YES
Problem:
a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
a____(X,nil()) -> mark(X)
a____(nil(),X) -> mark(X)
a__U11(tt()) -> a__U12(tt())
a__U12(tt()) -> tt()
a__isNePal(__(I,__(P,I))) -> a__U11(tt())
mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
mark(U11(X)) -> a__U11(mark(X))
mark(U12(X)) -> a__U12(mark(X))
mark(isNePal(X)) -> a__isNePal(mark(X))
mark(nil()) -> nil()
mark(tt()) -> tt()
a____(X1,X2) -> __(X1,X2)
a__U11(X) -> U11(X)
a__U12(X) -> U12(X)
a__isNePal(X) -> isNePal(X)
Proof:
DP Processor:
DPs:
a____#(__(X,Y),Z) -> mark#(Z)
a____#(__(X,Y),Z) -> mark#(Y)
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z))
a____#(__(X,Y),Z) -> mark#(X)
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z)))
a____#(X,nil()) -> mark#(X)
a____#(nil(),X) -> mark#(X)
a__U11#(tt()) -> a__U12#(tt())
a__isNePal#(__(I,__(P,I))) -> a__U11#(tt())
mark#(__(X1,X2)) -> mark#(X2)
mark#(__(X1,X2)) -> mark#(X1)
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
mark#(U11(X)) -> mark#(X)
mark#(U11(X)) -> a__U11#(mark(X))
mark#(U12(X)) -> mark#(X)
mark#(U12(X)) -> a__U12#(mark(X))
mark#(isNePal(X)) -> mark#(X)
mark#(isNePal(X)) -> a__isNePal#(mark(X))
TRS:
a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
a____(X,nil()) -> mark(X)
a____(nil(),X) -> mark(X)
a__U11(tt()) -> a__U12(tt())
a__U12(tt()) -> tt()
a__isNePal(__(I,__(P,I))) -> a__U11(tt())
mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
mark(U11(X)) -> a__U11(mark(X))
mark(U12(X)) -> a__U12(mark(X))
mark(isNePal(X)) -> a__isNePal(mark(X))
mark(nil()) -> nil()
mark(tt()) -> tt()
a____(X1,X2) -> __(X1,X2)
a__U11(X) -> U11(X)
a__U12(X) -> U12(X)
a__isNePal(X) -> isNePal(X)
TDG Processor:
DPs:
a____#(__(X,Y),Z) -> mark#(Z)
a____#(__(X,Y),Z) -> mark#(Y)
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z))
a____#(__(X,Y),Z) -> mark#(X)
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z)))
a____#(X,nil()) -> mark#(X)
a____#(nil(),X) -> mark#(X)
a__U11#(tt()) -> a__U12#(tt())
a__isNePal#(__(I,__(P,I))) -> a__U11#(tt())
mark#(__(X1,X2)) -> mark#(X2)
mark#(__(X1,X2)) -> mark#(X1)
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
mark#(U11(X)) -> mark#(X)
mark#(U11(X)) -> a__U11#(mark(X))
mark#(U12(X)) -> mark#(X)
mark#(U12(X)) -> a__U12#(mark(X))
mark#(isNePal(X)) -> mark#(X)
mark#(isNePal(X)) -> a__isNePal#(mark(X))
TRS:
a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
a____(X,nil()) -> mark(X)
a____(nil(),X) -> mark(X)
a__U11(tt()) -> a__U12(tt())
a__U12(tt()) -> tt()
a__isNePal(__(I,__(P,I))) -> a__U11(tt())
mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
mark(U11(X)) -> a__U11(mark(X))
mark(U12(X)) -> a__U12(mark(X))
mark(isNePal(X)) -> a__isNePal(mark(X))
mark(nil()) -> nil()
mark(tt()) -> tt()
a____(X1,X2) -> __(X1,X2)
a__U11(X) -> U11(X)
a__U12(X) -> U12(X)
a__isNePal(X) -> isNePal(X)
graph:
a__isNePal#(__(I,__(P,I))) -> a__U11#(tt()) ->
a__U11#(tt()) -> a__U12#(tt())
mark#(isNePal(X)) -> a__isNePal#(mark(X)) ->
a__isNePal#(__(I,__(P,I))) -> a__U11#(tt())
mark#(isNePal(X)) -> mark#(X) ->
mark#(isNePal(X)) -> a__isNePal#(mark(X))
mark#(isNePal(X)) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X)
mark#(isNePal(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X))
