The rewrite relation of the following TRS is considered.
minus(n__0,Y) | → | 0 | (1) |
minus(n__s(X),n__s(Y)) | → | minus(activate(X),activate(Y)) | (2) |
geq(X,n__0) | → | true | (3) |
geq(n__0,n__s(Y)) | → | false | (4) |
geq(n__s(X),n__s(Y)) | → | geq(activate(X),activate(Y)) | (5) |
div(0,n__s(Y)) | → | 0 | (6) |
div(s(X),n__s(Y)) | → | if(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0) | (7) |
if(true,X,Y) | → | activate(X) | (8) |
if(false,X,Y) | → | activate(Y) | (9) |
0 | → | n__0 | (10) |
s(X) | → | n__s(X) | (11) |
div(X1,X2) | → | n__div(X1,X2) | (12) |
minus(X1,X2) | → | n__minus(X1,X2) | (13) |
activate(n__0) | → | 0 | (14) |
activate(n__s(X)) | → | s(activate(X)) | (15) |
activate(n__div(X1,X2)) | → | div(activate(X1),X2) | (16) |
activate(n__minus(X1,X2)) | → | minus(X1,X2) | (17) |
activate(X) | → | X | (18) |
minus#(n__0,Y) | → | 0# | (19) |
minus#(n__s(X),n__s(Y)) | → | activate#(Y) | (20) |
minus#(n__s(X),n__s(Y)) | → | activate#(X) | (21) |
minus#(n__s(X),n__s(Y)) | → | minus#(activate(X),activate(Y)) | (22) |
geq#(n__s(X),n__s(Y)) | → | activate#(Y) | (23) |
geq#(n__s(X),n__s(Y)) | → | activate#(X) | (24) |
geq#(n__s(X),n__s(Y)) | → | geq#(activate(X),activate(Y)) | (25) |
div#(s(X),n__s(Y)) | → | activate#(Y) | (26) |
div#(s(X),n__s(Y)) | → | geq#(X,activate(Y)) | (27) |
div#(s(X),n__s(Y)) | → | if#(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0) | (28) |
if#(true,X,Y) | → | activate#(X) | (29) |
if#(false,X,Y) | → | activate#(Y) | (30) |
activate#(n__0) | → | 0# | (31) |
activate#(n__s(X)) | → | activate#(X) | (32) |
activate#(n__s(X)) | → | s#(activate(X)) | (33) |
activate#(n__div(X1,X2)) | → | activate#(X1) | (34) |
activate#(n__div(X1,X2)) | → | div#(activate(X1),X2) | (35) |
activate#(n__minus(X1,X2)) | → | minus#(X1,X2) | (36) |
The dependency pairs are split into 1 component.
if#(false,X,Y) | → | activate#(Y) | (30) |
activate#(n__s(X)) | → | activate#(X) | (32) |
activate#(n__div(X1,X2)) | → | activate#(X1) | (34) |
activate#(n__div(X1,X2)) | → | div#(activate(X1),X2) | (35) |
div#(s(X),n__s(Y)) | → | activate#(Y) | (26) |
activate#(n__minus(X1,X2)) | → | minus#(X1,X2) | (36) |
minus#(n__s(X),n__s(Y)) | → | activate#(Y) | (20) |
minus#(n__s(X),n__s(Y)) | → | activate#(X) | (21) |
minus#(n__s(X),n__s(Y)) | → | minus#(activate(X),activate(Y)) | (22) |
div#(s(X),n__s(Y)) | → | geq#(X,activate(Y)) | (27) |
geq#(n__s(X),n__s(Y)) | → | activate#(Y) | (23) |
geq#(n__s(X),n__s(Y)) | → | activate#(X) | (24) |
geq#(n__s(X),n__s(Y)) | → | geq#(activate(X),activate(Y)) | (25) |
div#(s(X),n__s(Y)) | → | if#(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0) | (28) |
if#(true,X,Y) | → | activate#(X) | (29) |
[if#(x1, x2, x3)] | = | -∞ · x1 + 0 · x2 + 4 · x3 + 0 |
[activate(x1)] | = | 0 · x1 + 0 |
[activate#(x1)] | = | 0 · x1 + 0 |
