The rewrite relation of the following TRS is considered.
active(f(a,b,X)) | → | mark(f(X,X,X)) | (1) |
active(c) | → | mark(a) | (2) |
active(c) | → | mark(b) | (3) |
mark(f(X1,X2,X3)) | → | active(f(X1,X2,mark(X3))) | (4) |
mark(a) | → | active(a) | (5) |
mark(b) | → | active(b) | (6) |
mark(c) | → | active(c) | (7) |
f(mark(X1),X2,X3) | → | f(X1,X2,X3) | (8) |
f(X1,mark(X2),X3) | → | f(X1,X2,X3) | (9) |
f(X1,X2,mark(X3)) | → | f(X1,X2,X3) | (10) |
f(active(X1),X2,X3) | → | f(X1,X2,X3) | (11) |
f(X1,active(X2),X3) | → | f(X1,X2,X3) | (12) |
f(X1,X2,active(X3)) | → | f(X1,X2,X3) | (13) |
active#(f(a,b,X)) | → | mark#(f(X,X,X)) | (14) |
active#(f(a,b,X)) | → | f#(X,X,X) | (15) |
active#(c) | → | mark#(a) | (16) |
active#(c) | → | mark#(b) | (17) |
mark#(f(X1,X2,X3)) | → | active#(f(X1,X2,mark(X3))) | (18) |
mark#(f(X1,X2,X3)) | → | f#(X1,X2,mark(X3)) | (19) |
mark#(f(X1,X2,X3)) | → | mark#(X3) | (20) |
mark#(a) | → | active#(a) | (21) |
mark#(b) | → | active#(b) | (22) |
mark#(c) | → | active#(c) | (23) |
f#(mark(X1),X2,X3) | → | f#(X1,X2,X3) | (24) |
f#(X1,mark(X2),X3) | → | f#(X1,X2,X3) | (25) |
f#(X1,X2,mark(X3)) | → | f#(X1,X2,X3) | (26) |
f#(active(X1),X2,X3) | → | f#(X1,X2,X3) | (27) |
f#(X1,active(X2),X3) | → | f#(X1,X2,X3) | (28) |
f#(X1,X2,active(X3)) | → | f#(X1,X2,X3) | (29) |
active#(f(a,b,X)) | → | f#(X,X,X) | (15) |
active#(c) | → | mark#(a) | (16) |
active#(c) | → | mark#(b) | (17) |
mark#(f(X1,X2,X3)) | → | f#(X1,X2,mark(X3)) | (19) |
mark#(a) | → | active#(a) | (21) |
mark#(b) | → | active#(b) | (22) |
mark#(c) | → | active#(c) | (23) |
f#(mark(X1),X2,X3) | → | f#(X1,X2,X3) | (24) |
f#(X1,mark(X2),X3) | → | f#(X1,X2,X3) | (25) |
f#(X1,X2,mark(X3)) | → | f#(X1,X2,X3) | (26) |
f#(active(X1),X2,X3) | → | f#(X1,X2,X3) | (27) |
f#(X1,active(X2),X3) | → | f#(X1,X2,X3) | (28) |
f#(X1,X2,active(X3)) | → | f#(X1,X2,X3) | (29) |
mark#(f(X1,X2,X3)) | → | mark#(X3) | (20) |
t0 | = | active#(f(active(c),active(c),mark(active(c)))) |
→R | active#(f(active(c),mark(b),mark(active(c)))) | |
→R | active#(f(mark(a),mark(b),mark(active(c)))) | |
→R | active#(f(mark(a),mark(b),active(c))) | |
→R | active#(f(mark(a),b,active(c))) | |
→R | active#(f(a,b,active(c))) | |
→P | mark#(f(active(c),active(c),active(c))) | |
→P | active#(f(active(c),active(c),mark(active(c)))) | |
= | t7 |