The rewrite relation of the following TRS is considered.
active(f(b,X,c)) | → | mark(f(X,c,X)) | (1) |
active(c) | → | mark(b) | (2) |
mark(f(X1,X2,X3)) | → | active(f(X1,mark(X2),X3)) | (3) |
mark(b) | → | active(b) | (4) |
mark(c) | → | active(c) | (5) |
f(mark(X1),X2,X3) | → | f(X1,X2,X3) | (6) |
f(X1,mark(X2),X3) | → | f(X1,X2,X3) | (7) |
f(X1,X2,mark(X3)) | → | f(X1,X2,X3) | (8) |
f(active(X1),X2,X3) | → | f(X1,X2,X3) | (9) |
f(X1,active(X2),X3) | → | f(X1,X2,X3) | (10) |
f(X1,X2,active(X3)) | → | f(X1,X2,X3) | (11) |
active#(f(b,X,c)) | → | mark#(f(X,c,X)) | (12) |
active#(f(b,X,c)) | → | f#(X,c,X) | (13) |
active#(c) | → | mark#(b) | (14) |
mark#(f(X1,X2,X3)) | → | active#(f(X1,mark(X2),X3)) | (15) |
mark#(f(X1,X2,X3)) | → | f#(X1,mark(X2),X3) | (16) |
mark#(f(X1,X2,X3)) | → | mark#(X2) | (17) |
mark#(b) | → | active#(b) | (18) |
mark#(c) | → | active#(c) | (19) |
f#(mark(X1),X2,X3) | → | f#(X1,X2,X3) | (20) |
f#(X1,mark(X2),X3) | → | f#(X1,X2,X3) | (21) |
f#(X1,X2,mark(X3)) | → | f#(X1,X2,X3) | (22) |
f#(active(X1),X2,X3) | → | f#(X1,X2,X3) | (23) |
f#(X1,active(X2),X3) | → | f#(X1,X2,X3) | (24) |
f#(X1,X2,active(X3)) | → | f#(X1,X2,X3) | (25) |
active#(f(b,X,c)) | → | f#(X,c,X) | (13) |
active#(c) | → | mark#(b) | (14) |
mark#(f(X1,X2,X3)) | → | f#(X1,mark(X2),X3) | (16) |
mark#(b) | → | active#(b) | (18) |
mark#(c) | → | active#(c) | (19) |
f#(mark(X1),X2,X3) | → | f#(X1,X2,X3) | (20) |
f#(X1,mark(X2),X3) | → | f#(X1,X2,X3) | (21) |
f#(X1,X2,mark(X3)) | → | f#(X1,X2,X3) | (22) |
f#(active(X1),X2,X3) | → | f#(X1,X2,X3) | (23) |
f#(X1,active(X2),X3) | → | f#(X1,X2,X3) | (24) |
f#(X1,X2,active(X3)) | → | f#(X1,X2,X3) | (25) |
mark#(f(X1,X2,X3)) | → | mark#(X2) | (17) |
t0 | = | active#(f(mark(c),mark(c),mark(c))) |
→R | active#(f(active(c),mark(c),mark(c))) | |
→R | active#(f(mark(b),mark(c),mark(c))) | |
→R | active#(f(mark(b),mark(c),c)) | |
→R | active#(f(b,mark(c),c)) | |
→P | mark#(f(mark(c),c,mark(c))) | |
→P | active#(f(mark(c),mark(c),mark(c))) | |
= | t6 |