mark#(isNePal(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X)
mark#(isNePal(X)) -> mark#(X) -> mark#(U11(X)) -> a__U11#(mark(X))
mark#(isNePal(X)) -> mark#(X) -> mark#(U11(X)) -> mark#(X)
mark#(isNePal(X)) -> mark#(X) ->
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1)
mark#(isNePal(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2)
mark#(U12(X)) -> mark#(X) -> mark#(isNePal(X)) -> a__isNePal#(mark(X))
mark#(U12(X)) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X)
mark#(U12(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X))
mark#(U12(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X)
mark#(U12(X)) -> mark#(X) -> mark#(U11(X)) -> a__U11#(mark(X))
mark#(U12(X)) -> mark#(X) -> mark#(U11(X)) -> mark#(X)
mark#(U12(X)) -> mark#(X) ->
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
mark#(U12(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1)
mark#(U12(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2)
mark#(U11(X)) -> a__U11#(mark(X)) -> a__U11#(tt()) -> a__U12#(tt())
mark#(U11(X)) -> mark#(X) -> mark#(isNePal(X)) -> a__isNePal#(mark(X))
mark#(U11(X)) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X)
mark#(U11(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X))
mark#(U11(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X)
mark#(U11(X)) -> mark#(X) -> mark#(U11(X)) -> a__U11#(mark(X))
mark#(U11(X)) -> mark#(X) -> mark#(U11(X)) -> mark#(X)
mark#(U11(X)) -> mark#(X) ->
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
mark#(U11(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1)
mark#(U11(X)) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2)
mark#(__(X1,X2)) -> mark#(X2) ->
mark#(isNePal(X)) -> a__isNePal#(mark(X))
mark#(__(X1,X2)) -> mark#(X2) -> mark#(isNePal(X)) -> mark#(X)
mark#(__(X1,X2)) -> mark#(X2) -> mark#(U12(X)) -> a__U12#(mark(X))
mark#(__(X1,X2)) -> mark#(X2) -> mark#(U12(X)) -> mark#(X)
mark#(__(X1,X2)) -> mark#(X2) -> mark#(U11(X)) -> a__U11#(mark(X))
mark#(__(X1,X2)) -> mark#(X2) -> mark#(U11(X)) -> mark#(X)
mark#(__(X1,X2)) -> mark#(X2) ->
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> mark#(X1)
mark#(__(X1,X2)) -> mark#(X2) -> mark#(__(X1,X2)) -> mark#(X2)
mark#(__(X1,X2)) -> mark#(X1) ->
mark#(isNePal(X)) -> a__isNePal#(mark(X))
mark#(__(X1,X2)) -> mark#(X1) -> mark#(isNePal(X)) -> mark#(X)
mark#(__(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X))
mark#(__(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X)
mark#(__(X1,X2)) -> mark#(X1) -> mark#(U11(X)) -> a__U11#(mark(X))
mark#(__(X1,X2)) -> mark#(X1) -> mark#(U11(X)) -> mark#(X)
mark#(__(X1,X2)) -> mark#(X1) ->
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
mark#(__(X1,X2)) -> mark#(X1) -> mark#(__(X1,X2)) -> mark#(X1)
mark#(__(X1,X2)) -> mark#(X1) ->
mark#(__(X1,X2)) -> mark#(X2)
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) ->
a____#(nil(),X) -> mark#(X)
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) ->
a____#(X,nil()) -> mark#(X)
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) ->
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z)))
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) ->
a____#(__(X,Y),Z) -> mark#(X)
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) ->
