R
↳Dependency Pair Analysis
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
SEL(s(X), cons(Y, Z)) -> SEL(X, activate(Z))
SEL(s(X), cons(Y, Z)) -> ACTIVATE(Z)
ACTIVATE(nfrom(X)) -> FROM(X)
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
R
↳DPs
→DP Problem 1
↳Polynomial Ordering
→DP Problem 2
↳Nar
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
ACTIVATE(nfirst(X1, X2)) -> FIRST(X1, X2)
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
POL(from(x1)) = x1 POL(n__from(x1)) = x1 POL(activate(x1)) = x1 POL(first(x1, x2)) = 1 + x2 POL(0) = 0 POL(cons(x1, x2)) = x1 + x2 POL(FIRST(x1, x2)) = x2 POL(nil) = 0 POL(s(x1)) = 0 POL(sel(x1, x2)) = 1 + x2 POL(ACTIVATE(x1)) = x1 POL(n__first(x1, x2)) = 1 + x2
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 3
↳Dependency Graph
→DP Problem 2
↳Nar
FIRST(s(X), cons(Y, Z)) -> ACTIVATE(Z)
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Narrowing Transformation
SEL(s(X), cons(Y, Z)) -> SEL(X, activate(Z))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
three new Dependency Pairs are created:
SEL(s(X), cons(Y, Z)) -> SEL(X, activate(Z))
SEL(s(X), cons(Y, nfrom(X''))) -> SEL(X, from(X''))
SEL(s(X), cons(Y, nfirst(X1', X2'))) -> SEL(X, first(X1', X2'))
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Narrowing Transformation
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
SEL(s(X), cons(Y, nfirst(X1', X2'))) -> SEL(X, first(X1', X2'))
SEL(s(X), cons(Y, nfrom(X''))) -> SEL(X, from(X''))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
two new Dependency Pairs are created:
SEL(s(X), cons(Y, nfrom(X''))) -> SEL(X, from(X''))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, nfrom(X'''))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 5
↳Narrowing Transformation
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X), cons(Y, nfirst(X1', X2'))) -> SEL(X, first(X1', X2'))
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
three new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(X1', X2'))) -> SEL(X, first(X1', X2'))
SEL(s(X), cons(Y, nfirst(0, X2''))) -> SEL(X, nil)
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
SEL(s(X), cons(Y, nfirst(X1'', X2''))) -> SEL(X, nfirst(X1'', X2''))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 6
↳Polynomial Ordering
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
SEL(s(X), cons(Y, Z')) -> SEL(X, Z')
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
POL(from(x1)) = 1 + x1 POL(n__from(x1)) = x1 POL(activate(x1)) = 1 + x1 POL(first(x1, x2)) = 1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 1 + x1 + x2 POL(SEL(x1, x2)) = 1 + x2 POL(nil) = 0 POL(s(x1)) = 0 POL(sel(x1, x2)) = 1 + x2 POL(n__first(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 7
↳Dependency Graph
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 8
↳Narrowing Transformation
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
three new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z')))) -> SEL(X, cons(Y'', nfirst(X'', activate(Z'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X'''))))) -> SEL(X, cons(Y'', nfirst(X'', from(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', first(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 10
↳Narrowing Transformation
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', first(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X'''))))) -> SEL(X, cons(Y'', nfirst(X'', from(X'''))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
two new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X'''))))) -> SEL(X, cons(Y'', nfirst(X'', from(X'''))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', nfrom(X''''))))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 12
↳Narrowing Transformation
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', first(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
three new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1', X2'))))) -> SEL(X, cons(Y'', nfirst(X'', first(X1', X2'))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(0, X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nil)))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(X1'', X2''))))) -> SEL(X, cons(Y'', nfirst(X'', nfirst(X1'', X2''))))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 14
↳Polynomial Ordering
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', Z'')))) -> SEL(X, cons(Y'', nfirst(X'', Z'')))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
POL(from(x1)) = 1 + x1 POL(n__from(x1)) = x1 POL(activate(x1)) = 1 + x1 POL(first(x1, x2)) = 1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 1 + x1 + x2 POL(SEL(x1, x2)) = 1 + x2 POL(nil) = 0 POL(s(x1)) = 0 POL(sel(x1, x2)) = 1 + x2 POL(n__first(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 16
↳Dependency Graph
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 17
↳Narrowing Transformation
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
