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__s(X),n__s(Y)) | → | activate#(X) | (19) |
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) | (20) |
geq#(n__s(X),n__s(Y)) | → | activate#(Y) | (21) |
div#(s(X),n__s(Y)) | → | activate#(Y) | (22) |
geq#(n__s(X),n__s(Y)) | → | geq#(activate(X),activate(Y)) | (23) |
geq#(n__s(X),n__s(Y)) | → | activate#(X) | (24) |
activate#(n__minus(X1,X2)) | → | minus#(X1,X2) | (25) |
activate#(n__s(X)) | → | activate#(X) | (26) |
div#(s(X),n__s(Y)) | → | geq#(X,activate(Y)) | (27) |
div#(s(X),n__s(Y)) | → | activate#(Y) | (22) |
activate#(n__0) | → | 0# | (28) |
minus#(n__0,Y) | → | 0# | (29) |
activate#(n__s(X)) | → | s#(activate(X)) | (30) |
activate#(n__div(X1,X2)) | → | activate#(X1) | (31) |
minus#(n__s(X),n__s(Y)) | → | activate#(Y) | (32) |
minus#(n__s(X),n__s(Y)) | → | minus#(activate(X),activate(Y)) | (33) |
div#(s(X),n__s(Y)) | → | activate#(Y) | (22) |
activate#(n__div(X1,X2)) | → | div#(activate(X1),X2) | (34) |
if#(false,X,Y) | → | activate#(Y) | (35) |
if#(true,X,Y) | → | activate#(X) | (36) |
The dependency pairs are split into 1 component.
if#(true,X,Y) | → | activate#(X) | (36) |
if#(false,X,Y) | → | activate#(Y) | (35) |
activate#(n__minus(X1,X2)) | → | minus#(X1,X2) | (25) |
activate#(n__div(X1,X2)) | → | div#(activate(X1),X2) | (34) |
geq#(n__s(X),n__s(Y)) | → | activate#(X) | (24) |
div#(s(X),n__s(Y)) | → | activate#(Y) | (22) |
minus#(n__s(X),n__s(Y)) | → | minus#(activate(X),activate(Y)) | (33) |
minus#(n__s(X),n__s(Y)) | → | activate#(Y) | (32) |
activate#(n__div(X1,X2)) | → | activate#(X1) | (31) |
geq#(n__s(X),n__s(Y)) | → | geq#(activate(X),activate(Y)) | (23) |
div#(s(X),n__s(Y)) | → | activate#(Y) | (22) |
geq#(n__s(X),n__s(Y)) | → | activate#(Y) | (21) |
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) | (20) |
div#(s(X),n__s(Y)) | → | activate#(Y) | (22) |
div#(s(X),n__s(Y)) | → | geq#(X,activate(Y)) | (27) |
minus#(n__s(X),n__s(Y)) | → | activate#(X) | (19) |
activate#(n__s(X)) | → | activate#(X) | (26) |
[0#] | = | 0 |
[div#(x1, x2)] | = | max(x1 + 4, x2 + 5, 0) |
[s(x1)] | = | x1 + 0 |
[minus(x1, x2)] | = | max(x1 + 0, x2 + 1, 0) |
[n__minus(x1, x2)] | = | max(x1 + 0, x2 + 1, 0) |
[activate(x1)] | = | x1 + 0 |
[geq#(x1, x2)] | = | max(x1 + 2, x2 + 3, 0) |
[activate#(x1)] | = | x1 + 1 |
[false] | = | 0 |
[div(x1, x2)] | = | max(x1 + 3, x2 + 4, 0) |
[geq(x1, x2)] | = | max(0) |
[true] | = | 0 |
[n__s(x1)] | = | x1 + 0 |
[n__div(x1, x2)] | = | max(x1 + 3, x2 + 4, 0) |
[0] | = | 3 |
[if(x1, x2, x3)] | = | max(x1 + 4, x2 + 0, x3 + 1, 0) |
[s#(x1)] | = | 0 |
[n__0] | = | 3 |
[minus#(x1, x2)] | = | max(x1 + 1, x2 + 2, 0) |
