The rewrite relation of the following TRS is considered.
app(f,app(s,x)) | → | app(f,x) | (1) |
app(g,app(app(cons,0),y)) | → | app(g,y) | (2) |
app(g,app(app(cons,app(s,x)),y)) | → | app(s,x) | (3) |
app(h,app(app(cons,x),y)) | → | app(h,app(g,app(app(cons,x),y))) | (4) |
app(app(map,fun),nil) | → | nil | (5) |
app(app(map,fun),app(app(cons,x),xs)) | → | app(app(cons,app(fun,x)),app(app(map,fun),xs)) | (6) |
app(app(filter,fun),nil) | → | nil | (7) |
app(app(filter,fun),app(app(cons,x),xs)) | → | app(app(app(app(filter2,app(fun,x)),fun),x),xs) | (8) |
app(app(app(app(filter2,true),fun),x),xs) | → | app(app(cons,x),app(app(filter,fun),xs)) | (9) |
app(app(app(app(filter2,false),fun),x),xs) | → | app(app(filter,fun),xs) | (10) |
app#(app(map,fun),app(app(cons,x),xs)) | → | app#(app(cons,app(fun,x)),app(app(map,fun),xs)) | (11) |
app#(app(app(app(filter2,true),fun),x),xs) | → | app#(app(cons,x),app(app(filter,fun),xs)) | (12) |
app#(app(filter,fun),app(app(cons,x),xs)) | → | app#(app(app(app(filter2,app(fun,x)),fun),x),xs) | (13) |
app#(app(app(app(filter2,true),fun),x),xs) | → | app#(filter,fun) | (14) |
app#(app(app(app(filter2,false),fun),x),xs) | → | app#(filter,fun) | (15) |
app#(f,app(s,x)) | → | app#(f,x) | (16) |
app#(app(filter,fun),app(app(cons,x),xs)) | → | app#(app(app(filter2,app(fun,x)),fun),x) | (17) |
app#(app(app(app(filter2,true),fun),x),xs) | → | app#(cons,x) | (18) |
app#(app(app(app(filter2,false),fun),x),xs) | → | app#(app(filter,fun),xs) | (19) |
app#(app(map,fun),app(app(cons,x),xs)) | → | app#(app(map,fun),xs) | (20) |
app#(app(filter,fun),app(app(cons,x),xs)) | → | app#(fun,x) | (21) |
app#(h,app(app(cons,x),y)) | → | app#(g,app(app(cons,x),y)) | (22) |
app#(app(filter,fun),app(app(cons,x),xs)) | → | app#(filter2,app(fun,x)) | (23) |
app#(app(map,fun),app(app(cons,x),xs)) | → | app#(cons,app(fun,x)) | (24) |
app#(g,app(app(cons,0),y)) | → | app#(g,y) | (25) |
app#(app(app(app(filter2,true),fun),x),xs) | → | app#(app(filter,fun),xs) | (26) |
app#(app(filter,fun),app(app(cons,x),xs)) | → | app#(app(filter2,app(fun,x)),fun) | (27) |
app#(app(map,fun),app(app(cons,x),xs)) | → | app#(fun,x) | (28) |
app#(h,app(app(cons,x),y)) | → | app#(h,app(g,app(app(cons,x),y))) | (29) |
The dependency pairs are split into 4 components.
