/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__isNatList(V1) a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(V) -> a__isNatList(V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(X) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) a__isNatIList(X) -> isNatIList(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [and](x0, x1) = x0 + x1, [U11](x0, x1) = 2x0 + x1 + 6, [isNat](x0) = x0, [isNatList](x0) = x0, [nil] = 0, [isNatIList](x0) = 4x0, [a__isNatIList](x0) = 4x0, [a__isNatList](x0) = x0, [length](x0) = x0 + 6, [a__isNat](x0) = x0, [a__and](x0, x1) = x0 + x1, [s](x0) = x0, [a__length](x0) = x0 + 6, [mark](x0) = x0, [a__U11](x0, x1) = 2x0 + x1 + 6, [tt] = 0, [cons](x0, x1) = 2x0 + 3x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),L) = L + 6 >= L + 6 = s(a__length(mark(L))) a__and(tt(),X) = X >= X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(length(V1)) = V1 + 6 >= V1 = a__isNatList(V1) a__isNat(s(V1)) = V1 >= V1 = a__isNat(V1) a__isNatIList(V) = 4V >= V = a__isNatList(V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 8V1 + 12V2 >= V1 + 4V2 = a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(nil()) = 0 >= 0 = tt() a__isNatList(cons(V1,V2)) = 2V1 + 3V2 >= V1 + V2 = a__and(a__isNat(V1),isNatList(V2)) a__length(nil()) = 6 >= 0 = 0() a__length(cons(N,L)) = 3L + 2N + 6 >= 3L + 2N + 6 = a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = 2X1 + X2 + 6 >= 2X1 + X2 + 6 = a__U11(mark(X1),X2) mark(length(X)) = X + 6 >= X + 6 = a__length(mark(X)) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = a__and(mark(X1),X2) mark(isNat(X)) = X >= X = a__isNat(X) mark(isNatList(X)) = X >= X = a__isNatList(X) mark(isNatIList(X)) = 4X >= 4X = a__isNatIList(X) mark(cons(X1,X2)) = 2X1 + 3X2 >= 2X1 + 3X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = 2X1 + X2 + 6 >= 2X1 + X2 + 6 = U11(X1,X2) a__length(X) = X + 6 >= X + 6 = length(X) a__and(X1,X2) = X1 + X2 >= X1 + X2 = and(X1,X2) a__isNat(X) = X >= X = isNat(X) a__isNatList(X) = X >= X = isNatList(X) a__isNatIList(X) = 4X >= 4X = isNatIList(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(V) -> a__isNatList(V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(X) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) a__isNatIList(X) -> isNatIList(X) Matrix Interpretation Processor: dim=1 interpretation: [and](x0, x1) = x0 + 2x1, [U11](x0, x1) = 2x0 + 4x1 + 4, [isNat](x0) = 7x0, [isNatList](x0) = 4x0, [nil] = 1, [isNatIList](x0) = 4x0, [a__isNatIList](x0) = 4x0, [a__isNatList](x0) = 4x0, [length](x0) = 4x0 + 4, [a__isNat](x0) = 7x0, [a__and](x0, x1) = x0 + 2x1, [s](x0) = x0, [a__length](x0) = 4x0 + 4, [mark](x0) = x0, [a__U11](x0, x1) = 2x0 + 4x1 + 4, [tt] = 0, [cons](x0, x1) = 7x0 + 3x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),L) = 4L + 4 >= 4L + 4 = s(a__length(mark(L))) a__and(tt(),X) = 2X >= X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(s(V1)) = 7V1 >= 7V1 = a__isNat(V1) a__isNatIList(V) = 4V >= 4V = a__isNatList(V) a__isNatIList(zeros()) = 0 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 28V1 + 12V2 >= 7V1 + 8V2 = a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(nil()) = 4 >= 0 = tt() a__isNatList(cons(V1,V2)) = 28V1 + 12V2 >= 7V1 + 8V2 = a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) = 12L + 28N + 4 >= 12L + 28N + 4 = a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = 2X1 + 4X2 + 4 >= 2X1 + 4X2 + 4 = a__U11(mark(X1),X2) mark(length(X)) = 4X + 4 >= 4X + 4 = a__length(mark(X)) mark(and(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = a__and(mark(X1),X2) mark(isNat(X)) = 7X >= 7X = a__isNat(X) mark(isNatList(X)) = 4X >= 4X = a__isNatList(X) mark(isNatIList(X)) = 4X >= 4X = a__isNatIList(X) mark(cons(X1,X2)) = 7X1 + 3X2 >= 7X1 + 3X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 1 >= 1 = nil() a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = 2X1 + 4X2 + 4 >= 2X1 + 4X2 + 4 = U11(X1,X2) a__length(X) = 4X + 4 >= 4X + 4 = length(X) a__and(X1,X2) = X1 + 2X2 >= X1 + 2X2 = and(X1,X2) a__isNat(X) = 7X >= 7X = isNat(X) a__isNatList(X) = 4X >= 4X = isNatList(X) a__isNatIList(X) = 4X >= 4X = isNatIList(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(V) -> a__isNatList(V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(X) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) a__isNatIList(X) -> isNatIList(X) Matrix Interpretation Processor: dim=1 interpretation: [and](x0, x1) = 3x0 + x1, [U11](x0, x1) = 2x0 + x1, [isNat](x0) = x0, [isNatList](x0) = x0, [nil] = 0, [isNatIList](x0) = x0 + 1, [a__isNatIList](x0) = x0 + 1, [a__isNatList](x0) = x0, [length](x0) = x0, [a__isNat](x0) = x0, [a__and](x0, x1) = 3x0 + x1, [s](x0) = x0, [a__length](x0) = x0, [mark](x0) = x0, [a__U11](x0, x1) = 2x0 + x1, [tt] = 0, [cons](x0, x1) = 4x0 + 7x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),L) = L >= L = s(a__length(mark(L))) a__and(tt(),X) = X >= X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(s(V1)) = V1 >= V1 = a__isNat(V1) a__isNatIList(V) = V + 1 >= V = a__isNatList(V) a__isNatIList(zeros()) = 1 >= 0 = tt() a__isNatIList(cons(V1,V2)) = 4V1 + 7V2 + 1 >= 3V1 + V2 + 1 = a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(cons(V1,V2)) = 4V1 + 7V2 >= 3V1 + V2 = a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) = 7L + 4N >= 7L + 2N = a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = a__U11(mark(X1),X2) mark(length(X)) = X >= X = a__length(mark(X)) mark(and(X1,X2)) = 3X1 + X2 >= 3X1 + X2 = a__and(mark(X1),X2) mark(isNat(X)) = X >= X = a__isNat(X) mark(isNatList(X)) = X >= X = a__isNatList(X) mark(isNatIList(X)) = X + 1 >= X + 1 = a__isNatIList(X) mark(cons(X1,X2)) = 4X1 + 7X2 >= 4X1 + 7X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = X >= X = s(mark(X)) mark(nil()) = 0 >= 0 = nil() a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = 2X1 + X2 >= 2X1 + X2 = U11(X1,X2) a__length(X) = X >= X = length(X) a__and(X1,X2) = 3X1 + X2 >= 3X1 + X2 = and(X1,X2) a__isNat(X) = X >= X = isNat(X) a__isNatList(X) = X >= X = isNatList(X) a__isNatIList(X) = X + 1 >= X + 1 = isNatIList(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(X) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) a__isNatIList(X) -> isNatIList(X) Matrix Interpretation Processor: dim=1 interpretation: [and](x0, x1) = x0 + x1, [U11](x0, x1) = x0 + 4x1, [isNat](x0) = x0, [isNatList](x0) = x0, [nil] = 4, [isNatIList](x0) = 2x0, [a__isNatIList](x0) = 