))))))))))))))))))) | → | 1(1(2(1(0(2(1(1(1(2(1(0(2(1(2(2(1(0(1(1(0(2(2(1(1(0(1(x1))))))))))))))))))))))))))) | (22) |
1(1(0(0(0(0(1(0(0(0(1(2(0(1(1(1(1(2(1(1(1(2(0(x1))))))))))))))))))))))) | → | 1(2(1(0(0(1(2(1(1(1(2(0(1(2(1(1(1(2(2(0(1(2(2(1(0(2(1(x1))))))))))))))))))))))))))) | (23) |
1(1(0(0(0(2(0(2(0(1(1(0(2(2(1(1(2(1(1(0(0(2(0(x1))))))))))))))))))))))) | → | 1(2(1(2(1(2(2(1(2(1(1(1(0(2(2(1(1(2(0(1(1(0(1(1(0(0(2(x1))))))))))))))))))))))))))) | (24) |
1(1(0(2(1(1(1(1(2(0(0(2(2(1(0(2(2(1(2(2(0(1(2(x1))))))))))))))))))))))) | → | 1(1(0(0(1(0(0(2(1(1(2(1(0(2(2(2(2(1(1(1(0(1(1(2(1(1(0(x1))))))))))))))))))))))))))) | (25) |
1(1(1(0(1(0(2(0(0(0(1(2(1(1(1(2(2(0(0(1(1(1(1(x1))))))))))))))))))))))) | → | 1(0(1(2(1(0(1(1(0(1(1(1(1(1(0(1(2(1(0(2(0(1(1(1(2(1(1(x1))))))))))))))))))))))))))) | (26) |
1(1(1(2(1(2(2(1(2(2(2(1(0(0(0(0(2(1(0(1(1(0(0(x1))))))))))))))))))))))) | → | 1(2(1(1(1(1(1(2(0(1(2(1(1(2(2(2(1(1(1(1(0(0(2(2(0(2(2(x1))))))))))))))))))))))))))) | (27) |
1(1(2(0(0(0(2(0(1(2(2(2(1(1(1(2(0(0(2(1(2(0(1(x1))))))))))))))))))))))) | → | 1(1(2(1(2(2(1(1(0(2(2(1(1(2(0(2(0(2(1(1(1(2(1(2(0(2(1(x1))))))))))))))))))))))))))) | (28) |
1(1(2(0(0(2(1(0(0(0(2(2(2(2(2(2(1(0(1(1(0(0(2(x1))))))))))))))))))))))) | → | 1(1(1(2(1(0(1(2(1(0(1(1(2(2(2(0(2(1(1(0(2(1(2(2(1(1(1(x1))))))))))))))))))))))))))) | (29) |
1(1(2(0(2(2(0(1(1(2(0(1(2(2(2(1(2(2(2(0(2(0(1(x1))))))))))))))))))))))) | → | 1(1(1(1(2(2(2(2(0(1(1(2(1(1(1(2(0(0(2(1(0(0(2(2(0(1(1(x1))))))))))))))))))))))))))) | (30) |
1(1(2(2(2(2(2(1(2(2(0(0(1(2(0(0(0(2(2(1(0(2(2(x1))))))))))))))))))))))) | → | 1(0(2(1(2(2(1(1(1(2(2(2(2(2(2(1(1(0(0(1(0(0(0(1(1(1(2(x1))))))))))))))))))))))))))) | (31) |
1(2(0(1(0(1(1(1(0(0(2(1(1(2(1(2(2(0(2(0(1(1(2(x1))))))))))))))))))))))) | → | 1(2(2(0(2(1(2(1(1(0(1(1(0(2(2(2(1(1(0(2(1(2(1(1(1(1(2(x1))))))))))))))))))))))))))) | (32) |
1(2(0(1(1(0(1(1(0(0(2(2(2(2(0(0(2(2(0(0(2(2(0(x1))))))))))))))))))))))) | → | 1(2(2(0(1(2(1(1(1(1(2(2(0(2(0(0(2(0(1(1(1(0(1(2(1(2(0(x1))))))))))))))))))))))))))) | (33) |