[if#(x1, x2, x3)] | = | max(x1 + 3, x2 + 1, x3 + 2, 0) |
activate(X) | → | X | (18) |
geq(n__0,n__s(Y)) | → | false | (4) |
activate(n__s(X)) | → | s(activate(X)) | (15) |
if(true,X,Y) | → | activate(X) | (8) |
minus(n__0,Y) | → | 0 | (1) |
geq(X,n__0) | → | true | (3) |
activate(n__div(X1,X2)) | → | div(activate(X1),X2) | (16) |
activate(n__minus(X1,X2)) | → | minus(X1,X2) | (17) |
geq(n__s(X),n__s(Y)) | → | geq(activate(X),activate(Y)) | (5) |
0 | → | n__0 | (10) |
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) |
activate(n__0) | → | 0 | (14) |
div(X1,X2) | → | n__div(X1,X2) | (12) |
s(X) | → | n__s(X) | (11) |
if(false,X,Y) | → | activate(Y) | (9) |
minus(X1,X2) | → | n__minus(X1,X2) | (13) |
div(0,n__s(Y)) | → | 0 | (6) |
minus(n__s(X),n__s(Y)) | → | minus(activate(X),activate(Y)) | (2) |
if#(false,X,Y) | → | activate#(Y) | (35) |
geq#(n__s(X),n__s(Y)) | → | activate#(X) | (24) |
div#(s(X),n__s(Y)) | → | activate#(Y) | (22) |
minus#(n__s(X),n__s(Y)) | → | activate#(Y) | (32) |
activate#(n__div(X1,X2)) | → | activate#(X1) | (31) |
div#(s(X),n__s(Y)) | → | activate#(Y) | (22) |
geq#(n__s(X),n__s(Y)) | → | activate#(Y) | (21) |
div#(s(X),n__s(Y)) | → | activate#(Y) | (22) |
div#(s(X),n__s(Y)) | → | geq#(X,activate(Y)) | (27) |
The dependency pairs are split into 2 components.
geq#(n__s(X),n__s(Y)) | → | geq#(activate(X),activate(Y)) | (23) |
[0#] | = | 0 |
[div#(x1, x2)] | = | 1 |
[s(x1)] | = | x1 + 45380 |
[minus(x1, x2)] | = | 0 |
[n__minus(x1, x2)] | = | 0 |
[activate(x1)] | = | x1 + 0 |
[geq#(x1, x2)] | = | x1 + 1 |
[activate#(x1)] | = | 1 |
[false] | = | 2 |
[div(x1, x2)] | = | x1 + 45545 |
[geq(x1, x2)] | = | 1 |
[true] | = | 2 |
[n__s(x1)] | = | x1 + 45380 |
[n__div(x1, x2)] | = | x1 + 45545 |
[0] | = | 0 |
[if(x1, x2, x3)] | = | x2 + x3 + 0 |
[s#(x1)] | = | 0 |
[n__0] | = | 0 |
[minus#(x1, x2)] | = | 1 |
[if#(x1, x2, x3)] | = | 0 |
activate(X) | → | X | (18) |
activate(n__s(X)) | → | s(activate(X)) | (15) |
if(true,X,Y) | → | activate(X) | (8) |
minus(n__0,Y) | → | 0 | (1) |
activate(n__div(X1,X2)) | → | div(activate(X1),X2) | (16) |
activate(n__minus(X1,X2)) | → | minus(X1,X2) | (17) |
0 | → | n__0 | (10) |
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) |
activate(n__0) | → | 0 | (14) |
div(X1,X2) | → | n__div(X1,X2) | (12) |
s(X) | → | n__s(X) | (11) |
if(false,X,Y) | → | activate(Y) | (9) |
minus(X1,X2) | → | n__minus(X1,X2) | (13) |
div(0,n__s(Y)) | → | 0 | (6) |
minus(n__s(X),n__s(Y)) | → | minus(activate(X),activate(Y)) | (2) |
geq#(n__s(X),n__s(Y)) | → | geq#(activate(X),activate(Y)) | (23) |
The dependency pairs are split into 0 components.