[div(x1, x2)] | = | 0 · x1 + 4 · x2 + 0 |
[minus(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[n__s(x1)] | = | 0 · x1 + 0 |
[geq#(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[div#(x1, x2)] | = | 0 · x1 + 4 · x2 + 0 |
[geq(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[n__minus(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[n__0] | = | 0 |
[false] | = | 1 |
[if(x1, x2, x3)] | = | -∞ · x1 + 0 · x2 + 4 · x3 + 4 |
[n__div(x1, x2)] | = | 0 · x1 + 4 · x2 + 0 |
[s(x1)] | = | 0 · x1 + 0 |
[minus#(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[true] | = | 1 |
[0] | = | 0 |
minus(n__0,Y) | → | 0 | (1) |
minus(n__s(X),n__s(Y)) | → | minus(activate(X),activate(Y)) | (2) |
div(0,n__s(Y)) | → | 0 | (6) |
div(s(X),n__s(Y)) | → | if(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0) | (7) |
if(true,X,Y) | → | activate(X) | (8) |
if(false,X,Y) | → | activate(Y) | (9) |
0 | → | n__0 | (10) |
s(X) | → | n__s(X) | (11) |
div(X1,X2) | → | n__div(X1,X2) | (12) |
minus(X1,X2) | → | n__minus(X1,X2) | (13) |
activate(n__0) | → | 0 | (14) |
activate(n__s(X)) | → | s(activate(X)) | (15) |
activate(n__div(X1,X2)) | → | div(activate(X1),X2) | (16) |
activate(n__minus(X1,X2)) | → | minus(X1,X2) | (17) |
activate(X) | → | X | (18) |
div#(s(X),n__s(Y)) | → | activate#(Y) | (26) |
[if#(x1, x2, x3)] | = | -∞ · x1 + 0 · x2 + 4 · x3 + 0 |
[activate(x1)] | = | 0 · x1 + 0 |
[activate#(x1)] | = | 0 · x1 + -∞ |
[div(x1, x2)] | = | 0 · x1 + 4 · x2 + 0 |
[minus(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[n__s(x1)] | = | 0 · x1 + 0 |
[geq#(x1, x2)] | = | 0 · x1 + 4 · x2 + 0 |
[div#(x1, x2)] | = | 0 · x1 + 4 · x2 + 0 |
[geq(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[n__minus(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[n__0] | = | 0 |
[false] | = | 0 |
[if(x1, x2, x3)] | = | -∞ · x1 + 0 · x2 + 3 · x3 + 0 |
[n__div(x1, x2)] | = | 0 · x1 + 4 · x2 + 0 |
[s(x1)] | = | 0 · x1 + 0 |
[minus#(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[true] | = | 4 |
[0] | = | 0 |
minus(n__0,Y) | → | 0 | (1) |
minus(n__s(X),n__s(Y)) | → | minus(activate(X),activate(Y)) | (2) |
div(0,n__s(Y)) | → | 0 | (6) |
div(s(X),n__s(Y)) | → | if(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0) | (7) |
if(true,X,Y) | → | activate(X) | (8) |
if(false,X,Y) | → | activate(Y) | (9) |
0 | → | n__0 | (10) |
s(X) | → | n__s(X) | (11) |
div(X1,X2) | → | n__div(X1,X2) | (12) |
minus(X1,X2) | → | n__minus(X1,X2) | (13) |
activate(n__0) | → | 0 | (14) |
activate(n__s(X)) | → | s(activate(X)) | (15) |
activate(n__div(X1,X2)) | → | div(activate(X1),X2) | (16) |
activate(n__minus(X1,X2)) | → | minus(X1,X2) | (17) |
activate(X) | → | X | (18) |
if#(false,X,Y) | → | activate#(Y) | (30) |
geq#(n__s(X),n__s(Y)) | → | activate#(Y) | (23) |
[if#(x1, x2, x3)] | = | -∞ · x1 + 0 · x2 + 2 · x3 + -∞ |
