R
↳Dependency Pair Analysis
APP(cons(X, XS), YS) -> APP(XS, YS)
FROM(X) -> FROM(s(X))
ZWADR(cons(X, XS), cons(Y, YS)) -> APP(Y, cons(X, nil))
ZWADR(cons(X, XS), cons(Y, YS)) -> ZWADR(XS, YS)
PREFIX(L) -> ZWADR(L, prefix(L))
PREFIX(L) -> PREFIX(L)
R
↳DPs
→DP Problem 1
↳Argument Filtering and Ordering
→DP Problem 2
↳Inst
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
APP(cons(X, XS), YS) -> APP(XS, YS)
app(nil, YS) -> YS
app(cons(X, XS), YS) -> cons(X, app(XS, YS))
from(X) -> cons(X, from(s(X)))
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil
zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS))
prefix(L) -> cons(nil, zWadr(L, prefix(L)))
innermost
APP(cons(X, XS), YS) -> APP(XS, YS)
POL(cons(x1, x2)) = 1 + x1 + x2 POL(APP(x1, x2)) = x1 + x2
APP(x1, x2) -> APP(x1, x2)
cons(x1, x2) -> cons(x1, x2)
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 5
↳Dependency Graph
→DP Problem 2
↳Inst
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
app(nil, YS) -> YS
app(cons(X, XS), YS) -> cons(X, app(XS, YS))
from(X) -> cons(X, from(s(X)))
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil
zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS))
prefix(L) -> cons(nil, zWadr(L, prefix(L)))
innermost
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Instantiation Transformation
→DP Problem 3
↳Remaining
→DP Problem 4
↳Remaining
FROM(X) -> FROM(s(X))
app(nil, YS) -> YS
app(cons(X, XS), YS) -> cons(X, app(XS, YS))
from(X) -> cons(X, from(s(X)))
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil
zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS))
prefix(L) -> cons(nil, zWadr(L, prefix(L)))
innermost
one new Dependency Pair is created:
FROM(X) -> FROM(s(X))
FROM(s(X'')) -> FROM(s(s(X'')))
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Inst
→DP Problem 3
↳Remaining Obligation(s)
→DP Problem 4
↳Remaining Obligation(s)
FROM(s(X'')) -> FROM(s(s(X'')))
app(nil, YS) -> YS
app(cons(X, XS), YS) -> cons(X, app(XS, YS))
from(X) -> cons(X, from(s(X)))
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil
zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS))
prefix(L) -> cons(nil, zWadr(L, prefix(L)))
innermost
ZWADR(cons(X, XS), cons(Y, YS)) -> ZWADR(XS, YS)
app(nil, YS) -> YS
app(cons(X, XS), YS) -> cons(X, app(XS, YS))
from(X) -> cons(X, from(s(X)))
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil
zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS))
prefix(L) -> cons(nil, zWadr(L, prefix(L)))
innermost
PREFIX(L) -> PREFIX(L)
app(nil, YS) -> YS
app(cons(X, XS), YS) -> cons(X, app(XS, YS))
from(X) -> cons(X, from(s(X)))
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil
zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS))
prefix(L) -> cons(nil, zWadr(L, prefix(L)))
innermost
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Inst
→DP Problem 3
↳Remaining Obligation(s)
→DP Problem 4
↳Remaining Obligation(s)
FROM(s(X'')) -> FROM(s(s(X'')))
app(nil, YS) -> YS
app(cons(X, XS), YS) -> cons(X, app(XS, YS))
from(X) -> cons(X, from(s(X)))
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil
zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS))
prefix(L) -> cons(nil, zWadr(L, prefix(L)))
innermost
ZWADR(cons(X, XS), cons(Y, YS)) -> ZWADR(XS, YS)
app(nil, YS) -> YS
app(cons(X, XS), YS) -> cons(X, app(XS, YS))
from(X) -> cons(X, from(s(X)))
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil
zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS))
prefix(L) -> cons(nil, zWadr(L, prefix(L)))
innermost
PREFIX(L) -> PREFIX(L)
app(nil, YS) -> YS
app(cons(X, XS), YS) -> cons(X, app(XS, YS))
from(X) -> cons(X, from(s(X)))
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil
zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS))
prefix(L) -> cons(nil, zWadr(L, prefix(L)))
innermost
R
↳DPs
→DP Problem 1
↳AFS
→DP Problem 2
↳Inst
→DP Problem 3
↳Remaining Obligation(s)
→DP Problem 4
↳Remaining Obligation(s)
FROM(s(X'')) -> FROM(s(s(X'')))
app(nil, YS) -> YS
app(cons(X, XS), YS) -> cons(X, app(XS, YS))
from(X) -> cons(X, from(s(X)))
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil
zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS))
prefix(L) -> cons(nil, zWadr(L, prefix(L)))
innermost
ZWADR(cons(X, XS), cons(Y, YS)) -> ZWADR(XS, YS)
app(nil, YS) -> YS
app(cons(X, XS), YS) -> cons(X, app(XS, YS))
from(X) -> cons(X, from(s(X)))
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil
zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS))
prefix(L) -> cons(nil, zWadr(L, prefix(L)))
innermost
PREFIX(L) -> PREFIX(L)
app(nil, YS) -> YS
app(cons(X, XS), YS) -> cons(X, app(XS, YS))
from(X) -> cons(X, from(s(X)))
zWadr(nil, YS) -> nil
zWadr(XS, nil) -> nil
zWadr(cons(X, XS), cons(Y, YS)) -> cons(app(Y, cons(X, nil)), zWadr(XS, YS))
prefix(L) -> cons(nil, zWadr(L, prefix(L)))
innermost