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z))
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) ->
a____#(__(X,Y),Z) -> mark#(Y)
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2)) ->
a____#(__(X,Y),Z) -> mark#(Z)
a____#(nil(),X) -> mark#(X) ->
mark#(isNePal(X)) -> a__isNePal#(mark(X))
a____#(nil(),X) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X)
a____#(nil(),X) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X))
a____#(nil(),X) -> mark#(X) -> mark#(U12(X)) -> mark#(X)
a____#(nil(),X) -> mark#(X) -> mark#(U11(X)) -> a__U11#(mark(X))
a____#(nil(),X) -> mark#(X) -> mark#(U11(X)) -> mark#(X)
a____#(nil(),X) -> mark#(X) ->
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
a____#(nil(),X) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1)
a____#(nil(),X) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2)
a____#(__(X,Y),Z) -> mark#(Z) ->
mark#(isNePal(X)) -> a__isNePal#(mark(X))
a____#(__(X,Y),Z) -> mark#(Z) -> mark#(isNePal(X)) -> mark#(X)
a____#(__(X,Y),Z) -> mark#(Z) -> mark#(U12(X)) -> a__U12#(mark(X))
a____#(__(X,Y),Z) -> mark#(Z) -> mark#(U12(X)) -> mark#(X)
a____#(__(X,Y),Z) -> mark#(Z) -> mark#(U11(X)) -> a__U11#(mark(X))
a____#(__(X,Y),Z) -> mark#(Z) -> mark#(U11(X)) -> mark#(X)
a____#(__(X,Y),Z) -> mark#(Z) ->
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
a____#(__(X,Y),Z) -> mark#(Z) -> mark#(__(X1,X2)) -> mark#(X1)
a____#(__(X,Y),Z) -> mark#(Z) -> mark#(__(X1,X2)) -> mark#(X2)
a____#(__(X,Y),Z) -> mark#(Y) ->
mark#(isNePal(X)) -> a__isNePal#(mark(X))
a____#(__(X,Y),Z) -> mark#(Y) -> mark#(isNePal(X)) -> mark#(X)
a____#(__(X,Y),Z) -> mark#(Y) -> mark#(U12(X)) -> a__U12#(mark(X))
a____#(__(X,Y),Z) -> mark#(Y) -> mark#(U12(X)) -> mark#(X)
a____#(__(X,Y),Z) -> mark#(Y) -> mark#(U11(X)) -> a__U11#(mark(X))
a____#(__(X,Y),Z) -> mark#(Y) -> mark#(U11(X)) -> mark#(X)
a____#(__(X,Y),Z) -> mark#(Y) ->
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
a____#(__(X,Y),Z) -> mark#(Y) -> mark#(__(X1,X2)) -> mark#(X1)
a____#(__(X,Y),Z) -> mark#(Y) -> mark#(__(X1,X2)) -> mark#(X2)
a____#(__(X,Y),Z) -> mark#(X) ->
mark#(isNePal(X)) -> a__isNePal#(mark(X))
a____#(__(X,Y),Z) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X)
a____#(__(X,Y),Z) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X))
a____#(__(X,Y),Z) -> mark#(X) -> mark#(U12(X)) -> mark#(X)
a____#(__(X,Y),Z) -> mark#(X) -> mark#(U11(X)) -> a__U11#(mark(X))
a____#(__(X,Y),Z) -> mark#(X) -> mark#(U11(X)) -> mark#(X)
a____#(__(X,Y),Z) -> mark#(X) ->
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
a____#(__(X,Y),Z) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1)
a____#(__(X,Y),Z) -> mark#(X) ->
mark#(__(X1,X2)) -> mark#(X2)
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) ->
a____#(nil(),X) -> mark#(X)
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) ->
a____#(X,nil()) -> mark#(X)
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) ->
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z)))
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) ->
a____#(__(X,Y),Z) -> mark#(X)
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) ->
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z))
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) ->