three new Dependency Pairs are created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', activate(Z'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', from(X'0))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', first(X1', X2'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', Z'')))))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 19
↳Polynomial Ordering
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', Z'')))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', first(X1', X2'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', from(X'0))))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', Z'')))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', Z'')))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
POL(from(x1)) = 1 + x1 POL(n__from(x1)) = x1 POL(activate(x1)) = 1 + x1 POL(first(x1, x2)) = 1 + x2 POL(0) = 0 POL(cons(x1, x2)) = 1 + x1 + x2 POL(SEL(x1, x2)) = 1 + x2 POL(nil) = 0 POL(s(x1)) = 0 POL(sel(x1, x2)) = 1 + x2 POL(n__first(x1, x2)) = x2
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 20
↳Remaining Obligation(s)
SEL(s(X''''''), cons(s(s(X'''''''''''')), nfrom(s(s(s(X''''''''''''')))))) -> SEL(X'''''', cons(s(s(s(X'''''''''''''))), nfrom(s(s(s(s(X''''''''''''')))))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', first(X1', X2'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', from(X'0))))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
SEL(s(X0), cons(Y', nfirst(s(X''0), cons(Y'''', nfrom(s(X''''''')))))) -> SEL(X0, cons(Y'''', nfirst(X''0, cons(s(X'''''''), nfrom(s(s(X''''''')))))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 18
↳Instantiation Transformation
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
one new Dependency Pair is created:
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfrom(X''''))))) -> SEL(X, cons(Y'', nfirst(X'', cons(X'''', nfrom(s(X''''))))))
SEL(s(X0), cons(Y', nfirst(s(X''0), cons(Y'''', nfrom(s(X''''''')))))) -> SEL(X0, cons(Y'''', nfirst(X''0, cons(s(X'''''''), nfrom(s(s(X''''''')))))))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 20
↳Remaining Obligation(s)
SEL(s(X''''''), cons(s(s(X'''''''''''')), nfrom(s(s(s(X''''''''''''')))))) -> SEL(X'''''', cons(s(s(s(X'''''''''''''))), nfrom(s(s(s(s(X''''''''''''')))))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', first(X1', X2'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', from(X'0))))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
SEL(s(X0), cons(Y', nfirst(s(X''0), cons(Y'''', nfrom(s(X''''''')))))) -> SEL(X0, cons(Y'''', nfirst(X''0, cons(s(X'''''''), nfrom(s(s(X''''''')))))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 9
↳Instantiation Transformation
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
one new Dependency Pair is created:
SEL(s(X), cons(Y, nfrom(X'''))) -> SEL(X, cons(X''', nfrom(s(X'''))))
SEL(s(X''), cons(Y', nfrom(s(X'''''')))) -> SEL(X'', cons(s(X''''''), nfrom(s(s(X'''''')))))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 11
↳Instantiation Transformation
SEL(s(X''), cons(Y', nfrom(s(X'''''')))) -> SEL(X'', cons(s(X''''''), nfrom(s(s(X'''''')))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
one new Dependency Pair is created:
SEL(s(X''), cons(Y', nfrom(s(X'''''')))) -> SEL(X'', cons(s(X''''''), nfrom(s(s(X'''''')))))
SEL(s(X''''), cons(s(X'''''''0), nfrom(s(s(X'''''''''))))) -> SEL(X'''', cons(s(s(X''''''''')), nfrom(s(s(s(X'''''''''))))))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 13
↳Instantiation Transformation
SEL(s(X''''), cons(s(X'''''''0), nfrom(s(s(X'''''''''))))) -> SEL(X'''', cons(s(s(X''''''''')), nfrom(s(s(s(X'''''''''))))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
one new Dependency Pair is created:
SEL(s(X''''), cons(s(X'''''''0), nfrom(s(s(X'''''''''))))) -> SEL(X'''', cons(s(s(X''''''''')), nfrom(s(s(s(X'''''''''))))))
SEL(s(X''''''), cons(s(s(X'''''''''''')), nfrom(s(s(s(X''''''''''''')))))) -> SEL(X'''''', cons(s(s(s(X'''''''''''''))), nfrom(s(s(s(s(X''''''''''''')))))))
R
↳DPs
→DP Problem 1
↳Polo
→DP Problem 2
↳Nar
→DP Problem 4
↳Nar
...
→DP Problem 20
↳Remaining Obligation(s)
SEL(s(X''''''), cons(s(s(X'''''''''''')), nfrom(s(s(s(X''''''''''''')))))) -> SEL(X'''''', cons(s(s(s(X'''''''''''''))), nfrom(s(s(s(s(X''''''''''''')))))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfirst(X1', X2'))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', first(X1', X2'))))))
SEL(s(X), cons(Y, nfirst(s(X''), cons(Y'', nfirst(s(X'''), cons(Y''', nfrom(X'0))))))) -> SEL(X, cons(Y'', nfirst(X'', cons(Y''', nfirst(X''', from(X'0))))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X
SEL(s(X0), cons(Y', nfirst(s(X''0), cons(Y'''', nfrom(s(X''''''')))))) -> SEL(X0, cons(Y'''', nfirst(X''0, cons(s(X'''''''), nfrom(s(s(X''''''')))))))
from(X) -> cons(X, nfrom(s(X)))
from(X) -> nfrom(X)
first(0, Z) -> nil
first(s(X), cons(Y, Z)) -> cons(Y, nfirst(X, activate(Z)))
first(X1, X2) -> nfirst(X1, X2)
sel(0, cons(X, Z)) -> X
sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
activate(nfrom(X)) -> from(X)
activate(nfirst(X1, X2)) -> first(X1, X2)
activate(X) -> X