/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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()) -> tt() a__U21(tt(),V2) -> a__U22(a__isList(V2)) a__U22(tt()) -> tt() a__U31(tt()) -> tt() a__U41(tt(),V2) -> a__U42(a__isNeList(V2)) a__U42(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isList(V2)) a__U52(tt()) -> tt() a__U61(tt()) -> tt() a__U71(tt(),P) -> a__U72(a__isPal(P)) a__U72(tt()) -> tt() a__U81(tt()) -> tt() a__isList(V) -> a__U11(a__isNeList(V)) a__isList(nil()) -> tt() a__isList(__(V1,V2)) -> a__U21(a__isList(V1),V2) a__isNeList(V) -> a__U31(a__isQid(V)) a__isNeList(__(V1,V2)) -> a__U41(a__isList(V1),V2) a__isNeList(__(V1,V2)) -> a__U51(a__isNeList(V1),V2) a__isNePal(V) -> a__U61(a__isQid(V)) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),P) a__isPal(V) -> a__U81(a__isNePal(V)) a__isPal(nil()) -> tt() a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(i()) -> tt() a__isQid(o()) -> tt() a__isQid(u()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X)) -> a__U11(mark(X)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isList(X)) -> a__isList(X) mark(U31(X)) -> a__U31(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U42(X)) -> a__U42(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U72(X)) -> a__U72(mark(X)) mark(isPal(X)) -> a__isPal(X) mark(U81(X)) -> a__U81(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isList(X) -> isList(X) a__U31(X) -> U31(X) a__U41(X1,X2) -> U41(X1,X2) a__U42(X) -> U42(X) a__isNeList(X) -> isNeList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X1,X2) -> U71(X1,X2) a__U72(X) -> U72(X) a__isPal(X) -> isPal(X) a__U81(X) -> U81(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [a__U72](x0) = x0, [tt] = 0, [a__U61](x0) = x0, [a__U22](x0) = x0, [a____](x0, x1) = 4x0 + x1, [nil] = 1, [a__U71](x0, x1) = x0 + 4x1, [a__isNePal](x0) = x0, [U52](x0) = x0, [u] = 4, [U41](x0, x1) = 4x0 + x1, [a__U81](x0) = 4x0, [a__isPal](x0) = 4x0, [U11](x0) = x0, [isNeList](x0) = x0, [a] = 0, [U21](x0, x1) = x0 + x1, [a__U11](x0) = x0, [U42](x0) = x0, [a__U41](x0, x1) = 4x0 + x1, [__](x0, x1) = 4x0 + x1, [U72](x0) = x0, [a__isList](x0) = x0, [a__isQid](x0) = x0, [o] = 0, [isList](x0) = x0, [a__U52](x0) = x0, [U31](x0) = x0, [a__U42](x0) = x0, [e] = 0, [i] = 6, [a__isNeList](x0) = x0, [a__U31](x0) = x0, [a__U51](x0, x1) = 2x0 + x1, [isPal](x0) = 4x0, [a__U21](x0, x1) = x0 + x1, [U71](x0, x1) = x0 + 4x1, [U61](x0) = x0, [U81](x0) = 4x0, [isQid](x0) = x0, [U51](x0, x1) = 2x0 + x1, [U22](x0) = x0, [isNePal](x0) = x0, [mark](x0) = x0 orientation: a____(__(X,Y),Z) = 16X + 4Y + Z >= 4X + 4Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 4X + 1 >= X = mark(X) a____(nil(),X) = X + 4 >= X = mark(X) a__U11(tt()) = 0 >= 0 = tt() a__U21(tt(),V2) = V2 >= V2 = a__U22(a__isList(V2)) a__U22(tt()) = 0 >= 0 = tt() a__U31(tt()) = 0 >= 0 = tt() a__U41(tt(),V2) = V2 >= V2 = a__U42(a__isNeList(V2)) a__U42(tt()) = 0 >= 0 = tt() a__U51(tt(),V2) = V2 >= V2 = a__U52(a__isList(V2)) a__U52(tt()) = 0 >= 0 = tt() a__U61(tt()) = 0 >= 0 = tt() a__U71(tt(),P) = 4P >= 4P = a__U72(a__isPal(P)) a__U72(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isNeList(V)) a__isList(nil()) = 1 >= 0 = tt() a__isList(__(V1,V2)) = 4V1 + V2 >= V1 + V2 = a__U21(a__isList(V1),V2) a__isNeList(V) = V >= V = a__U31(a__isQid(V)) a__isNeList(__(V1,V2)) = 4V1 + V2 >= 4V1 + V2 = a__U41(a__isList(V1),V2) a__isNeList(__(V1,V2)) = 4V1 + V2 >= 2V1 + V2 = a__U51(a__isNeList(V1),V2) a__isNePal(V) = V >= V = a__U61(a__isQid(V)) a__isNePal(__(I,__(P,I))) = 5I + 4P >= I + 4P = a__U71(a__isQid(I),P) a__isPal(V) = 4V >= 4V = a__U81(a__isNePal(V)) a__isPal(nil()) = 4 >= 0 = tt() a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 6 >= 0 = tt() a__isQid(o()) = 0 >= 0 = tt() a__isQid(u()) = 4 >= 0 = tt() mark(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X)) = X >= X = a__U11(mark(X)) mark(U21(X1,X2)) = X1 + X2 >= X1 + X2 = a__U21(mark(X1),X2) mark(U22(X)) = X >= X = a__U22(mark(X)) mark(isList(X)) = X >= X = a__isList(X) mark(U31(X)) = X >= X = a__U31(mark(X)) mark(U41(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = a__U41(mark(X1),X2) mark(U42(X)) = X >= X = a__U42(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U51(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X)) = X >= X = a__U61(mark(X)) mark(U71(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = a__U71(mark(X1),X2) mark(U72(X)) = X >= X = a__U72(mark(X)) mark(isPal(X)) = 4X >= 4X = a__isPal(X) mark(U81(X)) = 4X >= 4X = a__U81(mark(X)) mark(isQid(X)) = X >= X = a__isQid(X) mark(isNePal(X)) = X >= X = a__isNePal(X) mark(nil()) = 1 >= 1 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 6 >= 6 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 4 >= 4 = u() a____(X1,X2) = 4X1 + X2 >= 4X1 + X2 = __(X1,X2) a__U11(X) = X >= X = U11(X) a__U21(X1,X2) = X1 + X2 >= X1 + X2 = U21(X1,X2) a__U22(X) = X >= X = U22(X) a__isList(X) = X >= X = isList(X) a__U31(X) = X >= X = U31(X) a__U41(X1,X2) = 4X1 + X2 >= 4X1 + X2 = U41(X1,X2) a__U42(X) = X >= X = U42(X) a__isNeList(X) = X >= X = isNeList(X) a__U51(X1,X2) = 2X1 + X2 >= 2X1 + X2 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X) = X >= X = U61(X) a__U71(X1,X2) = X1 + 4X2 >= X1 + 4X2 = U71(X1,X2) a__U72(X) = X >= X = U72(X) a__isPal(X) = 4X >= 4X = isPal(X) a__U81(X) = 4X >= 4X = U81(X) a__isQid(X) = X >= X = isQid(X) a__isNePal(X) = X >= X = isNePal(X) problem: a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z))) a__U11(tt()) -> tt() a__U21(tt(),V2) -> a__U22(a__isList(V2)) a__U22(tt()) -> tt() a__U31(tt()) -> tt() a__U41(tt(),V2) -> a__U42(a__isNeList(V2)) a__U42(tt()) -> tt() a__U51(tt(),V2) -> a__U52(a__isList(V2)) a__U52(tt()) -> tt() a__U61(tt()) -> tt() a__U71(tt(),P) -> a__U72(a__isPal(P)) a__U72(tt()) -> tt() a__U81(tt()) -> tt() a__isList(V) -> a__U11(a__isNeList(V)) a__isList(__(V1,V2)) -> a__U21(a__isList(V1),V2) a__isNeList(V) -> a__U31(a__isQid(V)) a__isNeList(__(V1,V2)) -> a__U41(a__isList(V1),V2) a__isNeList(__(V1,V2)) -> a__U51(a__isNeList(V1),V2) a__isNePal(V) -> a__U61(a__isQid(V)) a__isNePal(__(I,__(P,I))) -> a__U71(a__isQid(I),P) a__isPal(V) -> a__U81(a__isNePal(V)) a__isQid(a()) -> tt() a__isQid(e()) -> tt() a__isQid(o()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X)) -> a__U11(mark(X)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isList(X)) -> a__isList(X) mark(U31(X)) -> a__U31(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U42(X)) -> a__U42(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U72(X)) -> a__U72(mark(X)) mark(isPal(X)) -> a__isPal(X) mark(U81(X)) -> a__U81(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isList(X) -> isList(X) a__U31(X) -> U31(X) a__U41(X1,X2) -> U41(X1,X2) a__U42(X) -> U42(X) a__isNeList(X) -> isNeList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X1,X2) -> U71(X1,X2) a__U72(X) -> U72(X) a__isPal(X) -> isPal(X) a__U81(X) -> U81(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [a__U72](x0) = x0 + 1, [tt] = 1, [a__U61](x0) = x0, [a__U22](x0) = x0 + 1, [a____](x0, x1) = 4x0 + x1 + 6, [nil] = 4, [a__U71](x0, x1) = x0 + 4x1, [a__isNePal](x0) = x0, [U52](x0) = x0, [u] = 0, [U41](x0, x1) = 4x0 + x1, [a__U81](x0) = 2x0, [a__isPal](x0) = 2x0, [U11](x0) = x0, [isNeList](x0) = x0 + 2, [a] = 4, [U21](x0, x1) = x0 + x1 + 2, [a__U11](x0) = x0, [U42](x0) = x0, [a__U41](x0, x1) = 4x0 + x1, [__](x0, x1) = 4x0 + x1 + 6, [U72](x0) = x0 + 1, [a__isList](x0) = x0 + 2, [a__isQid](x0) = x0, [o] = 2, [isList](x0) = x0 + 2, [a__U52](x0) = x0, [U31](x0) = x0 + 2, [a__U42](x0) = x0, [e] = 1, [i] = 4, [a__isNeList](x0) = x0 + 2, [a__U31](x0) = x0 + 2, [a__U51](x0, x1) = 4x0 + x1, [isPal](x0) = 2x0, [a__U21](x0, x1) = x0 + x1 + 2, [U71](x0, x1) = x0 + 4x1, [U61](x0) = x0, [U81](x0) = 2x0, [isQid](x0) = x0, [U51](x0, x1) = 4x0 + x1, [U22](x0) = x0 + 1, [isNePal](x0) = x0, [mark](x0) = x0 orientation: a____(__(X,Y),Z) = 16X + 4Y + Z + 30 >= 4X + 4Y + Z + 12 = a____(mark(X),a____(mark(Y),mark(Z))) a__U11(tt()) = 1 >= 1 = tt() a__U21(tt(),V2) = V2 + 3 >= V2 + 3 = a__U22(a__isList(V2)) a__U22(tt()) = 2 >= 1 = tt() a__U31(tt()) = 3 >= 1 = tt() a__U41(tt(),V2) = V2 + 4 >= V2 + 2 = a__U42(a__isNeList(V2)) a__U42(tt()) = 1 >= 1 = tt() a__U51(tt(),V2) = V2 + 4 >= V2 + 2 = a__U52(a__isList(V2)) a__U52(tt()) = 1 >= 1 = tt() a__U61(tt()) = 1 >= 1 = tt() a__U71(tt(),P) = 4P + 1 >= 2P + 1 = a__U72(a__isPal(P)) a__U72(tt()) = 2 >= 1 = tt() a__U81(tt()) = 2 >= 1 = tt() a__isList(V) = V + 2 >= V + 2 = a__U11(a__isNeList(V)) a__isList(__(V1,V2)) = 4V1 + V2 + 8 >= V1 + V2 + 4 = a__U21(a__isList(V1),V2) a__isNeList(V) = V + 2 >= V + 2 = a__U31(a__isQid(V)) a__isNeList(__(V1,V2)) = 4V1 + V2 + 8 >= 4V1 + V2 + 8 = a__U41(a__isList(V1),V2) a__isNeList(__(V1,V2)) = 4V1 + V2 + 8 >= 4V1 + V2 + 8 = a__U51(a__isNeList(V1),V2) a__isNePal(V) = V >= V = a__U61(a__isQid(V)) a__isNePal(__(I,__(P,I))) = 5I + 4P + 12 >= I + 4P = a__U71(a__isQid(I),P) a__isPal(V) = 2V >= 2V = a__U81(a__isNePal(V)) a__isQid(a()) = 4 >= 1 = tt() a__isQid(e()) = 1 >= 1 = tt() a__isQid(o()) = 2 >= 1 = tt() mark(__(X1,X2)) = 4X1 + X2 + 6 >= 4X1 + X2 + 6 = a____(mark(X1),mark(X2)) mark(U11(X)) = X >= X = a__U11(mark(X)) mark(U21(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = a__U21(mark(X1),X2) mark(U22(X)) = X + 1 >= X + 1 = a__U22(mark(X)) mark(isList(X)) = X + 2 >= X + 2 = a__isList(X) mark(U31(X)) = X + 2 >= X + 2 = a__U31(mark(X)) mark(U41(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = a__U41(mark(X1),X2) mark(U42(X)) = X >= X = a__U42(mark(X)) mark(isNeList(X)) = X + 2 >= X + 2 = a__isNeList(X) mark(U51(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = a__U51(mark(X1),X2) mark(U52(X)) = X >= X = a__U52(mark(X)) mark(U61(X)) = X >= X = a__U61(mark(X)) mark(U71(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = a__U71(mark(X1),X2) mark(U72(X)) = X + 1 >= X + 1 = a__U72(mark(X)) mark(isPal(X)) = 2X >= 2X = a__isPal(X) mark(U81(X)) = 2X >= 2X = a__U81(mark(X)) mark(isQid(X)) = X >= X = a__isQid(X) mark(isNePal(X)) = X >= X = a__isNePal(X) mark(nil()) = 4 >= 4 = nil() mark(tt()) = 1 >= 1 = tt() mark(a()) = 4 >= 4 = a() mark(e()) = 1 >= 1 = e() mark(i()) = 4 >= 4 = i() mark(o()) = 2 >= 2 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = 4X1 + X2 + 6 >= 4X1 + X2 + 6 = __(X1,X2) a__U11(X) = X >= X = U11(X) a__U21(X1,X2) = X1 + X2 + 2 >= X1 + X2 + 2 = U21(X1,X2) a__U22(X) = X + 1 >= X + 1 = U22(X) a__isList(X) = X + 2 >= X + 2 = isList(X) a__U31(X) = X + 2 >= X + 2 = U31(X) a__U41(X1,X2) = 4X1 + X2 >= 4X1 + X2 = U41(X1,X2) a__U42(X) = X >= X = U42(X) a__isNeList(X) = X + 2 >= X + 2 = isNeList(X) a__U51(X1,X2) = 4X1 + X2 >= 4X1 + X2 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X) = X >= X = U61(X) a__U71(X1,X2) = X1 + 4X2 >= X1 + 4X2 = U71(X1,X2) a__U72(X) = X + 1 >= X + 1 = U72(X) a__isPal(X) = 2X >= 2X = isPal(X) a__U81(X) = 2X >= 2X = U81(X) a__isQid(X) = X >= X = isQid(X) a__isNePal(X) = X >= X = isNePal(X) problem: a__U11(tt()) -> tt() a__U21(tt(),V2) -> a__U22(a__isList(V2)) a__U42(tt()) -> tt() a__U52(tt()) -> tt() a__U61(tt()) -> tt() a__U71(tt(),P) -> a__U72(a__isPal(P)) a__isList(V) -> a__U11(a__isNeList(V)) a__isNeList(V) -> a__U31(a__isQid(V)) a__isNeList(__(V1,V2)) -> a__U41(a__isList(V1),V2) a__isNeList(__(V1,V2)) -> a__U51(a__isNeList(V1),V2) a__isNePal(V) -> a__U61(a__isQid(V)) a__isPal(V) -> a__U81(a__isNePal(V)) a__isQid(e()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X)) -> a__U11(mark(X)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isList(X)) -> a__isList(X) mark(U31(X)) -> a__U31(