a____#(__(X,Y),Z) -> mark#(Y)
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z)) ->
a____#(__(X,Y),Z) -> mark#(Z)
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) ->
a____#(nil(),X) -> mark#(X)
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) ->
a____#(X,nil()) -> mark#(X)
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) ->
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z)))
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) ->
a____#(__(X,Y),Z) -> mark#(X)
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) ->
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z))
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) ->
a____#(__(X,Y),Z) -> mark#(Y)
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z))) ->
a____#(__(X,Y),Z) -> mark#(Z)
a____#(X,nil()) -> mark#(X) ->
mark#(isNePal(X)) -> a__isNePal#(mark(X))
a____#(X,nil()) -> mark#(X) -> mark#(isNePal(X)) -> mark#(X)
a____#(X,nil()) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X))
a____#(X,nil()) -> mark#(X) -> mark#(U12(X)) -> mark#(X)
a____#(X,nil()) -> mark#(X) -> mark#(U11(X)) -> a__U11#(mark(X))
a____#(X,nil()) -> mark#(X) -> mark#(U11(X)) -> mark#(X)
a____#(X,nil()) -> mark#(X) ->
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
a____#(X,nil()) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X1)
a____#(X,nil()) -> mark#(X) -> mark#(__(X1,X2)) -> mark#(X2)
SCC Processor:
#sccs: 1
#rules: 13
#arcs: 114/324
DPs:
mark#(isNePal(X)) -> mark#(X)
mark#(__(X1,X2)) -> mark#(X2)
mark#(__(X1,X2)) -> mark#(X1)
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
a____#(__(X,Y),Z) -> mark#(Z)
mark#(U11(X)) -> mark#(X)
mark#(U12(X)) -> mark#(X)
a____#(__(X,Y),Z) -> mark#(Y)
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z))
a____#(__(X,Y),Z) -> mark#(X)
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z)))
a____#(X,nil()) -> mark#(X)
a____#(nil(),X) -> mark#(X)
TRS:
a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
a____(X,nil()) -> mark(X)
a____(nil(),X) -> mark(X)
a__U11(tt()) -> a__U12(tt())
a__U12(tt()) -> tt()
a__isNePal(__(I,__(P,I))) -> a__U11(tt())
mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
mark(U11(X)) -> a__U11(mark(X))
mark(U12(X)) -> a__U12(mark(X))
mark(isNePal(X)) -> a__isNePal(mark(X))
mark(nil()) -> nil()
mark(tt()) -> tt()
a____(X1,X2) -> __(X1,X2)
a__U11(X) -> U11(X)
a__U12(X) -> U12(X)
a__isNePal(X) -> isNePal(X)
Arctic Interpretation Processor:
dimension: 1
interpretation:
[mark#](x0) = x0 + 0,
[a____#](x0, x1) = x0 + x1 + 0,
[isNePal](x0) = 2x0 + 1,
[U12](x0) = x0 + 0,
[U11](x0) = x0,
[a__isNePal](x0) = 2x0 + 1,
[a__U12](x0) = x0 + 0,
[a__U11](x0) = x0,
[tt] = 0,
[nil] = 0,
[mark](x0) = x0,
[a____](x0, x1) = x0 + x1 + 0,
[__](x0, x1) = x0 + x1 + 0
orientation:
mark#(isNePal(X)) = 2X + 1 >= X + 0 = mark#(X)
mark#(__(X1,X2)) = X1 + X2 + 0 >= X2 + 0 = mark#(X2)
mark#(__(X1,X2)) = X1 + X2 + 0 >= X1 + 0 = mark#(X1)
mark#(__(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = a____#(mark(X1),mark(X2))
a____#(__(X,Y),Z) = X + Y + Z + 0 >= Z + 0 = mark#(Z)
mark#(U11(X)) = X + 0 >= X + 0 = mark#(X)
mark#(U12(X)) = X + 0 >= X + 0 = mark#(X)
a____#(__(X,Y),Z) = X + Y + Z + 0 >= Y + 0 = mark#(Y)
a____#(__(X,Y),Z) = X + Y + Z + 0 >= Y + Z + 0 = a____#(mark(Y),mark(Z))