2x0, [a__isNatList](x0) = x0, [length](x0) = x0, [a__isNat](x0) = 2x0, [a__and](x0, x1) = x0 + 2x1, [s](x0) = 2x0, [a__length](x0) = x0, [mark](x0) = 2x0, [a__U11](x0, x1) = x0 + 4x1, [tt] = 0, [cons](x0, x1) = 4x0 + 5x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),L) = 4L >= 4L = s(a__length(mark(L))) a__and(tt(),X) = 2X >= 2X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(s(V1)) = 4V1 >= 2V1 = a__isNat(V1) a__isNatIList(cons(V1,V2)) = 8V1 + 10V2 >= 2V1 + 4V2 = a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(cons(V1,V2)) = 4V1 + 5V2 >= 2V1 + 2V2 = a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) = 5L + 4N >= 5L + 2N = a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = 2X1 + 8X2 >= 2X1 + 4X2 = a__U11(mark(X1),X2) mark(length(X)) = 2X >= 2X = a__length(mark(X)) mark(and(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = a__and(mark(X1),X2) mark(isNat(X)) = 2X >= 2X = a__isNat(X) mark(isNatList(X)) = 2X >= X = a__isNatList(X) mark(isNatIList(X)) = 4X >= 2X = a__isNatIList(X) mark(cons(X1,X2)) = 8X1 + 10X2 >= 8X1 + 5X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 4X >= 4X = s(mark(X)) mark(nil()) = 8 >= 4 = nil() a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = X1 + 4X2 >= X1 + 4X2 = U11(X1,X2) a__length(X) = X >= X = length(X) a__and(X1,X2) = X1 + 2X2 >= X1 + X2 = and(X1,X2) a__isNat(X) = 2X >= X = isNat(X) a__isNatList(X) = X >= X = isNatList(X) a__isNatIList(X) = 2X >= 2X = isNatIList(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(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__U11(X1,X2) -> U11(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) a__isNatIList(X) -> isNatIList(X) Matrix Interpretation Processor: dim=1 interpretation: [and](x0, x1) = x0 + 2x1, [U11](x0, x1) = 2x0 + 4x1, [isNat](x0) = x0, [isNatList](x0) = x0, [isNatIList](x0) = x0 + 2, [a__isNatIList](x0) = x0 + 4, [a__isNatList](x0) = x0, [length](x0) = x0, [a__isNat](x0) = 2x0, [a__and](x0, x1) = x0 + 2x1, [s](x0) = 2x0, [a__length](x0) = x0, [mark](x0) = 2x0, [a__U11](x0, x1) = 2x0 + 4x1, [tt] = 0, [cons](x0, x1) = 4x0 + 6x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),L) = 4L >= 4L = s(a__length(mark(L))) a__and(tt(),X) = 2X >= 2X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(s(V1)) = 4V1 >= 2V1 = a__isNat(V1) a__isNatIList(cons(V1,V2)) = 4V1 + 6V2 + 4 >= 2V1 + 2V2 + 4 = a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(cons(V1,V2)) = 4V1 + 6V2 >= 2V1 + 2V2 = a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) = 6L + 4N >= 6L + 4N = a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = 4X1 + 8X2 >= 4X1 + 4X2 = a__U11(mark(X1),X2) mark(length(X)) = 2X >= 2X = a__length(mark(X)) mark(and(X1,X2)) = 2X1 + 4X2 >= 2X1 + 2X2 = a__and(mark(X1),X2) mark(isNat(X)) = 2X >= 2X = a__isNat(X) mark(isNatList(X)) = 2X >= X = a__isNatList(X) mark(isNatIList(X)) = 2X + 4 >= X + 4 = a__isNatIList(X) mark(cons(X1,X2)) = 8X1 + 12X2 >= 8X1 + 6X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 4X >= 4X = s(mark(X)) a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = 2X1 + 4X2 >= 2X1 + 4X2 = U11(X1,X2) a__length(X) = X >= X = length(X) a__and(X1,X2) = X1 + 2X2 >= X1 + 2X2 = and(X1,X2) a__isNat(X) = 2X >= X = isNat(X) a__isNatList(X) = X >= X = isNatList(X) a__isNatIList(X) = X + 4 >= X + 2 = isNatIList(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(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__U11(X1,X2) -> U11(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) Matrix Interpretation Processor: dim=1 interpretation: [and](x0, x1) = x0 + 2x1, [U11](x0, x1) = x0 + 2x1 + 1, [isNat](x0) = 2x0, [isNatList](x0) = 2x0, [isNatIList](x0) = x0, [a__isNatIList](x0) = 2x0, [a__isNatList](x0) = 4x0, [length](x0) = 2x0 + 2, [a__isNat](x0) = 4x0, [a__and](x0, x1) = x0 + 2x1, [s](x0) = x0, [a__length](x0) = 2x0 + 2, [mark](x0) = 2x0, [a__U11](x0, x1) = x0 + 4x1 + 2, [tt] = 0, [cons](x0, x1) = 4x0 + 4x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),L) = 4L + 2 >= 4L + 2 = s(a__length(mark(L))) a__and(tt(),X) = 2X >= 2X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(s(V1)) = 4V1 >= 4V1 = a__isNat(V1) a__isNatIList(cons(V1,V2)) = 8V1 + 8V2 >= 4V1 + 2V2 = a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(cons(V1,V2)) = 16V1 + 16V2 >= 4V1 + 4V2 = a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) = 8L + 8N + 2 >= 8L + 4N + 2 = a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = 2X1 + 4X2 + 2 >= 2X1 + 4X2 + 2 = a__U11(mark(X1),X2) mark(length(X)) = 4X + 4 >= 4X + 2 = a__length(mark(X)) mark(and(X1,X2)) = 2X1 + 4X2 >= 2X1 + 2X2 = a__and(mark(X1),X2) mark(isNat(X)) = 4X >= 4X = a__isNat(X) mark(isNatList(X)) = 4X >= 4X = a__isNatList(X) mark(isNatIList(X)) = 2X >= 2X = a__isNatIList(X) mark(cons(X1,X2)) = 8X1 + 8X2 >= 8X1 + 4X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 2X >= 2X = s(mark(X)) a__zeros() = 0 >= 0 = zeros() a__U11(X1,X2) = X1 + 4X2 + 2 >= X1 + 2X2 + 1 = U11(X1,X2) a__length(X) = 2X + 2 >= 2X + 2 = length(X) a__and(X1,X2) = X1 + 2X2 >= X1 + 2X2 = and(X1,X2) a__isNat(X) = 4X >= 2X = isNat(X) a__isNatList(X) = 4X >= 2X = isNatList(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(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__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) Matrix Interpretation Processor: dim=1 interpretation: [and](x0, x1) = x0 + x1, [U11](x0, x1) = 4x0 + 4x1 + 5, [isNat](x0) = 2x0, [isNatList](x0) = 2x0, [isNatIList](x0) = 4x0, [a__isNatIList](x0) = 2x0, [a__isNatList](x0) = 2x0, [length](x0) = x0, [a__isNat](x0) = 2x0, [a__and](x0, x1) = x0 + x1, [s](x0) = 2x0, [a__length](x0) = 2x0, [mark](x0) = x0, [a__U11](x0, x1) = 4x0 + 4x1, [tt] = 0, [cons](x0, x1) = 4x0 + 6x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),L) = 4L >= 4L = s(a__length(mark(L))) a__and(tt(),X) = X >= X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(s(V1)) = 4V1 >= 2V1 = a__isNat(V1) a__isNatIList(cons(V1,V2)) = 8V1 + 12V2 >= 2V1 + 4V2 = a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(cons(V1,V2)) = 8V1 + 12V2 >= 2V1 + 2V2 = a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) = 12L + 8N >= 12L + 8N = a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(U11(X1,X2)) = 4X1 + 4X2 + 5 >= 4X1 + 4X2 = a__U11(mark(X1),X2) mark(and(X1,X2)) = X1 + X2 >= X1 + X2 = a__and(mark(X1),X2) mark(isNat(X)) = 2X >= 2X = a__isNat(X) mark(isNatList(X)) = 2X >= 2X = a__isNatList(X) mark(isNatIList(X)) = 