MAYBE
Problem:
a__zeros() -> cons(0(),zeros())
a__and(tt(),X) -> mark(X)
a__length(nil()) -> 0()
a__length(cons(N,L)) -> s(a__length(mark(L)))
mark(zeros()) -> a__zeros()
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(length(X)) -> a__length(mark(X))
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(0()) -> 0()
mark(tt()) -> tt()
mark(nil()) -> nil()
mark(s(X)) -> s(mark(X))
a__zeros() -> zeros()
a__and(X1,X2) -> and(X1,X2)
a__length(X) -> length(X)
Proof:
Matrix Interpretation Processor: dim=3
interpretation:
[1 0 0] [1]
[length](x0) = [0 0 0]x0 + [0]
[0 0 0] [0],
[1 0 0] [1 1 0]
[and](x0, x1) = [0 0 0]x0 + [0 0 0]x1
[0 0 0] [0 0 0] ,
[1 0 0]
[s](x0) = [0 0 0]x0
[0 0 0] ,
[1 0 0] [1]
[a__length](x0) = [0 0 0]x0 + [0]
[0 0 0] [0],
[0]
[nil] = [0]
[0],
[1 0 0]
[mark](x0) = [0 0 0]x0
[0 0 0] ,
[1 0 0] [1 1 0]
[a__and](x0, x1) = [0 1 0]x0 + [0 0 0]x1
[0 0 0] [0 0 0] ,
[0]
[tt] = [0]
[0],
[1 1 0] [1 0 1]
[cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1
[0 0 0] [0 0 0] ,
[1]
[zeros] = [0]
[0],
[0]
[0] = [0]
[0],
[1]
[a__zeros] = [0]
[0]
orientation:
[1] [1]
a__zeros() = [0] >= [0] = cons(0(),zeros())
[0] [0]
[1 1 0] [1 0 0]
a__and(tt(),X) = [0 0 0]X >= [0 0 0]X = mark(X)
[0 0 0] [0 0 0]
[1] [0]
a__length(nil()) = [0] >= [0] = 0()
[0] [0]
[1 0 1] [1 1 0] [1] [1 0 0] [1]
a__length(cons(N,L)) = [0 0 0]L + [0 0 0]N + [0] >= [0 0 0]L + [0] = s(a__length(mark(L)))
[0 0 0] [0 0 0] [0] [0 0 0] [0]
[1] [1]
mark(zeros()) = [0] >= [0] = a__zeros()
[0] [0]
[1 0 0] [1 1 0] [1 0 0] [1 1 0]
mark(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = a__and(mark(X1),X2)
[0 0 0] [0 0 0] [0 0 0] [0 0 0]
[1 0 0] [1] [1 0 0] [1]
mark(length(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = a__length(mark(X))
[0 0 0] [0] [0 0 0] [0]
[1 1 0] [1 0 1] [1 0 0] [1 0 1]
mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(mark(X1),X2)
[0 0 0] [0 0 0] [0 0 0] [0 0 0]
[0] [0]
mark(0()) = [0] >= [0] = 0()
[0] [0]
[0] [0]
mark(tt()) = [0] >= [0] = tt()
[0] [0]
[0] [0]
mark(nil()) = [0] >= [0] = nil()
[0] [0]
[1 0 0] [1 0 0]
mark(s(X)) = [0 0 0]X >= [0 0 0]X = s(mark(X))
[0 0 0] [0 0 0]
[1] [1]
a__zeros() = [0] >= [0] = zeros()
[0] [0]
[1 0 0] [1 1 0] [1 0 0] [1 1 0]
a__and(X1,X2) = [0 1 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2)
[0 0 0] [0 0 0] [0 0 0] [0 0 0]
[1 0 0] [1] [1 0 0] [1]
a__length(X) = [0 0 0]X + [0] >= [0 0 0]X + [0] = length(X)
[0 0 0] [0] [0 0 0] [0]
problem:
a__zeros() -> cons(0(),zeros())
a__and(tt(),X) -> mark(X)
a__length(cons(N,L)) -> s(a__length(mark(L)))
mark(zeros()) -> a__zeros()
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(length(X)) -> a__length(mark(X))
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(0()) -> 0()
mark(tt()) -> tt()
mark(nil()) -> nil()
mark(s(X)) -> s(mark(X))
a__zeros() -> zeros()
a__and(X1,X2) -> and(X1,X2)
a__length(X) -> length(X)
Matrix Interpretation Processor: dim=3
interpretation:
[1 0 0]
[length](x0) = [0 0 0]x0
[0 0 0] ,
[1 0 0] [1 0 1] [1]
[and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
[0 0 0] [0 0 0] [0],
[1 0 0]
[s](x0) = [0 0 0]x0
[0 0 0] ,
[1 0 0]
[a__length](x0) = [0 1 0]x0
[0 0 0] ,
[0]
[nil] = [0]
[0],
[1 0 0]
[mark](x0) = [1 0 0]x0
[0 0 0] ,
[1 0 0] [1 0 1] [1]
[a__and](x0, x1) = [0 1 0]x0 + [1 0 1]x1 + [0]
[0 0 0] [0 0 0] [0],
[0]
[tt] = [0]
[0],
[1 0 1] [1 1 1]
[cons](x0, x1) = [0 1 0]x0 + [0 0 0]x1
[0 0 0] [0 0 0] ,
[0]
[zeros] = [0]
[0],
[0]
[0] = [0]
[0],
[0]
[a__zeros] = [0]
[0]
orientation:
[0] [0]
a__zeros() = [0] >= [0] = cons(0(),zeros())
[0] [0]
[1 0 1] [1] [1 0 0]
a__and(tt(),X) = [1 0 1]X + [0] >= [1 0 0]X = mark(X)
[0 0 0] [0] [0 0 0]
[1 1 1] [1 0 1] [1 0 0]
a__length(cons(N,L)) = [0 0 0]L + [0 1 0]N >= [0 0 0]L = s(a__length(mark(L)))
[0 0 0] [0 0 0] [0 0 0]
[0] [0]
mark(zeros()) = [0] >= [0] = a__zeros()
[0] [0]
[1 0 0] [1 0 1] [1] [1 0 0] [1 0 1] [1]
mark(and(X1,X2)) = [1 0 0]X1 + [1 0 1]X2 + [1] >= [1 0 0]X1 + [1 0 1]X2 + [0] = a__and(mark(X1),X2)
[0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0]
[1 0 0] [1 0 0]
mark(length(X)) = [1 0 0]X >= [1 0 0]X = a__length(mark(X))
[0 0 0] [0 0 0]
[1 0 1] [1 1 1] [1 0 0] [1 1 1]
mark(cons(X1,X2)) = [1 0 1]X1 + [1 1 1]X2 >= [1 0 0]X1 + [0 0 0]X2 = cons(mark(X1),X2)
[0 0 0] [0 0 0] [0 0 0] [0 0 0]
[0] [0]
mark(0()) = [0] >= [0] = 0()
[0] [0]
[0] [0]
mark(tt()) = [0] >= [0] = tt()
[0] [0]
[0] [0]
mark(nil()) = [0] >= [0] = nil()
[0] [0]
[1 0 0] [1 0 0]
mark(s(X)) = [1 0 0]X >= [0 0 0]X = s(mark(X))
[0 0 0] [0 0 0]
[0] [0]
a__zeros() = [0] >= [0] = zeros()
[0] [0]
[1 0 0] [1 0 1] [1] [1 0 0] [1 0 1] [1]
a__and(X1,X2) = [0 1 0]X1 + [1 0 1]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = and(X1,X2)
[0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0]
[1 0 0] [1 0 0]
a__length(X) = [0 1 0]X >= [0 0 0]X = length(X)
[0 0 0] [0 0 0]
problem:
a__zeros() -> cons(0(),zeros())
a__length(cons(N,L)) -> s(a__length(mark(L)))
mark(zeros()) -> a__zeros()
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(length(X)) -> a__length(mark(X))
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(0()) -> 0()
mark(tt()) -> tt()
mark(nil()) -> nil()
mark(s(X)) -> s(mark(X))
a__zeros() -> zeros()
a__and(X1,X2) -> and(X1,X2)
a__length(X) -> length(X)
Matrix Interpretation Processor: dim=3
interpretation:
[1 0 0]
[length](x0) = [0 1 0]x0
[0 0 0] ,
[1 0 0] [1 0 0]
[and](x0, x1) = [0 1 0]x0 + [0 0 0]x1
[0 0 0] [0 0 0] ,
[1 0 0]
[s](x0) = [0 1 0]x0
[0 0 0] ,
[1 0 0] [0]
[a__length](x0) = [0 1 0]x0 + [0]
[0 0 0] [1],
[0]
[nil] = [1]
[0],
[1 1 0] [0]
[mark](x0) = [0 0 0]x0 + [1]
[0 0 0] [1],
[1 0 0] [1 0 0]
[a__and](x0, x1) = [0 1 0]x0 + [0 0 0]x1
[0 0 0] [0 0 0] ,
[1]
[tt] = [0]
[0],
[1 1 0] [1 1 0] [0]
[cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
[0 0 1] [0 0 0] [0],
[1]
[zeros] = [0]
[0],
[0]
[0] = [0]
[0],
[1]
[a__zeros] = [1]
[0]
orientation:
[1] [1]
a__zeros() = [1] >= [1] = cons(0(),zeros())
[0] [0]
[1 1 0] [1 1 0] [0] [1 1 0] [0]
a__length(cons(N,L)) = [0 0 0]L + [0 0 0]N + [1] >= [0 0 0]L + [1] = s(a__length(mark(L)))
[0 0 0] [0 0 0] [1] [0 0 0] [0]
[1] [1]
mark(zeros()) = [1] >= [1] = a__zeros()
[1] [0]
[1 1 0] [1 0 0] [0] [1 1 0] [1 0 0] [0]
mark(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = a__and(mark(X1),X2)
[0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0]
[1 1 0] [0] [1 1 0] [0]
mark(length(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__length(mark(X))
[0 0 0] [1] [0 0 0] [1]
[1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [1]
mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = cons(mark(X1),X2)
[0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1]
[0] [0]
mark(0()) = [1] >= [0] = 0()
[1] [0]
[1] [1]
mark(tt()) = [1] >= [0] = tt()
[1] [0]
[1] [0]
mark(nil()) = [1] >= [1] = nil()
[1] [0]
[1 1 0] [0] [1 1 0] [0]
mark(s(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = s(mark(X))
[0 0 0] [1] [0 0 0] [0]
[1] [1]
a__zeros() = [1] >= [0] = zeros()
[0] [0]
[1 0 0] [1 0 0] [1 0 0] [1 0 0]
a__and(X1,X2) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = and(X1,X2)
[0 0 0] [0 0 0] [0 0 0] [0 0 0]
[1 0 0] [0] [1 0 0]
a__length(X) = [0 1 0]X + [0] >= [0 1 0]X = length(X)
[0 0 0] [1] [0 0 0]
problem:
a__zeros() -> cons(0(),zeros())
a__length(cons(N,L)) -> s(a__length(mark(L)))
mark(zeros()) -> a__zeros()
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(length(X)) -> a__length(mark(X))
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(0()) -> 0()
mark(tt()) -> tt()
mark(s(X)) -> s(mark(X))
a__zeros() -> zeros()
a__and(X1,X2) -> and(X1,X2)
a__length(X) -> length(X)
Matrix Interpretation Processor: dim=1
interpretation:
[length](x0) = x0 + 2,
[and](x0, x1) = x0 + 5x1,
[s](x0) = x0,
[a__length](x0) = x0 + 2,
[mark](x0) = x0 + 1,
[a__and](x0, x1) = x0 + 5x1,
[tt] = 7,
[cons](x0, x1) = x0 + x1 + 1,
[zeros] = 0,
[0] = 0,
[a__zeros] = 1
orientation:
a__zeros() = 1 >= 1 = cons(0(),zeros())
a__length(cons(N,L)) = L + N + 3 >= L + 3 = s(a__length(mark(L)))
mark(zeros()) = 1 >= 1 = a__zeros()
mark(and(X1,X2)) = X1 + 5X2 + 1 >= X1 + 5X2 + 1 = a__and(mark(X1),X2)
mark(length(X)) = X + 3 >= X + 3 = a__length(mark(X))
mark(cons(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = cons(mark(X1),X2)
mark(0()) = 1 >= 0 = 0()
mark(tt()) = 8 >= 7 = tt()
mark(s(X)) = X + 1 >= X + 1 = s(mark(X))
a__zeros() = 1 >= 0 = zeros()
a__and(X1,X2) = X1 + 5X2 >= X1 + 5X2 = and(X1,X2)
a__length(X) = X + 2 >= X + 2 = length(X)
problem:
a__zeros() -> cons(0(),zeros())
a__length(cons(N,L)) -> s(a__length(mark(L)))
mark(zeros()) -> a__zeros()
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(length(X)) -> a__length(mark(X))
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(s(X)) -> s(mark(X))
a__and(X1,X2) -> and(X1,X2)
a__length(X) -> length(X)
DP Processor:
DPs:
a__length#(cons(N,L)) -> mark#(L)
a__length#(cons(N,L)) -> a__length#(mark(L))
mark#(zeros()) -> a__zeros#()
mark#(and(X1,X2)) -> mark#(X1)
mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
mark#(length(X)) -> mark#(X)
mark#(length(X)) -> a__length#(mark(X))
mark#(cons(X1,X2)) -> mark#(X1)
mark#(s(X)) -> mark#(X)
TRS:
a__zeros() -> cons(0(),zeros())
a__length(cons(N,L)) -> s(a__length(mark(L)))
mark(zeros()) -> a__zeros()
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(length(X)) -> a__length(mark(X))
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(s(X)) -> s(mark(X))
a__and(X1,X2) -> and(X1,X2)
a__length(X) -> length(X)
TDG Processor:
DPs:
a__length#(cons(N,L)) -> mark#(L)
a__length#(cons(N,L)) -> a__length#(mark(L))
mark#(zeros()) -> a__zeros#()
mark#(and(X1,X2)) -> mark#(X1)
mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
mark#(length(X)) -> mark#(X)
mark#(length(X)) -> a__length#(mark(X))
mark#(cons(X1,X2)) -> mark#(X1)
mark#(s(X)) -> mark#(X)
TRS:
a__zeros() -> cons(0(),zeros())
a__length(cons(N,L)) -> s(a__length(mark(L)))
mark(zeros()) -> a__zeros()
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(length(X)) -> a__length(mark(X))
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(s(X)) -> s(mark(X))
a__and(X1,X2) -> and(X1,X2)
a__length(X) -> length(X)
graph:
mark#(length(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
mark#(length(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
mark#(length(X)) -> mark#(X) ->
mark#(length(X)) -> a__length#(mark(X))
mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X)
mark#(length(X)) -> mark#(X) ->
mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
mark#(length(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1)
mark#(length(X)) -> mark#(X) ->
mark#(zeros()) -> a__zeros#()
mark#(length(X)) -> a__length#(mark(X)) ->
a__length#(cons(N,L)) -> a__length#(mark(L))
mark#(length(X)) -> a__length#(mark(X)) ->
a__length#(cons(N,L)) -> mark#(L)
mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
mark#(and(X1,X2)) -> mark#(X1) ->
mark#(cons(X1,X2)) -> mark#(X1)
mark#(and(X1,X2)) -> mark#(X1) ->
mark#(length(X)) -> a__length#(mark(X))
mark#(and(X1,X2)) -> mark#(X1) ->
mark#(length(X)) -> mark#(X)
mark#(and(X1,X2)) -> mark#(X1) ->
mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
mark#(and(X1,X2)) -> mark#(X1) ->
mark#(and(X1,X2)) -> mark#(X1)
mark#(and(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#()
mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X))
mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X)
mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1)
mark#(s(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#()
mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
mark#(cons(X1,X2)) -> mark#(X1) ->
mark#(cons(X1,X2)) -> mark#(X1)
mark#(cons(X1,X2)) -> mark#(X1) ->
mark#(length(X)) -> a__length#(mark(X))