[activate(x1)] | = | 0 · x1 + 0 |
[activate#(x1)] | = | 0 · x1 + -∞ |
[div(x1, x2)] | = | 0 · x1 + 2 · x2 + 0 |
[minus(x1, x2)] | = | 0 · x1 + 2 · x2 + 0 |
[n__s(x1)] | = | 0 · x1 + 0 |
[geq#(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[div#(x1, x2)] | = | 0 · x1 + 2 · x2 + 0 |
[geq(x1, x2)] | = | -∞ · x1 + 0 · x2 + 0 |
[n__minus(x1, x2)] | = | 0 · x1 + 2 · x2 + 0 |
[n__0] | = | 0 |
[false] | = | 0 |
[if(x1, x2, x3)] | = | -∞ · x1 + 0 · x2 + 0 · x3 + 0 |
[n__div(x1, x2)] | = | 0 · x1 + 2 · x2 + 0 |
[s(x1)] | = | 0 · x1 + 0 |
[minus#(x1, x2)] | = | 0 · x1 + 2 · x2 + 0 |
[true] | = | 2 |
[0] | = | 0 |
minus(n__0,Y) | → | 0 | (1) |
minus(n__s(X),n__s(Y)) | → | minus(activate(X),activate(Y)) | (2) |
div(0,n__s(Y)) | → | 0 | (6) |
div(s(X),n__s(Y)) | → | if(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0) | (7) |
if(true,X,Y) | → | activate(X) | (8) |
if(false,X,Y) | → | activate(Y) | (9) |
0 | → | n__0 | (10) |
s(X) | → | n__s(X) | (11) |
div(X1,X2) | → | n__div(X1,X2) | (12) |
minus(X1,X2) | → | n__minus(X1,X2) | (13) |
activate(n__0) | → | 0 | (14) |
activate(n__s(X)) | → | s(activate(X)) | (15) |
activate(n__div(X1,X2)) | → | div(activate(X1),X2) | (16) |
activate(n__minus(X1,X2)) | → | minus(X1,X2) | (17) |
activate(X) | → | X | (18) |
minus#(n__s(X),n__s(Y)) | → | activate#(Y) | (20) |
[if#(x1, x2, x3)] | = | -∞ · x1 + 0 · x2 + 4 · x3 + -∞ |
[activate(x1)] | = | 0 · x1 + 0 |
[activate#(x1)] | = | 0 · x1 + -∞ |
[div(x1, x2)] | = | 4 · x1 + 2 · x2 + 4 |
[minus(x1, x2)] | = | 0 · x1 + -∞ · x2 + 0 |
[n__s(x1)] | = | 0 · x1 + -∞ |
[geq#(x1, x2)] | = | 1 · x1 + 1 · x2 + 1 |
[div#(x1, x2)] | = | 4 · x1 + 2 · x2 + 0 |
[geq(x1, x2)] | = | 7 · x1 + 0 · x2 + 0 |
[n__minus(x1, x2)] | = | 0 · x1 + -∞ · x2 + 0 |
[n__0] | = | 0 |
[false] | = | 0 |
[if(x1, x2, x3)] | = | -∞ · x1 + 0 · x2 + 4 · x3 + 0 |
[n__div(x1, x2)] | = | 4 · x1 + 2 · x2 + 4 |
[s(x1)] | = | 0 · x1 + 0 |
[minus#(x1, x2)] | = | 0 · x1 + -∞ · x2 + 0 |
[true] | = | 5 |
[0] | = | 0 |
minus(n__0,Y) | → | 0 | (1) |
minus(n__s(X),n__s(Y)) | → | minus(activate(X),activate(Y)) | (2) |
div(0,n__s(Y)) | → | 0 | (6) |
div(s(X),n__s(Y)) | → | if(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0) | (7) |
if(true,X,Y) | → | activate(X) | (8) |
if(false,X,Y) | → | activate(Y) | (9) |
0 | → | n__0 | (10) |
s(X) | → | n__s(X) | (11) |
div(X1,X2) | → | n__div(X1,X2) | (12) |
minus(X1,X2) | → | n__minus(X1,X2) | (13) |
activate(n__0) | → | 0 | (14) |
activate(n__s(X)) | → | s(activate(X)) | (15) |
activate(n__div(X1,X2)) | → | div(activate(X1),X2) | (16) |
activate(n__minus(X1,X2)) | → | minus(X1,X2) | (17) |
activate(X) | → | X | (18) |
activate#(n__div(X1,X2)) | → | activate#(X1) | (34) |
div#(s(X),n__s(Y)) | → | geq#(X,activate(Y)) | (27) |
geq#(n__s(X),n__s(Y)) | → | activate#(X) | (24) |
The dependency pairs are split into 2 components.