1(2(0(2(2(2(0(0(1(1(0(1(1(2(1(0(2(2(0(2(2(0(1(x1))))))))))))))))))))))) | → | 1(1(1(1(0(1(2(0(0(0(0(1(1(1(2(1(1(2(1(1(2(0(2(2(2(0(1(x1))))))))))))))))))))))))))) | (34) |
1(2(1(2(1(1(1(0(2(0(1(2(2(2(0(1(1(1(2(2(0(0(0(x1))))))))))))))))))))))) | → | 1(2(0(1(2(2(1(2(1(1(0(1(1(1(0(1(0(1(2(1(1(0(2(2(0(2(2(x1))))))))))))))))))))))))))) | (35) |
2(0(2(0(1(1(0(0(0(1(1(0(0(1(2(2(1(1(2(0(2(0(1(x1))))))))))))))))))))))) | → | 2(2(1(0(2(1(2(2(1(0(0(2(0(2(2(1(1(1(0(2(2(2(2(2(1(0(1(x1))))))))))))))))))))))))))) | (36) |
2(1(1(0(2(0(2(1(1(2(1(1(0(0(0(0(0(2(2(1(1(1(2(x1))))))))))))))))))))))) | → | 2(2(1(1(2(2(0(2(1(0(2(1(1(1(1(0(2(2(2(1(1(1(1(0(2(2(2(x1))))))))))))))))))))))))))) | (37) |
2(1(1(1(2(2(1(0(1(1(2(2(2(0(0(0(0(2(0(2(0(1(2(x1))))))))))))))))))))))) | → | 2(1(0(1(2(0(0(2(2(1(1(0(1(1(2(0(1(1(0(0(0(2(1(1(1(1(1(x1))))))))))))))))))))))))))) | (38) |
2(2(0(0(1(2(0(0(0(1(1(0(2(2(2(2(1(1(2(1(2(0(2(x1))))))))))))))))))))))) | → | 2(0(1(1(1(0(0(0(1(2(2(2(0(1(1(0(2(2(0(1(1(1(0(2(2(2(0(x1))))))))))))))))))))))))))) | (39) |
2(2(0(1(2(2(1(2(2(0(2(0(1(1(2(2(1(0(1(0(0(2(0(x1))))))))))))))))))))))) | → | 2(2(1(0(1(1(0(0(2(2(0(1(0(1(1(1(2(1(1(1(0(2(1(2(2(1(2(x1))))))))))))))))))))))))))) | (40) |
{0(☐), 1(☐), 2(☐)}
We obtain the transformed TRS0(0(0(0(0(1(2(1(0(1(0(1(2(2(2(0(1(2(2(0(1(1(1(x1))))))))))))))))))))))) | → | 0(0(0(1(2(2(1(1(0(2(1(1(2(2(2(2(1(2(0(0(1(1(2(2(1(1(1(x1))))))))))))))))))))))))))) | (1) |
0(0(0(2(0(1(1(1(1(2(1(1(2(1(2(1(2(1(2(1(1(1(0(x1))))))))))))))))))))))) | → | 0(1(1(1(1(1(2(1(2(1(2(1(1(1(0(0(2(2(1(1(0(1(0(0(2(1(1(x1))))))))))))))))))))))))))) | (2) |
0(0(0(2(1(2(1(2(1(2(1(1(1(0(2(0(1(1(2(2(0(1(2(x1))))))))))))))))))))))) | → | 0(1(1(2(0(1(1(1(1(1(1(0(2(0(1(0(1(1(0(1(0(1(2(2(0(2(1(x1))))))))))))))))))))))))))) | (3) |
0(0(1(1(1(0(2(1(2(2(1(1(1(2(0(2(0(1(2(0(1(1(2(x1))))))))))))))))))))))) | → | 0(1(1(1(1(1(1(1(2(0(1(0(1(0(2(2(2(0(1(2(2(2(1(0(0(1(1(x1))))))))))))))))))))))))))) | (4) |
0(1(1(2(1(1(2(2(2(1(1(2(0(0(1(2(0(0(1(0(0(2(0(x1))))))))))))))))))))))) | → | 0(0(2(2(1(0(2(1(2(1(1(2(1(2(2(1(1(1(1(1(0(0(1(2(1(2(0(x1))))))))))))))))))))))))))) | (8) |
