The rewrite relation of the following TRS is considered.
a__f(X) | → | a__if(mark(X),c,f(true)) | (1) |
a__if(true,X,Y) | → | mark(X) | (2) |
a__if(false,X,Y) | → | mark(Y) | (3) |
mark(f(X)) | → | a__f(mark(X)) | (4) |
mark(if(X1,X2,X3)) | → | a__if(mark(X1),mark(X2),X3) | (5) |
mark(c) | → | c | (6) |
mark(true) | → | true | (7) |
mark(false) | → | false | (8) |
a__f(X) | → | f(X) | (9) |
a__if(X1,X2,X3) | → | if(X1,X2,X3) | (10) |
mark#(if(X1,X2,X3)) | → | a__if#(mark(X1),mark(X2),X3) | (11) |
a__f#(X) | → | a__if#(mark(X),c,f(true)) | (12) |
mark#(f(X)) | → | mark#(X) | (13) |
a__f#(X) | → | mark#(X) | (14) |
a__if#(false,X,Y) | → | mark#(Y) | (15) |
mark#(if(X1,X2,X3)) | → | mark#(X1) | (16) |
a__if#(true,X,Y) | → | mark#(X) | (17) |
mark#(f(X)) | → | a__f#(mark(X)) | (18) |
mark#(if(X1,X2,X3)) | → | mark#(X2) | (19) |
The dependency pairs are split into 1 component.
mark#(if(X1,X2,X3)) | → | mark#(X2) | (19) |
mark#(f(X)) | → | a__f#(mark(X)) | (18) |
a__if#(true,X,Y) | → | mark#(X) | (17) |
mark#(if(X1,X2,X3)) | → | mark#(X1) | (16) |
mark#(f(X)) | → | mark#(X) | (13) |
a__f#(X) | → | a__if#(mark(X),c,f(true)) | (12) |
a__if#(false,X,Y) | → | mark#(Y) | (15) |
a__f#(X) | → | mark#(X) | (14) |
mark#(if(X1,X2,X3)) | → | a__if#(mark(X1),mark(X2),X3) | (11) |
[a__f(x1)] | = | x1 + 10451 |
[false] | = | 1 |
[c] | = | 0 |
[true] | = | 0 |
[f(x1)] | = | x1 + 10451 |
[mark#(x1)] | = | x1 + 0 |
[if(x1, x2, x3)] | = | x1 + x2 + x3 + 0 |
[mark(x1)] | = | x1 + 0 |
[a__if#(x1, x2, x3)] | = | x2 + x3 + 0 |
[a__f#(x1)] | = | x1 + 10451 |
[a__if(x1, x2, x3)] | = | x1 + x2 + x3 + 0 |
mark(f(X)) | → | a__f(mark(X)) | (4) |
mark(false) | → | false | (8) |
a__f(X) | → | a__if(mark(X),c,f(true)) | (1) |
a__if(false,X,Y) | → | mark(Y) | (3) |
mark(if(X1,X2,X3)) | → | a__if(mark(X1),mark(X2),X3) | (5) |
a__if(X1,X2,X3) | → | if(X1,X2,X3) | (10) |
mark(true) | → | true | (7) |
a__f(X) | → | f(X) | (9) |
mark(c) | → | c | (6) |
a__if(true,X,Y) | → | mark(X) | (2) |
mark#(f(X)) | → | mark#(X) | (13) |
a__f#(X) | → | mark#(X) | (14) |
The dependency pairs are split into 1 component.
mark#(f(X)) | → | a__f#(mark(X)) | (18) |
a__f#(X) | → | a__if#(mark(X),c,f(true)) | (12) |
a__if#(false,X,Y) | → | mark#(Y) | (15) |
mark#(if(X1,X2,X3)) | → | mark#(X2) | (19) |
mark#(if(X1,X2,X3)) | → | mark#(X1) | (16) |
mark#(if(X1,X2,X3)) | → | a__if#(mark(X1),mark(X2),X3) | (11) |
a__if#(true,X,Y) | → | mark#(X) | (17) |
[a__f(x1)] | = | x1 + 19781 |
[false] | = | 1 |
[c] | = | 0 |
[true] | = | 0 |
[f(x1)] | = | x1 + 19781 |
[mark#(x1)] | = | x1 + 0 |
[if(x1, x2, x3)] | = | x1 + x2 + x3 + 0 |
[mark(x1)] | = | x1 + 0 |
[a__if#(x1, x2, x3)] | = | x1 + x2 + x3 + 0 |
[a__f#(x1)] | = | x1 + 19781 |
[a__if(x1, x2, x3)] | = | x1 + x2 + x3 + 0 |
mark(f(X)) | → | a__f(mark(X)) | (4) |
mark(false) | → | false | (8) |
a__f(X) | → | a__if(mark(X),c,f(true)) | (1) |
a__if(false,X,Y) | → | mark(Y) | (3) |
mark(if(X1,X2,X3)) | → | a__if(mark(X1),mark(X2),X3) | (5) |
a__if(X1,X2,X3) | → | if(X1,X2,X3) | (10) |
mark(true) | → | true | (7) |
a__f(X) | → | f(X) | (9) |
mark(c) | → | c | (6) |
a__if(true,X,Y) | → | mark(X) | (2) |
a__if#(false,X,Y) | → | mark#(Y) | (15) |
The dependency pairs are split into 1 component.