geq#(n__s(X),n__s(Y)) | → | geq#(activate(X),activate(Y)) | (25) |
[activate(x1)] | = | 0 · x1 + 0 |
[div(x1, x2)] | = | 0 · x1 + -∞ · x2 + 0 |
[minus(x1, x2)] | = | 0 · x1 + -∞ · x2 + 0 |
[n__s(x1)] | = | 1 · x1 + 1 |
[geq#(x1, x2)] | = | 0 · x1 + 4 · x2 + 1 |
[geq(x1, x2)] | = | 0 · x1 + -∞ · x2 + 1 |
[n__minus(x1, x2)] | = | 0 · x1 + -∞ · x2 + 0 |
[n__0] | = | 0 |
[false] | = | 1 |
[if(x1, x2, x3)] | = | 0 · x1 + 0 · x2 + 1 · x3 + 1 |
[n__div(x1, x2)] | = | 0 · x1 + -∞ · x2 + -∞ |
[s(x1)] | = | 1 · x1 + 1 |
[true] | = | 0 |
[0] | = | 0 |
minus(n__0,Y) | → | 0 | (1) |
minus(n__s(X),n__s(Y)) | → | minus(activate(X),activate(Y)) | (2) |
geq(X,n__0) | → | true | (3) |
geq(n__0,n__s(Y)) | → | false | (4) |
geq(n__s(X),n__s(Y)) | → | geq(activate(X),activate(Y)) | (5) |
div(0,n__s(Y)) | → | 0 | (6) |
div(s(X),n__s(Y)) | → | if(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0) | (7) |
if(true,X,Y) | → | activate(X) | (8) |
if(false,X,Y) | → | activate(Y) | (9) |
0 | → | n__0 | (10) |
s(X) | → | n__s(X) | (11) |
div(X1,X2) | → | n__div(X1,X2) | (12) |
minus(X1,X2) | → | n__minus(X1,X2) | (13) |
activate(n__0) | → | 0 | (14) |
activate(n__s(X)) | → | s(activate(X)) | (15) |
activate(n__div(X1,X2)) | → | div(activate(X1),X2) | (16) |
activate(n__minus(X1,X2)) | → | minus(X1,X2) | (17) |
activate(X) | → | X | (18) |
geq#(n__s(X),n__s(Y)) | → | geq#(activate(X),activate(Y)) | (25) |
There are no pairs anymore.