0(1(2(1(2(0(0(1(0(1(1(2(1(1(2(2(1(1(1(2(2(0(2(x1))))))))))))))))))))))) | → | 0(1(2(0(1(1(0(1(2(1(1(1(2(0(1(0(1(1(0(1(2(2(1(2(1(2(1(x1))))))))))))))))))))))))))) | (9) |
0(2(0(2(1(2(0(0(2(0(0(1(0(0(2(2(0(1(1(0(1(0(1(x1))))))))))))))))))))))) | → | 0(1(0(2(0(0(2(1(1(1(0(0(2(1(0(2(2(2(1(1(0(1(1(1(1(0(1(x1))))))))))))))))))))))))))) | (10) |
0(2(2(2(1(2(2(0(0(2(1(2(2(1(0(1(1(1(1(1(2(0(0(x1))))))))))))))))))))))) | → | 0(1(1(1(2(0(0(0(1(1(2(2(0(1(1(2(1(1(1(1(1(1(1(2(2(2(2(x1))))))))))))))))))))))))))) | (17) |
1(0(0(0(0(2(1(1(1(2(2(2(1(2(1(0(0(1(0(0(2(1(0(x1))))))))))))))))))))))) | → | 1(1(2(1(1(2(2(0(2(0(1(1(0(1(1(0(0(1(0(1(1(1(2(1(2(1(0(x1))))))))))))))))))))))))))) | (19) |
1(0(0(1(1(1(1(0(1(0(0(1(0(2(0(2(1(1(2(0(2(1(1(x1))))))))))))))))))))))) | → | 1(2(2(1(1(2(2(1(0(2(2(2(1(2(2(1(2(0(2(1(2(1(1(1(1(0(1(x1))))))))))))))))))))))))))) | (20) |
1(0(2(2(0(2(2(2(1(0(2(2(2(1(0(0(2(0(2(0(2(1(1(x1))))))))))))))))))))))) | → | 1(0(0(1(1(1(0(2(0(0(0(1(2(1(2(1(1(1(1(1(1(0(0(0(2(1(1(x1))))))))))))))))))))))))))) | (21) |
1(0(2(2(1(1(0(0(2(1(2(1(0(2(1(0(0(2(2(0(1(2(1(x1))))))))))))))))))))))) | → | 1(1(2(1(0(2(1(1(1(2(1(0(2(1(2(2(1(0(1(1(0(2(2(1(1(0(1(x1))))))))))))))))))))))))))) | (22) |
1(1(0(0(0(0(1(0(0(0(1(2(0(1(1(1(1(2(1(1(1(2(0(x1))))))))))))))))))))))) | → | 1(2(1(0(0(1(2(1(1(1(2(0(1(2(1(1(1(2(2(0(1(2(2(1(0(2(1(x1))))))))))))))))))))))))))) | (23) |
1(1(0(0(0(2(0(2(0(1(1(0(2(2(1(1(2(1(1(0(0(2(0(x1))))))))))))))))))))))) | → | 1(2(1(2(1(2(2(1(2(1(1(1(0(2(2(1(1(2(0(1(1(0(1(1(0(0(2(x1))))))))))))))))))))))))))) | (24) |
1(1(0(2(1(1(1(1(2(0(0(2(2(1(0(2(2(1(2(2(0(1(2(x1))))))))))))))))))))))) | → | 1(1(0(0(1(0(0(2(1(1(2(1(0(2(2(2(2(1(1(1(0(1(1(2(1(1(0(x1))))))))))))))))))))))))))) | (25) |
1(1(1(0(1(0(2(0(0(0(1(2(1(1(1(2(2(0(0(1(1(1(1(x1))))))))))))))))))))))) | → | 1(0(1(2(1(0(1(1(0(1(1(1(1(1(0(1(2(1(0(2(0(1(1(1(2(1(1(x1))))))))))))))))))))))))))) | (26) |