activate#(n__s(X)) | → | activate#(X) | (26) |
if#(true,X,Y) | → | activate#(X) | (36) |
activate#(n__div(X1,X2)) | → | div#(activate(X1),X2) | (34) |
activate#(n__minus(X1,X2)) | → | minus#(X1,X2) | (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) | (20) |
minus#(n__s(X),n__s(Y)) | → | activate#(X) | (19) |
minus#(n__s(X),n__s(Y)) | → | minus#(activate(X),activate(Y)) | (33) |
[0#] | = | 0 |
[div#(x1, x2)] | = | x1 + 2 |
[s(x1)] | = | x1 + 1 |
[minus(x1, x2)] | = | x1 + 0 |
[n__minus(x1, x2)] | = | x1 + 0 |
[activate(x1)] | = | x1 + 0 |
[geq#(x1, x2)] | = | x1 + 1 |
[activate#(x1)] | = | x1 + 1 |
[false] | = | 2 |
[div(x1, x2)] | = | x1 + 1 |
[geq(x1, x2)] | = | 1 |
[true] | = | 2 |
[n__s(x1)] | = | x1 + 1 |
[n__div(x1, x2)] | = | x1 + 1 |
[0] | = | 0 |
[if(x1, x2, x3)] | = | x2 + x3 + 0 |
[s#(x1)] | = | 0 |
[n__0] | = | 0 |
[minus#(x1, x2)] | = | x1 + 0 |
[if#(x1, x2, x3)] | = | x2 + 1 |
activate(X) | → | X | (18) |
activate(n__s(X)) | → | s(activate(X)) | (15) |
if(true,X,Y) | → | activate(X) | (8) |
minus(n__0,Y) | → | 0 | (1) |
activate(n__div(X1,X2)) | → | div(activate(X1),X2) | (16) |
activate(n__minus(X1,X2)) | → | minus(X1,X2) | (17) |
0 | → | n__0 | (10) |
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) |
activate(n__0) | → | 0 | (14) |
div(X1,X2) | → | n__div(X1,X2) | (12) |
s(X) | → | n__s(X) | (11) |
if(false,X,Y) | → | activate(Y) | (9) |
minus(X1,X2) | → | n__minus(X1,X2) | (13) |
div(0,n__s(Y)) | → | 0 | (6) |
minus(n__s(X),n__s(Y)) | → | minus(activate(X),activate(Y)) | (2) |
activate#(n__s(X)) | → | activate#(X) | (26) |
activate#(n__minus(X1,X2)) | → | minus#(X1,X2) | (25) |
minus#(n__s(X),n__s(Y)) | → | minus#(activate(X),activate(Y)) | (33) |
The dependency pairs are split into 1 component.
if#(true,X,Y) | → | activate#(X) | (36) |
activate#(n__div(X1,X2)) | → | div#(activate(X1),X2) | (34) |
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) | (20) |
[0#] | = | 0 |
[div#(x1, x2)] | = | x1 + x2 + 2 |
[s(x1)] | = | 114 |
[minus(x1, x2)] | = | 45671 |
[n__minus(x1, x2)] | = | 45671 |
[activate(x1)] | = | x1 + 120 |
[geq#(x1, x2)] | = | x1 + 1 |
[activate#(x1)] | = | x1 + 114 |
[false] | = | 2 |
[div(x1, x2)] | = | x1 + x2 + 9 |
[geq(x1, x2)] | = | 1 |
[true] | = | 2 |
[n__s(x1)] | = | 1 |
[n__div(x1, x2)] | = | x1 + x2 + 9 |
[0] | = | 0 |
[if(x1, x2, x3)] | = | x2 + x3 + 120 |
[s#(x1)] | = | 0 |
[n__0] | = | 0 |
[minus#(x1, x2)] | = | x1 + 0 |
[if#(x1, x2, x3)] | = | x2 + 115 |
activate(X) | → | X | (18) |
activate(n__s(X)) | → | s(activate(X)) | (15) |
if(true,X,Y) | → | activate(X) | (8) |
minus(n__0,Y) | → | 0 | (1) |
activate(n__div(X1,X2)) | → | div(activate(X1),X2) | (16) |
activate(n__minus(X1,X2)) | → | minus(X1,X2) | (17) |
0 | → | n__0 | (10) |
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) |
activate(n__0) | → | 0 | (14) |
div(X1,X2) | → | n__div(X1,X2) | (12) |
s(X) | → | n__s(X) | (11) |
if(false,X,Y) | → | activate(Y) | (9) |
minus(X1,X2) | → | n__minus(X1,X2) | (13) |
div(0,n__s(Y)) | → | 0 | (6) |
minus(n__s(X),n__s(Y)) | → | minus(activate(X),activate(Y)) | (2) |
if#(true,X,Y) | → | activate#(X) | (36) |
activate#(n__div(X1,X2)) | → | div#(activate(X1),X2) | (34) |
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) | (20) |
The dependency pairs are split into 0 components.