if#(true,X,Y) | → | activate#(X) | (29) |
activate#(n__s(X)) | → | activate#(X) | (32) |
activate#(n__div(X1,X2)) | → | div#(activate(X1),X2) | (35) |
div#(s(X),n__s(Y)) | → | if#(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0) | (28) |
activate#(n__minus(X1,X2)) | → | minus#(X1,X2) | (36) |
minus#(n__s(X),n__s(Y)) | → | activate#(X) | (21) |
minus#(n__s(X),n__s(Y)) | → | minus#(activate(X),activate(Y)) | (22) |
[if#(x1, x2, x3)] | = | 0 · x1 + 2 · x2 + 0 · x3 + 0 |
[activate(x1)] | = | 1 · x1 + 0 |
[activate#(x1)] | = | 2 · x1 + 0 |
[div(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[minus(x1, x2)] | = | 2 · x1 + 0 · x2 + 1 |
[n__s(x1)] | = | 2 · x1 + 0 |
[div#(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[geq(x1, x2)] | = | 0 · x1 + 0 · x2 + 4 |
[n__minus(x1, x2)] | = | 2 · x1 + 0 · x2 + 1 |
[n__0] | = | 0 |
[false] | = | 0 |
[if(x1, x2, x3)] | = | 0 · x1 + 1 · x2 + 4 · x3 + 0 |
[n__div(x1, x2)] | = | 0 · x1 + 0 · x2 + 0 |
[s(x1)] | = | 2 · x1 + 0 |
[minus#(x1, x2)] | = | 2 · x1 + 0 · x2 + 0 |
[true] | = | 0 |
[0] | = | 0 |
minus(n__0,Y) | → | 0 | (1) |
minus(n__s(X),n__s(Y)) | → | minus(activate(X),activate(Y)) | (2) |
div(0,n__s(Y)) | → | 0 | (6) |
div(s(X),n__s(Y)) | → | if(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0) | (7) |
if(true,X,Y) | → | activate(X) | (8) |
if(false,X,Y) | → | activate(Y) | (9) |
0 | → | n__0 | (10) |
s(X) | → | n__s(X) | (11) |
div(X1,X2) | → | n__div(X1,X2) | (12) |
minus(X1,X2) | → | n__minus(X1,X2) | (13) |
activate(n__0) | → | 0 | (14) |
activate(n__s(X)) | → | s(activate(X)) | (15) |
activate(n__div(X1,X2)) | → | div(activate(X1),X2) | (16) |
activate(n__minus(X1,X2)) | → | minus(X1,X2) | (17) |
activate(X) | → | X | (18) |
activate#(n__minus(X1,X2)) | → | minus#(X1,X2) | (36) |
The dependency pairs are split into 2 components.
minus#(n__s(X),n__s(Y)) | → | minus#(activate(X),activate(Y)) | (22) |
[activate(x1)] | = | 0 · x1 + 0 |
[div(x1, x2)] | = | 0 · x1 + -∞ · x2 + 0 |
[minus(x1, x2)] | = | 0 · x1 + -∞ · x2 + 0 |
[n__s(x1)] | = | 1 · x1 + 1 |
[geq(x1, x2)] | = | 0 · x1 + -∞ · x2 + 1 |
[n__minus(x1, x2)] | = | 0 · x1 + -∞ · x2 + 0 |
[n__0] | = | 0 |
[false] | = | 1 |
[if(x1, x2, x3)] | = | 0 · x1 + 0 · x2 + 1 · x3 + 1 |
[n__div(x1, x2)] | = | 0 · x1 + -∞ · x2 + -∞ |
[s(x1)] | = | 1 · x1 + 1 |
[minus#(x1, x2)] | = | 0 · x1 + 4 · x2 + 1 |
[true] | = | 0 |
[0] | = | 0 |
minus(n__0,Y) | → | 0 | (1) |
minus(n__s(X),n__s(Y)) | → | minus(activate(X),activate(Y)) | (2) |
geq(X,n__0) | → | true | (3) |
geq(n__0,n__s(Y)) | → | false | (4) |
geq(n__s(X),n__s(Y)) | → | geq(activate(X),activate(Y)) | (5) |
div(0,n__s(Y)) | → | 0 | (6) |
div(s(X),n__s(Y)) | → | if(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0) | (7) |
if(true,X,Y) | → | activate(X) | (8) |
if(false,X,Y) | → | activate(Y) | (9) |
0 | → | n__0 | (10) |
s(X) | → | n__s(X) | (11) |
div(X1,X2) | → | n__div(X1,X2) | (12) |
minus(X1,X2) | → | n__minus(X1,X2) | (13) |
activate(n__0) | → | 0 | (14) |
activate(n__s(X)) | → | s(activate(X)) | (15) |
activate(n__div(X1,X2)) | → | div(activate(X1),X2) | (16) |
activate(n__minus(X1,X2)) | → | minus(X1,X2) | (17) |
activate(X) | → | X | (18) |
minus#(n__s(X),n__s(Y)) | → | minus#(activate(X),activate(Y)) | (22) |
There are no pairs anymore.