1(1(1(2(1(2(2(1(2(2(2(1(0(0(0(0(2(1(0(1(1(0(0(x1))))))))))))))))))))))) | → | 1(2(1(1(1(1(1(2(0(1(2(1(1(2(2(2(1(1(1(1(0(0(2(2(0(2(2(x1))))))))))))))))))))))))))) | (27) |
1(1(2(0(0(0(2(0(1(2(2(2(1(1(1(2(0(0(2(1(2(0(1(x1))))))))))))))))))))))) | → | 1(1(2(1(2(2(1(1(0(2(2(1(1(2(0(2(0(2(1(1(1(2(1(2(0(2(1(x1))))))))))))))))))))))))))) | (28) |
1(1(2(0(0(2(1(0(0(0(2(2(2(2(2(2(1(0(1(1(0(0(2(x1))))))))))))))))))))))) | → | 1(1(1(2(1(0(1(2(1(0(1(1(2(2(2(0(2(1(1(0(2(1(2(2(1(1(1(x1))))))))))))))))))))))))))) | (29) |
1(1(2(0(2(2(0(1(1(2(0(1(2(2(2(1(2(2(2(0(2(0(1(x1))))))))))))))))))))))) | → | 1(1(1(1(2(2(2(2(0(1(1(2(1(1(1(2(0(0(2(1(0(0(2(2(0(1(1(x1))))))))))))))))))))))))))) | (30) |
1(1(2(2(2(2(2(1(2(2(0(0(1(2(0(0(0(2(2(1(0(2(2(x1))))))))))))))))))))))) | → | 1(0(2(1(2(2(1(1(1(2(2(2(2(2(2(1(1(0(0(1(0(0(0(1(1(1(2(x1))))))))))))))))))))))))))) | (31) |
1(2(0(1(0(1(1(1(0(0(2(1(1(2(1(2(2(0(2(0(1(1(2(x1))))))))))))))))))))))) | → | 1(2(2(0(2(1(2(1(1(0(1(1(0(2(2(2(1(1(0(2(1(2(1(1(1(1(2(x1))))))))))))))))))))))))))) | (32) |
1(2(0(1(1(0(1(1(0(0(2(2(2(2(0(0(2(2(0(0(2(2(0(x1))))))))))))))))))))))) | → | 1(2(2(0(1(2(1(1(1(1(2(2(0(2(0(0(2(0(1(1(1(0(1(2(1(2(0(x1))))))))))))))))))))))))))) | (33) |
1(2(0(2(2(2(0(0(1(1(0(1(1(2(1(0(2(2(0(2(2(0(1(x1))))))))))))))))))))))) | → | 1(1(1(1(0(1(2(0(0(0(0(1(1(1(2(1(1(2(1(1(2(0(2(2(2(0(1(x1))))))))))))))))))))))))))) | (34) |
1(2(1(2(1(1(1(0(2(0(1(2(2(2(0(1(1(1(2(2(0(0(0(x1))))))))))))))))))))))) | → | 1(2(0(1(2(2(1(2(1(1(0(1(1(1(0(1(0(1(2(1(1(0(2(2(0(2(2(x1))))))))))))))))))))))))))) | (35) |
2(0(2(0(1(1(0(0(0(1(1(0(0(1(2(2(1(1(2(0(2(0(1(x1))))))))))))))))))))))) | → | 2(2(1(0(2(1(2(2(1(0(0(2(0(2(2(1(1(1(0(2(2(2(2(2(1(0(1(x1))))))))))))))))))))))))))) | (36) |
2(1(1(0(2(0(2(1(1(2(1(1(0(0(0(0(0(2(2(1(1(1(2(x1))))))))))))))))))))))) | → | 2(2(1(1(2(2(0(2(1(0(2(1(1(1(1(0(2(2(2(1(1(1(1(0(2(2(2(x1))))))))))))))))))))))))))) | (37) |
2(1(1(1(2(2(1(0(1(1(2(2(2(0(0(0(0(2(0(2(0(1(2(x1))))))))))))))))))))))) | → | 2(1(0(1(2(0(0(2(2(1(1(0(1(1(2(0(1(1(0(0(0(2(1(1(1(1(1(x1))))))))))))))))))))))))))) | (38) |