a____#(__(X,Y),Z) = X + Y + Z + 0 >= X + 0 = mark#(X)
a____#(__(X,Y),Z) = X + Y + Z + 0 >= X + Y + Z + 0 = a____#(mark(X),a____(mark(Y),mark(Z)))
a____#(X,nil()) = X + 0 >= X + 0 = mark#(X)
a____#(nil(),X) = X + 0 >= X + 0 = mark#(X)
a____(__(X,Y),Z) = X + Y + Z + 0 >= X + Y + Z + 0 = a____(mark(X),a____(mark(Y),mark(Z)))
a____(X,nil()) = X + 0 >= X = mark(X)
a____(nil(),X) = X + 0 >= X = mark(X)
a__U11(tt()) = 0 >= 0 = a__U12(tt())
a__U12(tt()) = 0 >= 0 = tt()
a__isNePal(__(I,__(P,I))) = 2I + 2P + 2 >= 0 = a__U11(tt())
mark(__(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = a____(mark(X1),mark(X2))
mark(U11(X)) = X >= X = a__U11(mark(X))
mark(U12(X)) = X + 0 >= X + 0 = a__U12(mark(X))
mark(isNePal(X)) = 2X + 1 >= 2X + 1 = a__isNePal(mark(X))
mark(nil()) = 0 >= 0 = nil()
mark(tt()) = 0 >= 0 = tt()
a____(X1,X2) = X1 + X2 + 0 >= X1 + X2 + 0 = __(X1,X2)
a__U11(X) = X >= X = U11(X)
a__U12(X) = X + 0 >= X + 0 = U12(X)
a__isNePal(X) = 2X + 1 >= 2X + 1 = isNePal(X)
problem:
DPs:
mark#(__(X1,X2)) -> mark#(X2)
mark#(__(X1,X2)) -> mark#(X1)
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
a____#(__(X,Y),Z) -> mark#(Z)
mark#(U11(X)) -> mark#(X)
mark#(U12(X)) -> mark#(X)
a____#(__(X,Y),Z) -> mark#(Y)
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z))
a____#(__(X,Y),Z) -> mark#(X)
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z)))
a____#(X,nil()) -> mark#(X)
a____#(nil(),X) -> mark#(X)
TRS:
a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
a____(X,nil()) -> mark(X)
a____(nil(),X) -> mark(X)
a__U11(tt()) -> a__U12(tt())
a__U12(tt()) -> tt()
a__isNePal(__(I,__(P,I))) -> a__U11(tt())
mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
mark(U11(X)) -> a__U11(mark(X))
mark(U12(X)) -> a__U12(mark(X))
mark(isNePal(X)) -> a__isNePal(mark(X))
mark(nil()) -> nil()
mark(tt()) -> tt()
a____(X1,X2) -> __(X1,X2)
a__U11(X) -> U11(X)
a__U12(X) -> U12(X)
a__isNePal(X) -> isNePal(X)
Arctic Interpretation Processor:
dimension: 1
interpretation:
[mark#](x0) = x0,
[a____#](x0, x1) = x0 + x1,
[isNePal](x0) = 5,
[U12](x0) = x0 + 0,
[U11](x0) = 4x0 + 2,
[a__isNePal](x0) = 5,
[a__U12](x0) = x0 + 0,
[a__U11](x0) = 4x0 + 2,
[tt] = 1,
[nil] = 2,
[mark](x0) = x0,
[a____](x0, x1) = x0 + x1 + 0,
[__](x0, x1) = x0 + x1 + 0
orientation:
mark#(__(X1,X2)) = X1 + X2 + 0 >= X2 = mark#(X2)
mark#(__(X1,X2)) = X1 + X2 + 0 >= X1 = mark#(X1)
mark#(__(X1,X2)) = X1 + X2 + 0 >= X1 + X2 = a____#(mark(X1),mark(X2))
a____#(__(X,Y),Z) = X + Y + Z + 0 >= Z = mark#(Z)
mark#(U11(X)) = 4X + 2 >= X = mark#(X)
mark#(U12(X)) = X + 0 >= X = mark#(X)
a____#(__(X,Y),Z) = X + Y + Z + 0 >= Y = mark#(Y)
a____#(__(X,Y),Z) = X + Y + Z + 0 >= Y + Z = a____#(mark(Y),mark(Z))
a____#(__(X,Y),Z) = X + Y + Z + 0 >= X = mark#(X)
a____#(__(X,Y),Z) = X + Y + Z + 0 >= X + Y + Z + 0 = a____#(mark(X),a____(mark(Y),mark(Z)))
a____#(X,nil()) = X + 2 >= X = mark#(X)
a____#(nil(),X) = X + 2 >= X = mark#(X)
a____(__(X,Y),Z) = X + Y + Z + 0 >= X + Y + Z + 0 = a____(mark(X),a____(mark(Y),mark(Z)))
a____(X,nil()) = X + 2 >= X = mark(X)
a____(nil(),X) = X + 2 >= X = mark(X)
a__U11(tt()) = 5 >= 1 = a__U12(tt())
a__U12(tt()) = 1 >= 1 = tt()
a__isNePal(__(I,__(P,I))) = 5 >= 5 = a__U11(tt())