if#(true,X,Y) | → | activate#(X) | (29) |
activate#(n__s(X)) | → | activate#(X) | (32) |
activate#(n__div(X1,X2)) | → | div#(activate(X1),X2) | (35) |
div#(s(X),n__s(Y)) | → | if#(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0) | (28) |
[if#(x1, x2, x3)] | = | 0 · x1 + 0 · x2 + 4 · x3 + 0 |
[activate(x1)] | = | 1 · x1 + 0 |
[activate#(x1)] | = | 0 · x1 + 0 |
[div(x1, x2)] | = | 2 · x1 + -∞ · x2 + 2 |
[minus(x1, x2)] | = | -∞ · x1 + -∞ · x2 + 1 |
[n__s(x1)] | = | 0 · x1 + 3 |
[div#(x1, x2)] | = | 0 · x1 + -∞ · x2 + 0 |
[geq(x1, x2)] | = | -∞ · x1 + -∞ · x2 + 0 |
[n__minus(x1, x2)] | = | -∞ · x1 + -∞ · x2 + 1 |
[n__0] | = | 0 |
[false] | = | 0 |
[if(x1, x2, x3)] | = | -∞ · x1 + 1 · x2 + 6 · x3 + 0 |
[n__div(x1, x2)] | = | 2 · x1 + -∞ · x2 + 1 |
[s(x1)] | = | 0 · x1 + 4 |
[true] | = | 0 |
[0] | = | 1 |
minus(n__0,Y) | → | 0 | (1) |
minus(n__s(X),n__s(Y)) | → | minus(activate(X),activate(Y)) | (2) |
geq(X,n__0) | → | true | (3) |
geq(n__0,n__s(Y)) | → | false | (4) |
geq(n__s(X),n__s(Y)) | → | geq(activate(X),activate(Y)) | (5) |
div(0,n__s(Y)) | → | 0 | (6) |
div(s(X),n__s(Y)) | → | if(geq(X,activate(Y)),n__s(n__div(n__minus(X,activate(Y)),n__s(activate(Y)))),n__0) | (7) |
if(true,X,Y) | → | activate(X) | (8) |
if(false,X,Y) | → | activate(Y) | (9) |
0 | → | n__0 | (10) |
s(X) | → | n__s(X) | (11) |
div(X1,X2) | → | n__div(X1,X2) | (12) |
minus(X1,X2) | → | n__minus(X1,X2) | (13) |
activate(n__0) | → | 0 | (14) |
activate(n__s(X)) | → | s(activate(X)) | (15) |
activate(n__div(X1,X2)) | → | div(activate(X1),X2) | (16) |
activate(n__minus(X1,X2)) | → | minus(X1,X2) | (17) |
activate(X) | → | X | (18) |
activate#(n__div(X1,X2)) | → | div#(activate(X1),X2) | (35) |
The dependency pairs are split into 1 component.
activate#(n__s(X)) | → | activate#(X) | (32) |
Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.
activate#(n__s(X)) | → | activate#(X) | (32) |
1 | > | 1 |
As there is no critical graph in the transitive closure, there are no infinite chains.