2(2(0(0(1(2(0(0(0(1(1(0(2(2(2(2(1(1(2(1(2(0(2(x1))))))))))))))))))))))) | → | 2(0(1(1(1(0(0(0(1(2(2(2(0(1(1(0(2(2(0(1(1(1(0(2(2(2(0(x1))))))))))))))))))))))))))) | (39) |
2(2(0(1(2(2(1(2(2(0(2(0(1(1(2(2(1(0(1(0(0(2(0(x1))))))))))))))))))))))) | → | 2(2(1(0(1(1(0(0(2(2(0(1(0(1(1(1(2(1(1(1(0(2(1(2(2(1(2(x1))))))))))))))))))))))))))) | (40) |
0(0(0(1(1(1(1(2(2(0(0(1(1(0(2(2(1(0(1(1(2(0(1(0(x1)))))))))))))))))))))))) | → | 0(2(2(1(1(2(2(2(0(1(1(1(2(0(1(1(1(2(1(2(1(0(1(2(2(1(1(0(x1)))))))))))))))))))))))))))) | (41) |
1(0(0(1(1(1(1(2(2(0(0(1(1(0(2(2(1(0(1(1(2(0(1(0(x1)))))))))))))))))))))))) | → | 1(2(2(1(1(2(2(2(0(1(1(1(2(0(1(1(1(2(1(2(1(0(1(2(2(1(1(0(x1)))))))))))))))))))))))))))) | (42) |
2(0(0(1(1(1(1(2(2(0(0(1(1(0(2(2(1(0(1(1(2(0(1(0(x1)))))))))))))))))))))))) | → | 2(2(2(1(1(2(2(2(0(1(1(1(2(0(1(1(1(2(1(2(1(0(1(2(2(1(1(0(x1)))))))))))))))))))))))))))) | (43) |
0(0(1(0(1(1(2(0(1(1(2(2(0(0(2(1(0(2(0(2(2(2(0(2(x1)))))))))))))))))))))))) | → | 0(2(1(2(1(1(2(1(1(0(1(0(1(0(1(2(1(0(0(2(1(1(1(2(1(1(1(2(x1)))))))))))))))))))))))))))) | (44) |
1(0(1(0(1(1(2(0(1(1(2(2(0(0(2(1(0(2(0(2(2(2(0(2(x1)))))))))))))))))))))))) | → | 1(2(1(2(1(1(2(1(1(0(1(0(1(0(1(2(1(0(0(2(1(1(1(2(1(1(1(2(x1)))))))))))))))))))))))))))) | (45) |
2(0(1(0(1(1(2(0(1(1(2(2(0(0(2(1(0(2(0(2(2(2(0(2(x1)))))))))))))))))))))))) | → | 2(2(1(2(1(1(2(1(1(0(1(0(1(0(1(2(1(0(0(2(1(1(1(2(1(1(1(2(x1)))))))))))))))))))))))))))) | (46) |
0(0(1(1(0(2(1(0(2(1(0(2(0(2(2(0(1(1(0(1(2(2(1(1(x1)))))))))))))))))))))))) | → | 0(2(1(0(1(0(0(1(1(1(2(0(0(2(2(2(1(1(2(1(1(0(1(1(0(1(1(1(x1)))))))))))))))))))))))))))) | (47) |
1(0(1(1(0(2(1(0(2(1(0(2(0(2(2(0(1(1(0(1(2(2(1(1(x1)))))))))))))))))))))))) | → | 1(2(1(0(1(0(0(1(1(1(2(0(0(2(2(2(1(1(2(1(1(0(1(1(0(1(1(1(x1)))))))))))))))))))))))))))) | (48) |
2(0(1(1(0(2(1(0(2(1(0(2(0(2(2(0(1(1(0(1(2(2(1(1(x1)))))))))))))))))))))))) | → | 2(2(1(0(1(0(0(1(1(1(2(0(0(2(2(2(1(1(2(1(1(0(1(1(0(1(1(1(x1)))))))))))))))))))))))))))) | (49) |
0(0(2(0(2(1(2(1(0(0(1(1(2(1(1(0(1(0(1(0(2(2(2(1(x1)))))))))))))))))))))))) | → | 0(1(2(1(2(2(1(1(1(1(1(1(0(2(2(2(1(1(2(1(2(1(0(2(1(1(0(1(x1)))))))))))))))))))))))))))) | (50) |