mark(__(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = a____(mark(X1),mark(X2))
mark(U11(X)) = 4X + 2 >= 4X + 2 = a__U11(mark(X))
mark(U12(X)) = X + 0 >= X + 0 = a__U12(mark(X))
mark(isNePal(X)) = 5 >= 5 = a__isNePal(mark(X))
mark(nil()) = 2 >= 2 = nil()
mark(tt()) = 1 >= 1 = tt()
a____(X1,X2) = X1 + X2 + 0 >= X1 + X2 + 0 = __(X1,X2)
a__U11(X) = 4X + 2 >= 4X + 2 = U11(X)
a__U12(X) = X + 0 >= X + 0 = U12(X)
a__isNePal(X) = 5 >= 5 = isNePal(X)
problem:
DPs:
mark#(__(X1,X2)) -> mark#(X2)
mark#(__(X1,X2)) -> mark#(X1)
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
a____#(__(X,Y),Z) -> mark#(Z)
mark#(U12(X)) -> mark#(X)
a____#(__(X,Y),Z) -> mark#(Y)
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z))
a____#(__(X,Y),Z) -> mark#(X)
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z)))
a____#(X,nil()) -> mark#(X)
a____#(nil(),X) -> mark#(X)
TRS:
a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
a____(X,nil()) -> mark(X)
a____(nil(),X) -> mark(X)
a__U11(tt()) -> a__U12(tt())
a__U12(tt()) -> tt()
a__isNePal(__(I,__(P,I))) -> a__U11(tt())
mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
mark(U11(X)) -> a__U11(mark(X))
mark(U12(X)) -> a__U12(mark(X))
mark(isNePal(X)) -> a__isNePal(mark(X))
mark(nil()) -> nil()
mark(tt()) -> tt()
a____(X1,X2) -> __(X1,X2)
a__U11(X) -> U11(X)
a__U12(X) -> U12(X)
a__isNePal(X) -> isNePal(X)
Arctic Interpretation Processor:
dimension: 1
interpretation:
[mark#](x0) = x0 + 1,
[a____#](x0, x1) = 1x0 + x1 + 1,
[isNePal](x0) = x0,
[U12](x0) = x0,
[U11](x0) = 0,
[a__isNePal](x0) = x0 + 0,
[a__U12](x0) = x0 + 0,
[a__U11](x0) = 0,
[tt] = 0,
[nil] = 0,
[mark](x0) = x0 + 0,
[a____](x0, x1) = 1x0 + x1 + 1,
[__](x0, x1) = 1x0 + x1 + 1
orientation:
mark#(__(X1,X2)) = 1X1 + X2 + 1 >= X2 + 1 = mark#(X2)
mark#(__(X1,X2)) = 1X1 + X2 + 1 >= X1 + 1 = mark#(X1)
mark#(__(X1,X2)) = 1X1 + X2 + 1 >= 1X1 + X2 + 1 = a____#(mark(X1),mark(X2))
a____#(__(X,Y),Z) = 2X + 1Y + Z + 2 >= Z + 1 = mark#(Z)
mark#(U12(X)) = X + 1 >= X + 1 = mark#(X)
a____#(__(X,Y),Z) = 2X + 1Y + Z + 2 >= Y + 1 = mark#(Y)
a____#(__(X,Y),Z) = 2X + 1Y + Z + 2 >= 1Y + Z + 1 = a____#(mark(Y),mark(Z))
a____#(__(X,Y),Z) = 2X + 1Y + Z + 2 >= X + 1 = mark#(X)
a____#(__(X,Y),Z) = 2X + 1Y + Z + 2 >= 1X + 1Y + Z + 1 = a____#(mark(X),a____(mark(Y),mark(Z)))
a____#(X,nil()) = 1X + 1 >= X + 1 = mark#(X)
a____#(nil(),X) = X + 1 >= X + 1 = mark#(X)
a____(__(X,Y),Z) = 2X + 1Y + Z + 2 >= 1X + 1Y + Z + 1 = a____(mark(X),a____(mark(Y),mark(Z)))
a____(X,nil()) = 1X + 1 >= X + 0 = mark(X)
a____(nil(),X) = X + 1 >= X + 0 = mark(X)
a__U11(tt()) = 0 >= 0 = a__U12(tt())
a__U12(tt()) = 0 >= 0 = tt()
a__isNePal(__(I,__(P,I))) = 1I + 1P + 1 >= 0 = a__U11(tt())
mark(__(X1,X2)) = 1X1 + X2 + 1 >= 1X1 + X2 + 1 = a____(mark(X1),mark(X2))
mark(U11(X)) = 0 >= 0 = a__U11(mark(X))
mark(U12(X)) = X + 0 >= X + 0 = a__U12(mark(X))
mark(isNePal(X)) = X + 0 >= X + 0 = a__isNePal(mark(X))
mark(nil()) = 0 >= 0 = nil()
mark(tt()) = 0 >= 0 = tt()
a____(X1,X2) = 1X1 + X2 + 1 >= 1X1 + X2 + 1 = __(X1,X2)
a__U11(X) = 0 >= 0 = U11(X)
a__U12(X) = X + 0 >= X = U12(X)
a__isNePal(X) = X + 0 >= X = isNePal(X)
problem:
DPs:
mark#(__(X1,X2)) -> mark#(X2)
mark#(__(X1,X2)) -> mark#(X1)
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
a____#(__(X,Y),Z) -> mark#(Z)