mark#(f(X)) | → | a__f#(mark(X)) | (18) |
a__f#(X) | → | a__if#(mark(X),c,f(true)) | (12) |
mark#(if(X1,X2,X3)) | → | mark#(X2) | (19) |
mark#(if(X1,X2,X3)) | → | mark#(X1) | (16) |
mark#(if(X1,X2,X3)) | → | a__if#(mark(X1),mark(X2),X3) | (11) |
a__if#(true,X,Y) | → | mark#(X) | (17) |
[a__f(x1)] | = | x1 + 2 |
[false] | = | 1 |
[c] | = | 0 |
[true] | = | 0 |
[f(x1)] | = | x1 + 2 |
[mark#(x1)] | = | x1 + 0 |
[if(x1, x2, x3)] | = | x1 + x2 + x3 + 0 |
[mark(x1)] | = | x1 + 0 |
[a__if#(x1, x2, x3)] | = | x1 + x2 + 0 |
[a__f#(x1)] | = | x1 + 1 |
[a__if(x1, x2, x3)] | = | x1 + x2 + x3 + 0 |
mark(f(X)) | → | a__f(mark(X)) | (4) |
mark(false) | → | false | (8) |
a__f(X) | → | a__if(mark(X),c,f(true)) | (1) |
a__if(false,X,Y) | → | mark(Y) | (3) |
mark(if(X1,X2,X3)) | → | a__if(mark(X1),mark(X2),X3) | (5) |
a__if(X1,X2,X3) | → | if(X1,X2,X3) | (10) |
mark(true) | → | true | (7) |
a__f(X) | → | f(X) | (9) |
mark(c) | → | c | (6) |
a__if(true,X,Y) | → | mark(X) | (2) |
mark#(f(X)) | → | a__f#(mark(X)) | (18) |
a__f#(X) | → | a__if#(mark(X),c,f(true)) | (12) |
The dependency pairs are split into 1 component.
mark#(if(X1,X2,X3)) | → | mark#(X2) | (19) |
mark#(if(X1,X2,X3)) | → | mark#(X1) | (16) |
mark#(if(X1,X2,X3)) | → | a__if#(mark(X1),mark(X2),X3) | (11) |
a__if#(true,X,Y) | → | mark#(X) | (17) |
[a__f(x1)] | = | x1 + 5857 |
[false] | = | 1 |
[c] | = | 4681 |
[true] | = | 0 |
[f(x1)] | = | x1 + 5857 |
[mark#(x1)] | = | x1 + 30613 |
[if(x1, x2, x3)] | = | max(x1 + 4, x2 + 2, x3 + 0, 0) |
[mark(x1)] | = | x1 + 0 |
[a__if#(x1, x2, x3)] | = | max(x1 + 30616, x2 + 30614, 0) |
[a__f#(x1)] | = | 0 |
[a__if(x1, x2, x3)] | = | max(x1 + 4, x2 + 2, x3 + 0, 0) |
mark(f(X)) | → | a__f(mark(X)) | (4) |
mark(false) | → | false | (8) |
a__f(X) | → | a__if(mark(X),c,f(true)) | (1) |
a__if(false,X,Y) | → | mark(Y) | (3) |
mark(if(X1,X2,X3)) | → | a__if(mark(X1),mark(X2),X3) | (5) |
a__if(X1,X2,X3) | → | if(X1,X2,X3) | (10) |
mark(true) | → | true | (7) |
a__f(X) | → | f(X) | (9) |
mark(c) | → | c | (6) |
a__if(true,X,Y) | → | mark(X) | (2) |
mark#(if(X1,X2,X3)) | → | mark#(X2) | (19) |
mark#(if(X1,X2,X3)) | → | mark#(X1) | (16) |
mark#(if(X1,X2,X3)) | → | a__if#(mark(X1),mark(X2),X3) | (11) |
a__if#(true,X,Y) | → | mark#(X) | (17) |
The dependency pairs are split into 0 components.