1(0(2(0(2(1(2(1(0(0(1(1(2(1(1(0(1(0(1(0(2(2(2(1(x1)))))))))))))))))))))))) | → | 1(1(2(1(2(2(1(1(1(1(1(1(0(2(2(2(1(1(2(1(2(1(0(2(1(1(0(1(x1)))))))))))))))))))))))))))) | (51) |
2(0(2(0(2(1(2(1(0(0(1(1(2(1(1(0(1(0(1(0(2(2(2(1(x1)))))))))))))))))))))))) | → | 2(1(2(1(2(2(1(1(1(1(1(1(0(2(2(2(1(1(2(1(2(1(0(2(1(1(0(1(x1)))))))))))))))))))))))))))) | (52) |
0(0(2(1(0(2(0(0(2(0(1(1(1(2(0(1(1(2(1(1(0(1(0(0(x1)))))))))))))))))))))))) | → | 0(1(2(2(2(0(1(1(2(0(0(1(1(0(1(0(1(1(1(0(1(1(1(1(2(2(1(1(x1)))))))))))))))))))))))))))) | (53) |
1(0(2(1(0(2(0(0(2(0(1(1(1(2(0(1(1(2(1(1(0(1(0(0(x1)))))))))))))))))))))))) | → | 1(1(2(2(2(0(1(1(2(0(0(1(1(0(1(0(1(1(1(0(1(1(1(1(2(2(1(1(x1)))))))))))))))))))))))))))) | (54) |
2(0(2(1(0(2(0(0(2(0(1(1(1(2(0(1(1(2(1(1(0(1(0(0(x1)))))))))))))))))))))))) | → | 2(1(2(2(2(0(1(1(2(0(0(1(1(0(1(0(1(1(1(0(1(1(1(1(2(2(1(1(x1)))))))))))))))))))))))))))) | (55) |
0(0(2(1(2(1(1(0(0(1(1(0(2(2(0(1(2(0(2(0(1(1(0(0(x1)))))))))))))))))))))))) | → | 0(2(1(1(1(2(2(0(1(1(1(1(2(2(2(2(1(0(0(2(0(2(1(2(1(1(2(2(x1)))))))))))))))))))))))))))) | (56) |
1(0(2(1(2(1(1(0(0(1(1(0(2(2(0(1(2(0(2(0(1(1(0(0(x1)))))))))))))))))))))))) | → | 1(2(1(1(1(2(2(0(1(1(1(1(2(2(2(2(1(0(0(2(0(2(1(2(1(1(2(2(x1)))))))))))))))))))))))))))) | (57) |
2(0(2(1(2(1(1(0(0(1(1(0(2(2(0(1(2(0(2(0(1(1(0(0(x1)))))))))))))))))))))))) | → | 2(2(1(1(1(2(2(0(1(1(1(1(2(2(2(2(1(0(0(2(0(2(1(2(1(1(2(2(x1)))))))))))))))))))))))))))) | (58) |
0(0(2(1(2(2(0(1(0(1(0(1(0(2(1(0(0(1(1(1(2(1(0(0(x1)))))))))))))))))))))))) | → | 0(2(2(2(2(2(1(1(2(2(1(0(1(1(1(1(0(1(1(2(2(1(1(1(2(0(1(2(x1)))))))))))))))))))))))))))) | (59) |
1(0(2(1(2(2(0(1(0(1(0(1(0(2(1(0(0(1(1(1(2(1(0(0(x1)))))))))))))))))))))))) | → | 1(2(2(2(2(2(1(1(2(2(1(0(1(1(1(1(0(1(1(2(2(1(1(1(2(0(1(2(x1)))))))))))))))))))))))))))) | (60) |
2(0(2(1(2(2(0(1(0(1(0(1(0(2(1(0(0(1(1(1(2(1(0(0(x1)))))))))))))))))))))))) | → | 2(2(2(2(2(2(1(1(2(2(1(0(1(1(1(1(0(1(1(2(2(1(1(1(2(0(1(2(x1)))))))))))))))))))))))))))) | (61) |