mark#(U12(X)) -> mark#(X)
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z))
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z)))
a____#(X,nil()) -> mark#(X)
a____#(nil(),X) -> mark#(X)
TRS:
a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
a____(X,nil()) -> mark(X)
a____(nil(),X) -> mark(X)
a__U11(tt()) -> a__U12(tt())
a__U12(tt()) -> tt()
a__isNePal(__(I,__(P,I))) -> a__U11(tt())
mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
mark(U11(X)) -> a__U11(mark(X))
mark(U12(X)) -> a__U12(mark(X))
mark(isNePal(X)) -> a__isNePal(mark(X))
mark(nil()) -> nil()
mark(tt()) -> tt()
a____(X1,X2) -> __(X1,X2)
a__U11(X) -> U11(X)
a__U12(X) -> U12(X)
a__isNePal(X) -> isNePal(X)
Arctic Interpretation Processor:
dimension: 1
interpretation:
[mark#](x0) = x0,
[a____#](x0, x1) = x0 + x1,
[isNePal](x0) = 2x0,
[U12](x0) = 2x0,
[U11](x0) = 2x0 + 0,
[a__isNePal](x0) = 2x0,
[a__U12](x0) = 2x0,
[a__U11](x0) = 2x0 + 0,
[tt] = 0,
[nil] = 7,
[mark](x0) = x0,
[a____](x0, x1) = x0 + x1 + 0,
[__](x0, x1) = x0 + x1 + 0
orientation:
mark#(__(X1,X2)) = X1 + X2 + 0 >= X2 = mark#(X2)
mark#(__(X1,X2)) = X1 + X2 + 0 >= X1 = mark#(X1)
mark#(__(X1,X2)) = X1 + X2 + 0 >= X1 + X2 = a____#(mark(X1),mark(X2))
a____#(__(X,Y),Z) = X + Y + Z + 0 >= Z = mark#(Z)
mark#(U12(X)) = 2X >= X = mark#(X)
a____#(__(X,Y),Z) = X + Y + Z + 0 >= Y + Z = a____#(mark(Y),mark(Z))
a____#(__(X,Y),Z) = X + Y + Z + 0 >= X + Y + Z + 0 = a____#(mark(X),a____(mark(Y),mark(Z)))
a____#(X,nil()) = X + 7 >= X = mark#(X)
a____#(nil(),X) = X + 7 >= X = mark#(X)
a____(__(X,Y),Z) = X + Y + Z + 0 >= X + Y + Z + 0 = a____(mark(X),a____(mark(Y),mark(Z)))
a____(X,nil()) = X + 7 >= X = mark(X)
a____(nil(),X) = X + 7 >= X = mark(X)
a__U11(tt()) = 2 >= 2 = a__U12(tt())
a__U12(tt()) = 2 >= 0 = tt()
a__isNePal(__(I,__(P,I))) = 2I + 2P + 2 >= 2 = a__U11(tt())
mark(__(X1,X2)) = X1 + X2 + 0 >= X1 + X2 + 0 = a____(mark(X1),mark(X2))
mark(U11(X)) = 2X + 0 >= 2X + 0 = a__U11(mark(X))
mark(U12(X)) = 2X >= 2X = a__U12(mark(X))
mark(isNePal(X)) = 2X >= 2X = a__isNePal(mark(X))
mark(nil()) = 7 >= 7 = nil()
mark(tt()) = 0 >= 0 = tt()
a____(X1,X2) = X1 + X2 + 0 >= X1 + X2 + 0 = __(X1,X2)
a__U11(X) = 2X + 0 >= 2X + 0 = U11(X)
a__U12(X) = 2X >= 2X = U12(X)
a__isNePal(X) = 2X >= 2X = isNePal(X)
problem:
DPs:
mark#(__(X1,X2)) -> mark#(X2)
mark#(__(X1,X2)) -> mark#(X1)
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
a____#(__(X,Y),Z) -> mark#(Z)
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z))
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z)))
a____#(X,nil()) -> mark#(X)
a____#(nil(),X) -> mark#(X)
TRS:
a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
a____(X,nil()) -> mark(X)
a____(nil(),X) -> mark(X)
a__U11(tt()) -> a__U12(tt())
a__U12(tt()) -> tt()
a__isNePal(__(I,__(P,I))) -> a__U11(tt())
mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
mark(U11(X)) -> a__U11(mark(X))
mark(U12(X)) -> a__U12(mark(X))
mark(isNePal(X)) -> a__isNePal(mark(X))
mark(nil()) -> nil()
mark(tt()) -> tt()
a____(X1,X2) -> __(X1,X2)
a__U11(X) -> U11(X)
a__U12(X) -> U12(X)
a__isNePal(X) -> isNePal(X)
Arctic Interpretation Processor:
dimension: 1
interpretation:
[mark#](x0) = 2x0 + 0,
[a____#](x0, x1) = 4x0 + 2x1,
[isNePal](x0) = 0,
[U12](x0) = 0,