4X >= 2X = a__isNatIList(X) mark(cons(X1,X2)) = 4X1 + 6X2 >= 4X1 + 6X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 2X >= 2X = s(mark(X)) a__zeros() = 0 >= 0 = zeros() a__length(X) = 2X >= X = length(X) a__and(X1,X2) = X1 + X2 >= X1 + X2 = and(X1,X2) a__isNat(X) = 2X >= 2X = isNat(X) a__isNatList(X) = 2X >= 2X = isNatList(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) -> a__zeros() mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(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__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) Matrix Interpretation Processor: dim=1 interpretation: [and](x0, x1) = x0 + 2x1, [isNat](x0) = x0, [isNatList](x0) = x0, [isNatIList](x0) = 5x0, [a__isNatIList](x0) = 4x0, [a__isNatList](x0) = x0, [length](x0) = x0, [a__isNat](x0) = 2x0, [a__and](x0, x1) = x0 + 4x1, [s](x0) = x0, [a__length](x0) = x0 + 2, [mark](x0) = 4x0, [a__U11](x0, x1) = x0 + 4x1 + 2, [tt] = 0, [cons](x0, x1) = 4x0 + 5x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__U11(tt(),L) = 4L + 2 >= 4L + 2 = s(a__length(mark(L))) a__and(tt(),X) = 4X >= 4X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(s(V1)) = 2V1 >= 2V1 = a__isNat(V1) a__isNatIList(cons(V1,V2)) = 16V1 + 20V2 >= 2V1 + 20V2 = a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(cons(V1,V2)) = 4V1 + 5V2 >= 2V1 + 4V2 = a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) = 5L + 4N + 2 >= 5L + 4N + 2 = a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(and(X1,X2)) = 4X1 + 8X2 >= 4X1 + 4X2 = a__and(mark(X1),X2) mark(isNat(X)) = 4X >= 2X = a__isNat(X) mark(isNatList(X)) = 4X >= X = a__isNatList(X) mark(isNatIList(X)) = 20X >= 4X = a__isNatIList(X) mark(cons(X1,X2)) = 16X1 + 20X2 >= 16X1 + 5X2 = cons(mark(X1),X2) mark(0()) = 0 >= 0 = 0() mark(tt()) = 0 >= 0 = tt() mark(s(X)) = 4X >= 4X = s(mark(X)) a__zeros() = 0 >= 0 = zeros() a__length(X) = X + 2 >= X = length(X) a__and(X1,X2) = X1 + 4X2 >= X1 + 2X2 = and(X1,X2) a__isNat(X) = 2X >= X = isNat(X) a__isNatList(X) = X >= X = isNatList(X) problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) -> a__zeros() mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(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__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) Matrix Interpretation Processor: dim=1 interpretation: [and](x0, x1) = x0 + x1, [isNat](x0) = x0, [isNatList](x0) = x0, [isNatIList](x0) = x0 + 1, [a__isNatIList](x0) = 4x0, [a__isNatList](x0) = x0 + 1, [a__isNat](x0) = x0 + 2, [a__and](x0, x1) = x0 + 4x1, [s](x0) = x0, [a__length](x0) = x0, [mark](x0) = 4x0 + 2, [a__U11](x0, x1) = x0 + 4x1 + 1, [tt] = 2, [cons](x0, x1) = 4x0 + 5x1 + 2, [zeros] = 0, [0] = 0, [a__zeros] = 2 orientation: a__zeros() = 2 >= 2 = cons(0(),zeros()) a__U11(tt(),L) = 4L + 3 >= 4L + 2 = s(a__length(mark(L))) a__and(tt(),X) = 4X + 2 >= 4X + 2 = mark(X) a__isNat(0()) = 2 >= 2 = tt() a__isNat(s(V1)) = V1 + 2 >= V1 + 2 = a__isNat(V1) a__isNatIList(cons(V1,V2)) = 16V1 + 20V2 + 8 >= V1 + 4V2 + 6 = a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(cons(V1,V2)) = 4V1 + 5V2 + 3 >= V1 + 4V2 + 2 = a__and(a__isNat(V1),isNatList(V2)) a__length(cons(N,L)) = 5L + 4N + 2 >= 5L + 4N + 2 = a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) = 2 >= 2 = a__zeros() mark(and(X1,X2)) = 4X1 + 4X2 + 2 >= 4X1 + 4X2 + 2 = a__and(mark(X1),X2) mark(isNat(X)) = 4X + 2 >= X + 2 = a__isNat(X) mark(isNatList(X)) = 4X + 2 >= X + 1 = a__isNatList(X) mark(isNatIList(X)) = 4X + 6 >= 4X = a__isNatIList(X) mark(cons(X1,X2)) = 16X1 + 20X2 + 10 >= 16X1 + 5X2 + 10 = cons(mark(X1),X2) mark(0()) = 2 >= 0 = 0() mark(tt()) = 10 >= 2 = tt() mark(s(X)) = 4X + 2 >= 4X + 2 = s(mark(X)) a__zeros() = 2 >= 0 = zeros() a__and(X1,X2) = X1 + 4X2 >= X1 + X2 = and(X1,X2) a__isNat(X) = X + 2 >= X = isNat(X) a__isNatList(X) = X + 1 >= X = isNatList(X) problem: a__zeros() -> cons(0(),zeros()) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(s(V1)) -> a__isNat(V1) a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) -> a__zeros() mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(s(X)) -> s(mark(X)) a__and(X1,X2) -> and(X1,X2) Matrix Interpretation Processor: dim=1 interpretation: [and](x0, x1) = 2x0 + 5x1, [isNat](x0) = 2x0, [a__isNatList](x0) = 6x0, [a__isNat](x0) = 2x0, [a__and](x0, x1) = 2x0 + 5x1, [s](x0) = x0 + 1, [a__length](x0) = 5x0 + 1, [mark](x0) = 4x0, [a__U11](x0, x1) = x0 + 3x1 + 1, [tt] = 0, [cons](x0, x1) = 2x0 + 3x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__and(tt(),X) = 5X >= 4X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__isNat(s(V1)) = 2V1 + 2 >= 2V1 = a__isNat(V1) a__length(cons(N,L)) = 15L + 10N + 1 >= 15L + 10N + 1 = a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(and(X1,X2)) = 8X1 + 20X2 >= 8X1 + 5X2 = a__and(mark(X1),X2) mark(isNat(X)) = 8X >= 2X = a__isNat(X) mark(cons(X1,X2)) = 8X1 + 12X2 >= 8X1 + 3X2 = cons(mark(X1),X2) mark(s(X)) = 4X + 4 >= 4X + 1 = s(mark(X)) a__and(X1,X2) = 2X1 + 5X2 >= 2X1 + 5X2 = and(X1,X2) problem: a__zeros() -> cons(0(),zeros()) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) -> a__zeros() mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(cons(X1,X2)) -> cons(mark(X1),X2) a__and(X1,X2) -> and(X1,X2) Matrix Interpretation Processor: dim=1 interpretation: [and](x0, x1) = 4x0 + 2x1 + 1, [isNat](x0) = 4x0, [a__isNatList](x0) = 7x0, [a__isNat](x0) = 2x0, [a__and](x0, x1) = 4x0 + 2x1 + 1, [a__length](x0) = 6x0 + 7, [mark](x0) = x0, [a__U11](x0, x1) = x0 + 2x1 + 6, [tt] = 0, [cons](x0, x1) = 2x0 + 5x1, [zeros] = 0, [0] = 0, [a__zeros] = 0 orientation: a__zeros() = 0 >= 0 = cons(0(),zeros()) a__and(tt(),X) = 2X + 1 >= X = mark(X) a__isNat(0()) = 0 >= 0 = tt() a__length(cons(N,L)) = 30L + 12N + 7 >= 30L + 8N + 7 = a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) = 0 >= 0 = a__zeros() mark(and(X1,X2)) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = a__and(mark(X1),X2) mark(isNat(X)) = 4X >= 2X = a__isNat(X) mark(cons(X1,X2)) = 2X1 + 5X2 >= 2X1 + 5X2 = cons(mark(X1),X2) a__and(X1,X2) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = and(X1,X2) problem: a__zeros() -> cons(0(),zeros()) a__isNat(0()) -> tt() a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) -> a__zeros() mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(cons(X1,X2)) -> cons(mark(X1),X2) a__and(X1,X2) -> and(X1,X2) Matrix Interpretation Processor: dim=1 interpretation: [and](x0, x1) = x0 + x1, [isNat](x0) = 