The rewrite relation of the following TRS is considered.
app(f,app(app(cons,nil),y)) |
→ |
y |
(1) |
app(f,app(app(cons,app(f,app(app(cons,nil),y))),z)) |
→ |
app(app(app(copy,n),y),z) |
(2) |
app(app(app(copy,0),y),z) |
→ |
app(f,z) |
(3) |
app(app(app(copy,app(s,x)),y),z) |
→ |
app(app(app(copy,x),y),app(app(cons,app(f,y)),z)) |
(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#(f,app(app(cons,app(f,app(app(cons,nil),y))),z)) |
→ |
app#(copy,n) |
(11) |
app#(f,app(app(cons,app(f,app(app(cons,nil),y))),z)) |
→ |
app#(app(copy,n),y) |
(12) |
app#(f,app(app(cons,app(f,app(app(cons,nil),y))),z)) |
→ |
app#(app(app(copy,n),y),z) |
(13) |
app#(app(app(copy,0),y),z) |
→ |
app#(f,z) |
(14) |
app#(app(app(copy,app(s,x)),y),z) |
→ |
app#(f,y) |
(15) |
app#(app(app(copy,app(s,x)),y),z) |
→ |
app#(cons,app(f,y)) |
(16) |
app#(app(app(copy,app(s,x)),y),z) |
→ |
app#(app(cons,app(f,y)),z) |
(17) |
app#(app(app(copy,app(s,x)),y),z) |
→ |
app#(copy,x) |
(18) |
app#(app(app(copy,app(s,x)),y),z) |
→ |
app#(app(copy,x),y) |
(19) |
app#(app(app(copy,app(s,x)),y),z) |
→ |
app#(app(app(copy,x),y),app(app(cons,app(f,y)),z)) |
(20) |
app#(app(map,fun),app(app(cons,x),xs)) |
→ |
app#(app(map,fun),xs) |
(21) |
app#(app(map,fun),app(app(cons,x),xs)) |
→ |
app#(fun,x) |
(22) |
app#(app(map,fun),app(app(cons,x),xs)) |
→ |
app#(cons,app(fun,x)) |
(23) |
app#(app(map,fun),app(app(cons,x),xs)) |
→ |
app#(app(cons,app(fun,x)),app(app(map,fun),xs)) |
(24) |
app#(app(filter,fun),app(app(cons,x),xs)) |
→ |
app#(fun,x) |
(25) |
app#(app(filter,fun),app(app(cons,x),xs)) |
→ |
app#(filter2,app(fun,x)) |
(26) |
app#(app(filter,fun),app(app(cons,x),xs)) |
→ |
app#(app(filter2,app(fun,x)),fun) |
(27) |
app#(app(filter,fun),app(app(cons,x),xs)) |
→ |
app#(app(app(filter2,app(fun,x)),fun),x) |
(28) |
app#(app(filter,fun),app(app(cons,x),xs)) |
→ |
app#(app(app(app(filter2,app(fun,x)),fun),x),xs) |
(29) |
app#(app(app(app(filter2,true),fun),x),xs) |
→ |
app#(filter,fun) |
(30) |
app#(app(app(app(filter2,true),fun),x),xs) |
→ |
app#(app(filter,fun),xs) |
(31) |
app#(app(app(app(filter2,true),fun),x),xs) |
→ |
app#(cons,x) |
(32) |
app#(app(app(app(filter2,true),fun),x),xs) |
→ |
app#(app(cons,x),app(app(filter,fun),xs)) |
(33) |
app#(app(app(app(filter2,false),fun),x),xs) |
→ |
app#(filter,fun) |
(34) |
app#(app(app(app(filter2,false),fun),x),xs) |
→ |
app#(app(filter,fun),xs) |
(35) |
The dependency pairs are split into 2
components.