[U11](x0) = x0,
[a__isNePal](x0) = 0,
[a__U12](x0) = 0,
[a__U11](x0) = x0,
[tt] = 0,
[nil] = 0,
[mark](x0) = x0,
[a____](x0, x1) = 2x0 + x1 + 2,
[__](x0, x1) = 2x0 + x1 + 2
orientation:
mark#(__(X1,X2)) = 4X1 + 2X2 + 4 >= 2X2 + 0 = mark#(X2)
mark#(__(X1,X2)) = 4X1 + 2X2 + 4 >= 2X1 + 0 = mark#(X1)
mark#(__(X1,X2)) = 4X1 + 2X2 + 4 >= 4X1 + 2X2 = a____#(mark(X1),mark(X2))
a____#(__(X,Y),Z) = 6X + 4Y + 2Z + 6 >= 2Z + 0 = mark#(Z)
a____#(__(X,Y),Z) = 6X + 4Y + 2Z + 6 >= 4Y + 2Z = a____#(mark(Y),mark(Z))
a____#(__(X,Y),Z) = 6X + 4Y + 2Z + 6 >= 4X + 4Y + 2Z + 4 = a____#(mark(X),a____(mark(Y),mark(Z)))
a____#(X,nil()) = 4X + 2 >= 2X + 0 = mark#(X)
a____#(nil(),X) = 2X + 4 >= 2X + 0 = mark#(X)
a____(__(X,Y),Z) = 4X + 2Y + Z + 4 >= 2X + 2Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z)))
a____(X,nil()) = 2X + 2 >= X = mark(X)
a____(nil(),X) = X + 2 >= X = mark(X)
a__U11(tt()) = 0 >= 0 = a__U12(tt())
a__U12(tt()) = 0 >= 0 = tt()
a__isNePal(__(I,__(P,I))) = 0 >= 0 = a__U11(tt())
mark(__(X1,X2)) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = a____(mark(X1),mark(X2))
mark(U11(X)) = X >= X = a__U11(mark(X))
mark(U12(X)) = 0 >= 0 = a__U12(mark(X))
mark(isNePal(X)) = 0 >= 0 = a__isNePal(mark(X))
mark(nil()) = 0 >= 0 = nil()
mark(tt()) = 0 >= 0 = tt()
a____(X1,X2) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = __(X1,X2)
a__U11(X) = X >= X = U11(X)
a__U12(X) = 0 >= 0 = U12(X)
a__isNePal(X) = 0 >= 0 = isNePal(X)
problem:
DPs:
mark#(__(X1,X2)) -> mark#(X2)
mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
a____#(__(X,Y),Z) -> mark#(Z)
a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z))
a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z)))
a____#(nil(),X) -> mark#(X)
TRS:
a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
a____(X,nil()) -> mark(X)
a____(nil(),X) -> mark(X)
a__U11(tt()) -> a__U12(tt())
a__U12(tt()) -> tt()
a__isNePal(__(I,__(P,I))) -> a__U11(tt())
mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
mark(U11(X)) -> a__U11(mark(X))
mark(U12(X)) -> a__U12(mark(X))
mark(isNePal(X)) -> a__isNePal(mark(X))
mark(nil()) -> nil()
mark(tt()) -> tt()
a____(X1,X2) -> __(X1,X2)
a__U11(X) -> U11(X)
a__U12(X) -> U12(X)
a__isNePal(X) -> isNePal(X)
KBO Processor:
argument filtering:
pi(__) = [0,1]
pi(a____) = [0,1]
pi(mark) = [0]
pi(nil) = []
pi(tt) = []
pi(a__U11) = [0]
pi(a__U12) = []
pi(a__isNePal) = 0
pi(U11) = [0]
pi(U12) = []
pi(isNePal) = 0
pi(a____#) = [0,1]
pi(mark#) = 0
weight function:
w0 = 1
w(isNePal) = w(U12) = w(U11) = w(a__isNePal) = w(a__U12) = w(
a__U11) = w(tt) = w(nil) = w(a____) = w(__) = 1
w(mark#) = w(a____#) = w(mark) = 0
precedence:
mark > a__U12 ~ a__U11 > a____ > mark# ~ a____# ~ isNePal ~
U12 ~ U11 ~ a__isNePal ~ tt ~ nil ~ __
problem:
DPs:
TRS:
a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
a____(X,nil()) -> mark(X)
a____(nil(),X) -> mark(X)
a__U11(tt()) -> a__U12(tt())
a__U12(tt()) -> tt()
a__isNePal(__(I,__(P,I))) -> a__U11(tt())
mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
mark(U11(X)) -> a__U11(mark(X))
mark(U12(X)) -> a__U12(mark(X))
mark(isNePal(X)) -> a__isNePal(mark(X))
mark(nil()) -> nil()
mark(tt()) -> tt()
a____(X1,X2) -> __(X1,X2)
a__U11(X) -> U11(X)
a__U12(X) -> U12(X)
a__isNePal(X) -> isNePal(X)
Qed