app#(app(map,fun),app(app(cons,x),xs)) | → | app#(fun,x) | (28) |
app#(app(app(app(filter2,true),fun),x),xs) | → | app#(app(filter,fun),xs) | (26) |
app#(app(filter,fun),app(app(cons,x),xs)) | → | app#(app(app(app(filter2,app(fun,x)),fun),x),xs) | (13) |
app#(app(filter,fun),app(app(cons,x),xs)) | → | app#(fun,x) | (21) |
app#(app(map,fun),app(app(cons,x),xs)) | → | app#(app(map,fun),xs) | (20) |
app#(app(app(app(filter2,false),fun),x),xs) | → | app#(app(filter,fun),xs) | (19) |
[h] | = | 0 |
[s] | = | 1 |
[false] | = | 32106 |
[true] | = | 25907 |
[f] | = | 0 |
[filter2] | = | 20534 |
[0] | = | 46558 |
[nil] | = | 22119 |
[app#(x1, x2)] | = | x2 + 0 |
[map] | = | 32173 |
[cons] | = | 23535 |
[filter] | = | 70533 |
[g] | = | 42207 |
[app(x1, x2)] | = | x1 + x2 + 8946 |
app#(app(map,fun),app(app(cons,x),xs)) | → | app#(fun,x) | (28) |
app#(app(filter,fun),app(app(cons,x),xs)) | → | app#(app(app(app(filter2,app(fun,x)),fun),x),xs) | (13) |
app#(app(filter,fun),app(app(cons,x),xs)) | → | app#(fun,x) | (21) |
app#(app(map,fun),app(app(cons,x),xs)) | → | app#(app(map,fun),xs) | (20) |
The dependency pairs are split into 0 components.
app#(f,app(s,x)) | → | app#(f,x) | (16) |
[h] | = | 0 |
[s] | = | 1 |
[false] | = | 9119 |
[true] | = | 28224 |
[f] | = | 0 |
[filter2] | = | 44735 |
[0] | = | 20334 |
[nil] | = | 1458 |
[app#(x1, x2)] | = | x2 + 0 |
[map] | = | 30374 |
[cons] | = | 31205 |
[filter] | = | 96331 |
[g] | = | 40519 |
[app(x1, x2)] | = | x1 + x2 + 21238 |
app#(f,app(s,x)) | → | app#(f,x) | (16) |
The dependency pairs are split into 0 components.
app#(h,app(app(cons,x),y)) | → | app#(h,app(g,app(app(cons,x),y))) | (29) |
[h] | = | 0 |
[s] | = | 0 |
[false] | = | 0 |
[true] | = | 0 |
[f] | = | 0 |
[filter2] | = | 37895 |
[0] | = | 0 |
[nil] | = | 0 |
[app#(x1, x2)] | = | x2 + 0 |
[map] | = | 50174 |
[cons] | = | 37895 |
[filter] | = | 37895 |
[g] | = | 37894 |
[app(x1, x2)] | = | x1 + 0 |
app(h,app(app(cons,x),y)) | → | app(h,app(g,app(app(cons,x),y))) | (4) |
app(app(filter,fun),app(app(cons,x),xs)) | → | app(app(app(app(filter2,app(fun,x)),fun),x),xs) | (8) |
app(f,app(s,x)) | → | app(f,x) | (1) |
app(g,app(app(cons,app(s,x)),y)) | → | app(s,x) | (3) |
app(app(map,fun),nil) | → | nil | (5) |
app(app(app(app(filter2,false),fun),x),xs) | → | app(app(filter,fun),xs) | (10) |
app(app(filter,fun),nil) | → | nil | (7) |
app(app(app(app(filter2,true),fun),x),xs) | → | app(app(cons,x),app(app(filter,fun),xs)) | (9) |
app(app(map,fun),app(app(cons,x),xs)) | → | app(app(cons,app(fun,x)),app(app(map,fun),xs)) | (6) |
app(g,app(app(cons,0),y)) | → | app(g,y) | (2) |
app#(h,app(app(cons,x),y)) | → | app#(h,app(g,app(app(cons,x),y))) | (29) |
The dependency pairs are split into 0 components.
app#(g,app(app(cons,0),y)) | → | app#(g,y) | (25) |
[h] | = | 0 |
[s] | = | 0 |
[false] | = | 0 |
[true] | = | 0 |
[f] | = | 0 |
[filter2] | = | 0 |
[0] | = | 2437 |
[nil] | = | 0 |
[app#(x1, x2)] | = | max(x1 + 1, x2 + 1, 0) |
[map] | = | 0 |
[cons] | = | 2 |
[filter] | = | 0 |
[g] | = | 1 |
[app(x1, x2)] | = | max(x1 + 11797, x2 + 2, 0) |
app#(g,app(app(cons,0),y)) | → | app#(g,y) | (25) |
The dependency pairs are split into 0 components.