The rewrite relation of the following TRS is considered.
app(nil,YS) | → | YS | (1) |
app(cons(X,XS),YS) | → | cons(X,n__app(activate(XS),YS)) | (2) |
from(X) | → | cons(X,n__from(s(X))) | (3) |
zWadr(nil,YS) | → | nil | (4) |
zWadr(XS,nil) | → | nil | (5) |
zWadr(cons(X,XS),cons(Y,YS)) | → | cons(app(Y,cons(X,n__nil)),n__zWadr(activate(XS),activate(YS))) | (6) |
prefix(L) | → | cons(nil,n__zWadr(L,prefix(L))) | (7) |
app(X1,X2) | → | n__app(X1,X2) | (8) |
from(X) | → | n__from(X) | (9) |
nil | → | n__nil | (10) |
zWadr(X1,X2) | → | n__zWadr(X1,X2) | (11) |
activate(n__app(X1,X2)) | → | app(X1,X2) | (12) |
activate(n__from(X)) | → | from(X) | (13) |
activate(n__nil) | → | nil | (14) |
activate(n__zWadr(X1,X2)) | → | zWadr(X1,X2) | (15) |
activate(X) | → | X | (16) |
app#(cons(X,XS),YS) | → | activate#(XS) | (17) |
zWadr#(cons(X,XS),cons(Y,YS)) | → | app#(Y,cons(X,n__nil)) | (18) |
zWadr#(cons(X,XS),cons(Y,YS)) | → | activate#(XS) | (19) |
zWadr#(cons(X,XS),cons(Y,YS)) | → | activate#(YS) | (20) |
prefix#(L) | → | nil# | (21) |
prefix#(L) | → | prefix#(L) | (22) |
activate#(n__app(X1,X2)) | → | app#(X1,X2) | (23) |
activate#(n__from(X)) | → | from#(X) | (24) |
activate#(n__nil) | → | nil# | (25) |
activate#(n__zWadr(X1,X2)) | → | zWadr#(X1,X2) | (26) |
app#(cons(X,XS),YS) | → | activate#(XS) | (17) |
zWadr#(cons(X,XS),cons(Y,YS)) | → | app#(Y,cons(X,n__nil)) | (18) |
zWadr#(cons(X,XS),cons(Y,YS)) | → | activate#(XS) | (19) |
zWadr#(cons(X,XS),cons(Y,YS)) | → | activate#(YS) | (20) |
prefix#(L) | → | nil# | (21) |
activate#(n__app(X1,X2)) | → | app#(X1,X2) | (23) |
activate#(n__from(X)) | → | from#(X) | (24) |
activate#(n__nil) | → | nil# | (25) |
activate#(n__zWadr(X1,X2)) | → | zWadr#(X1,X2) | (26) |
app(nil,YS) | → | YS | (1) |
app(cons(X,XS),YS) | → | cons(X,n__app(activate(XS),YS)) | (2) |
from(X) | → | cons(X,n__from(s(X))) | (3) |
zWadr(nil,YS) | → | nil | (4) |
zWadr(XS,nil) | → | nil | (5) |
zWadr(cons(X,XS),cons(Y,YS)) | → | cons(app(Y,cons(X,n__nil)),n__zWadr(activate(XS),activate(YS))) | (6) |
prefix(L) | → | cons(nil,n__zWadr(L,prefix(L))) | (7) |
app(X1,X2) | → | n__app(X1,X2) | (8) |
from(X) | → | n__from(X) | (9) |
nil | → | n__nil | (10) |
zWadr(X1,X2) | → | n__zWadr(X1,X2) | (11) |
activate(n__app(X1,X2)) | → | app(X1,X2) | (12) |
activate(n__from(X)) | → | from(X) | (13) |
activate(n__nil) | → | nil | (14) |
activate(n__zWadr(X1,X2)) | → | zWadr(X1,X2) | (15) |
activate(X) | → | X | (16) |
t0 | = | prefix#(L) |
→P | prefix#(L) | |
= | t1 |