mark#(cons(X1,X2)) -> mark#(X1) ->
mark#(length(X)) -> mark#(X)
mark#(cons(X1,X2)) -> mark#(X1) ->
mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
mark#(cons(X1,X2)) -> mark#(X1) ->
mark#(and(X1,X2)) -> mark#(X1)
mark#(cons(X1,X2)) -> mark#(X1) ->
mark#(zeros()) -> a__zeros#()
a__length#(cons(N,L)) -> mark#(L) ->
mark#(s(X)) -> mark#(X)
a__length#(cons(N,L)) -> mark#(L) ->
mark#(cons(X1,X2)) -> mark#(X1)
a__length#(cons(N,L)) -> mark#(L) ->
mark#(length(X)) -> a__length#(mark(X))
a__length#(cons(N,L)) -> mark#(L) ->
mark#(length(X)) -> mark#(X)
a__length#(cons(N,L)) -> mark#(L) ->
mark#(and(X1,X2)) -> a__and#(mark(X1),X2)
a__length#(cons(N,L)) -> mark#(L) ->
mark#(and(X1,X2)) -> mark#(X1)
a__length#(cons(N,L)) -> mark#(L) ->
mark#(zeros()) -> a__zeros#()
a__length#(cons(N,L)) -> a__length#(mark(L)) ->
a__length#(cons(N,L)) -> a__length#(mark(L))
a__length#(cons(N,L)) -> a__length#(mark(L)) -> a__length#(cons(N,L)) -> mark#(L)
SCC Processor:
#sccs: 1
#rules: 7
#arcs: 39/81
DPs:
mark#(length(X)) -> mark#(X)
mark#(and(X1,X2)) -> mark#(X1)
mark#(length(X)) -> a__length#(mark(X))
a__length#(cons(N,L)) -> mark#(L)
mark#(cons(X1,X2)) -> mark#(X1)
mark#(s(X)) -> mark#(X)
a__length#(cons(N,L)) -> a__length#(mark(L))
TRS:
a__zeros() -> cons(0(),zeros())
a__length(cons(N,L)) -> s(a__length(mark(L)))
mark(zeros()) -> a__zeros()
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(length(X)) -> a__length(mark(X))
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(s(X)) -> s(mark(X))
a__and(X1,X2) -> and(X1,X2)
a__length(X) -> length(X)
CDG Processor:
DPs:
mark#(length(X)) -> mark#(X)
mark#(and(X1,X2)) -> mark#(X1)
mark#(length(X)) -> a__length#(mark(X))
a__length#(cons(N,L)) -> mark#(L)
mark#(cons(X1,X2)) -> mark#(X1)
mark#(s(X)) -> mark#(X)
a__length#(cons(N,L)) -> a__length#(mark(L))
TRS:
a__zeros() -> cons(0(),zeros())
a__length(cons(N,L)) -> s(a__length(mark(L)))
mark(zeros()) -> a__zeros()
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(length(X)) -> a__length(mark(X))
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(s(X)) -> s(mark(X))
a__and(X1,X2) -> and(X1,X2)
a__length(X) -> length(X)
graph:
mark#(length(X)) -> a__length#(mark(X)) ->
a__length#(cons(N,L)) -> mark#(L)
mark#(length(X)) -> a__length#(mark(X)) ->
a__length#(cons(N,L)) -> a__length#(mark(L))
a__length#(cons(N,L)) -> a__length#(mark(L)) ->
a__length#(cons(N,L)) -> mark#(L)
a__length#(cons(N,L)) -> a__length#(mark(L)) ->
a__length#(cons(N,L)) -> a__length#(mark(L))
SCC Processor:
#sccs: 1
#rules: 1
#arcs: 4/49
DPs:
a__length#(cons(N,L)) -> a__length#(mark(L))
TRS:
a__zeros() -> cons(0(),zeros())
a__length(cons(N,L)) -> s(a__length(mark(L)))
mark(zeros()) -> a__zeros()
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(length(X)) -> a__length(mark(X))
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(s(X)) -> s(mark(X))
a__and(X1,X2) -> and(X1,X2)
a__length(X) -> length(X)
Open