0(0(2(2(1(1(1(1(2(2(1(2(1(2(0(0(1(2(1(0(0(2(0(0(x1)))))))))))))))))))))))) | → | 0(2(2(2(1(1(2(2(2(0(2(0(1(0(1(1(2(2(2(0(1(2(1(1(0(0(2(2(x1)))))))))))))))))))))))))))) | (62) |
1(0(2(2(1(1(1(1(2(2(1(2(1(2(0(0(1(2(1(0(0(2(0(0(x1)))))))))))))))))))))))) | → | 1(2(2(2(1(1(2(2(2(0(2(0(1(0(1(1(2(2(2(0(1(2(1(1(0(0(2(2(x1)))))))))))))))))))))))))))) | (63) |
2(0(2(2(1(1(1(1(2(2(1(2(1(2(0(0(1(2(1(0(0(2(0(0(x1)))))))))))))))))))))))) | → | 2(2(2(2(1(1(2(2(2(0(2(0(1(0(1(1(2(2(2(0(1(2(1(1(0(0(2(2(x1)))))))))))))))))))))))))))) | (64) |
0(0(2(2(2(0(1(2(2(1(2(1(0(1(0(2(2(1(2(1(0(2(1(2(x1)))))))))))))))))))))))) | → | 0(1(0(2(2(1(2(2(2(1(2(0(2(1(0(1(0(1(2(2(1(1(0(1(1(1(1(2(x1)))))))))))))))))))))))))))) | (65) |
1(0(2(2(2(0(1(2(2(1(2(1(0(1(0(2(2(1(2(1(0(2(1(2(x1)))))))))))))))))))))))) | → | 1(1(0(2(2(1(2(2(2(1(2(0(2(1(0(1(0(1(2(2(1(1(0(1(1(1(1(2(x1)))))))))))))))))))))))))))) | (66) |
2(0(2(2(2(0(1(2(2(1(2(1(0(1(0(2(2(1(2(1(0(2(1(2(x1)))))))))))))))))))))))) | → | 2(1(0(2(2(1(2(2(2(1(2(0(2(1(0(1(0(1(2(2(1(1(0(1(1(1(1(2(x1)))))))))))))))))))))))))))) | (67) |
0(0(2(2(2(2(0(1(1(2(1(0(1(2(2(1(1(2(2(0(2(1(0(0(x1)))))))))))))))))))))))) | → | 0(1(2(1(1(1(2(2(1(1(1(0(1(1(0(1(2(2(1(2(1(2(0(0(1(1(1(1(x1)))))))))))))))))))))))))))) | (68) |
1(0(2(2(2(2(0(1(1(2(1(0(1(2(2(1(1(2(2(0(2(1(0(0(x1)))))))))))))))))))))))) | → | 1(1(2(1(1(1(2(2(1(1(1(0(1(1(0(1(2(2(1(2(1(2(0(0(1(1(1(1(x1)))))))))))))))))))))))))))) | (69) |
2(0(2(2(2(2(0(1(1(2(1(0(1(2(2(1(1(2(2(0(2(1(0(0(x1)))))))))))))))))))))))) | → | 2(1(2(1(1(1(2(2(1(1(1(0(1(1(0(1(2(2(1(2(1(2(0(0(1(1(1(1(x1)))))))))))))))))))))))))))) | (70) |
Root-labeling is applied.
We obtain the labeled TRSThere are 180 ruless (increase limit for explicit display).
[00(x1)] | = | 1 · x1 + 52 |
[01(x1)] | = | 1 · x1 + 21 |
[12(x1)] | = | 1 · x1 + 42 |
[21(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 + 12 |
[20(x1)] | = | 1 · x1 + 22 |
[11(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 + 71 |
There are 170 ruless (increase limit for explicit display).