4x0, [a__isNatList](x0) = x0, [a__isNat](x0) = 4x0, [a__and](x0, x1) = x0 + 2x1, [a__length](x0) = 4x0 + 2, [mark](x0) = 2x0, [a__U11](x0, x1) = x0 + x1, [tt] = 0, [cons](x0, x1) = 2x0 + x1, [zeros] = 2, [0] = 0, [a__zeros] = 3 orientation: a__zeros() = 3 >= 2 = cons(0(),zeros()) a__isNat(0()) = 0 >= 0 = tt() a__length(cons(N,L)) = 4L + 8N + 2 >= 2L + 8N = a__U11(a__and(a__isNatList(L),isNat(N)),L) mark(zeros()) = 4 >= 3 = a__zeros() mark(and(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = a__and(mark(X1),X2) mark(isNat(X)) = 8X >= 4X = a__isNat(X) mark(cons(X1,X2)) = 4X1 + 2X2 >= 4X1 + X2 = cons(mark(X1),X2) a__and(X1,X2) = X1 + 2X2 >= X1 + X2 = and(X1,X2) problem: a__isNat(0()) -> tt() mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(cons(X1,X2)) -> cons(mark(X1),X2) a__and(X1,X2) -> and(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [and](x0, x1) = [0 0 1]x0 + [0 0 0]x1 [0 1 1] [0 0 0] , [1 0 1] [isNat](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [a__isNat](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__and](x0, x1) = [0 0 1]x0 + [0 0 0]x1 [0 1 1] [0 0 0] , [1 0 1] [1] [mark](x0) = [0 1 0]x0 + [0] [0 0 1] [0], [0] [tt] = [0] [0], [1 0 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [0] [0] = [0] [1] orientation: [1] [0] a__isNat(0()) = [0] >= [0] = tt() [0] [0] [1 1 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] mark(and(X1,X2)) = [0 0 1]X1 + [0 0 0]X2 + [0] >= [0 0 1]X1 + [0 0 0]X2 + [0] = a__and(mark(X1),X2) [0 1 1] [0 0 0] [0] [0 1 1] [0 0 0] [0] [1 0 1] [1] [1 0 1] mark(isNat(X)) = [0 0 0]X + [0] >= [0 0 0]X = a__isNat(X) [0 0 0] [0] [0 0 0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(mark(X1),X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__and(X1,X2) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = and(X1,X2) [0 1 1] [0 0 0] [0 1 1] [0 0 0] problem: mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(cons(X1,X2)) -> cons(mark(X1),X2) a__and(X1,X2) -> and(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [0] [and](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [1] [0 1 1] [0 0 0] [0], [1 0 0] [1 1 0] [0] [a__and](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [1] [0 1 1] [0 0 0] [0], [1 1 1] [mark](x0) = [0 1 0]x0 [0 0 1] , [1 0 0] [0] [cons](x0, x1) = x0 + [0 0 0]x1 + [1] [0 0 0] [0] orientation: [1 1 1] [1 1 0] [1] [1 1 1] [1 1 0] [0] mark(and(X1,X2)) = [0 0 0]X1 + [0 1 0]X2 + [1] >= [0 0 0]X1 + [0 1 0]X2 + [1] = a__and(mark(X1),X2) [0 1 1] [0 0 0] [0] [0 1 1] [0 0 0] [0] [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] [0] mark(cons(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [0 0 0]X2 + [1] = cons(mark(X1),X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 0] [1 1 0] [0] [1 0 0] [1 0 0] [0] a__and(X1,X2) = [0 0 0]X1 + [0 1 0]X2 + [1] >= [0 0 0]X1 + [0 1 0]X2 + [1] = and(X1,X2) [0 1 1] [0 0 0] [0] [0 1 1] [0 0 0] [0] problem: a__and(X1,X2) -> and(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [1] [a__and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 1] [0] orientation: [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] a__and(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 1] [0] [0 0 0] [0 0 0] problem: Qed