[00(x1)] | = | 1 · x1 + 19 |
[01(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 + 15 |
[21(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 + 18 |
[20(x1)] | = | 1 · x1 + 32 |
[11(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
01(12(21(12(20(00(01(10(01(11(12(21(11(12(22(21(11(11(12(22(20(02(22(x1))))))))))))))))))))))) | → | 01(12(20(01(11(10(01(12(21(11(11(12(20(01(10(01(11(10(01(12(22(21(12(21(12(21(12(x1))))))))))))))))))))))))))) | (88) |
[00(x1)] | = | 1 · x1 + 1 |
[01(x1)] | = | 1 · x1 |
[12(x1)] | = | 1 · x1 + 1 |
[21(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 + 3 |
[22(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 + 1 |
[11(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
00(00(00(00(01(12(21(10(01(10(01(12(22(22(20(01(12(22(20(01(11(11(10(x1))))))))))))))))))))))) | → | 00(00(01(12(22(21(11(10(02(21(11(12(22(22(22(21(12(20(00(01(11(12(22(21(11(11(10(x1))))))))))))))))))))))))))) | (71) |
00(00(00(00(01(12(21(10(01(10(01(12(22(22(20(01(12(22(20(01(11(11(11(x1))))))))))))))))))))))) | → | 00(00(01(12(22(21(11(10(02(21(11(12(22(22(22(21(12(20(00(01(11(12(22(21(11(11(11(x1))))))))))))))))))))))))))) | (72) |
00(00(00(00(01(12(21(10(01(10(01(12(22(22(20(01(12(22(20(01(11(11(12(x1))))))))))))))))))))))) | → | 00(00(01(12(22(21(11(10(02(21(11(12(22(22(22(21(12(20(00(01(11(12(22(21(11(11(12(x1))))))))))))))))))))))))))) | (73) |
[12(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 + 1 |
[10(x1)] | = | 1 · x1 + 3 |
[00(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 + 1 |
[22(x1)] | = | 1 · x1 |
[21(x1)] | = | 1 · x1 |
12(20(01(11(10(01(11(10(00(02(22(22(22(20(00(02(22(20(00(02(22(20(00(x1))))))))))))))))))))))) | → | 12(22(20(01(12(21(11(11(11(12(22(20(02(20(00(02(20(01(11(11(10(01(12(21(12(20(00(x1))))))))))))))))))))))))))) | (137) |
12(20(01(11(10(01(11(10(00(02(22(22(22(20(00(02(22(20(00(02(22(20(01(x1))))))))))))))))))))))) | → | 12(22(20(01(12(21(11(11(11(12(22(20(02(20(00(02(20(01(11(11(10(01(12(21(12(20(01(x1))))))))))))))))))))))))))) | (138) |
12(20(01(11(10(01(11(10(00(02(22(22(22(20(00(02(22(20(00(02(22(20(02(x1))))))))))))))))))))))) | → | 12(22(20(01(12(21(11(11(11(12(22(20(02(20(00(02(20(01(11(11(10(01(12(21(12(20(02(x1))))))))))))))))))))))))))) | (139) |
[12(x1)] | = | 1 · x1 |
[20(x1)] | = | 1 · x1 |
[02(x1)] | = | 1 · x1 |
[22(x1)] | = | 1 · x1 |
[00(x1)] | = | 1 · x1 |
[01(x1)] | = | 1 · x1 |
[11(x1)] | = | 1 · x1 |
[10(x1)] | = | 1 · x1 + 1 |
[21(x1)] | = | 1 · x1 |
12(20(02(22(22(20(00(01(11(10(01(11(12(21(10(02(22(20(02(22(20(01(10(x1))))))))))))))))))))))) | → | 11(11(11(10(01(12(20(00(00(00(01(11(11(12(21(11(12(21(11(12(20(02(22(22(20(01(10(x1))))))))))))))))))))))))))) | (140) |
12(20(02(22(22(20(00(01(11(10(01(11(12(21(10(02(22(20(02(22(20(01(11(x1))))))))))))))))))))))) | → | 11(11(11(10(01(12(20(00(00(00(01(11(11(12(21(11(12(21(11(12(20(02(22(22(20(01(11(x1))))))))))))))))))))))))))) | (141) |
12(20(02(22(22(20(00(01(11(10(01(11(12(21(10(02(22(20(02(22(20(01(12(x1))))))))))))))))))))))) | → | 11(11(11(10(01(12(20(00(00(00(01(11(11(12(21(11(12(21(11(12(20(02(22(22(20(01(12(x1))))))))))))))))))))))))))) | (142) |
There are no rules in the TRS. Hence, it is terminating.