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U42(X)) -> a__U42(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U72(X)) -> a__U72(mark(X)) mark(isPal(X)) -> a__isPal(X) mark(U81(X)) -> a__U81(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(nil()) -> nil() mark(tt()) -> tt() mark(a()) -> a() mark(e()) -> e() mark(i()) -> i() mark(o()) -> o() mark(u()) -> u() a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isList(X) -> isList(X) a__U31(X) -> U31(X) a__U41(X1,X2) -> U41(X1,X2) a__U42(X) -> U42(X) a__isNeList(X) -> isNeList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U71(X1,X2) -> U71(X1,X2) a__U72(X) -> U72(X) a__isPal(X) -> isPal(X) a__U81(X) -> U81(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [a__U72](x0) = x0 + 2, [tt] = 3, [a__U61](x0) = x0, [a__U22](x0) = x0 + 3, [a____](x0, x1) = 2x0 + x1, [nil] = 2, [a__U71](x0, x1) = 6x0 + x1 + 4, [a__isNePal](x0) = x0, [U52](x0) = x0, [u] = 1, [U41](x0, x1) = x0 + x1, [a__U81](x0) = x0, [a__isPal](x0) = x0 + 1, [U11](x0) = x0, [isNeList](x0) = 4x0, [a] = 2, [U21](x0, x1) = x0 + 4x1, [a__U11](x0) = x0, [U42](x0) = x0, [a__U41](x0, x1) = x0 + 2x1, [__](x0, x1) = 2x0 + x1, [U72](x0) = x0 + 2, [a__isList](x0) = 4x0, [a__isQid](x0) = x0, [o] = 0, [isList](x0) = 4x0, [a__U52](x0) = x0, [U31](x0) = 4x0, [a__U42](x0) = x0, [e] = 3, [i] = 3, [a__isNeList](x0) = 4x0, [a__U31](x0) = 4x0, [a__U51](x0, x1) = 2x0 + 2x1, [isPal](x0) = x0 + 1, [a__U21](x0, x1) = x0 + 4x1, [U71](x0, x1) = 6x0 + x1 + 2, [U61](x0) = x0, [U81](x0) = x0, [isQid](x0) = x0, [U51](x0, x1) = 2x0 + x1, [U22](x0) = x0 + 2, [isNePal](x0) = x0, [mark](x0) = 2x0 orientation: a__U11(tt()) = 3 >= 3 = tt() a__U21(tt(),V2) = 4V2 + 3 >= 4V2 + 3 = a__U22(a__isList(V2)) a__U42(tt()) = 3 >= 3 = tt() a__U52(tt()) = 3 >= 3 = tt() a__U61(tt()) = 3 >= 3 = tt() a__U71(tt(),P) = P + 22 >= P + 3 = a__U72(a__isPal(P)) a__isList(V) = 4V >= 4V = a__U11(a__isNeList(V)) a__isNeList(V) = 4V >= 4V = a__U31(a__isQid(V)) a__isNeList(__(V1,V2)) = 8V1 + 4V2 >= 4V1 + 2V2 = a__U41(a__isList(V1),V2) a__isNeList(__(V1,V2)) = 8V1 + 4V2 >= 8V1 + 2V2 = a__U51(a__isNeList(V1),V2) a__isNePal(V) = V >= V = a__U61(a__isQid(V)) a__isPal(V) = V + 1 >= V = a__U81(a__isNePal(V)) a__isQid(e()) = 3 >= 3 = tt() mark(__(X1,X2)) = 4X1 + 2X2 >= 4X1 + 2X2 = a____(mark(X1),mark(X2)) mark(U11(X)) = 2X >= 2X = a__U11(mark(X)) mark(U21(X1,X2)) = 2X1 + 8X2 >= 2X1 + 4X2 = a__U21(mark(X1),X2) mark(U22(X)) = 2X + 4 >= 2X + 3 = a__U22(mark(X)) mark(isList(X)) = 8X >= 4X = a__isList(X) mark(U31(X)) = 8X >= 8X = a__U31(mark(X)) mark(U41(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = a__U41(mark(X1),X2) mark(U42(X)) = 2X >= 2X = a__U42(mark(X)) mark(isNeList(X)) = 8X >= 4X = a__isNeList(X) mark(U51(X1,X2)) = 4X1 + 2X2 >= 4X1 + 2X2 = a__U51(mark(X1),X2) mark(U52(X)) = 2X >= 2X = a__U52(mark(X)) mark(U61(X)) = 2X >= 2X = a__U61(mark(X)) mark(U71(X1,X2)) = 12X1 + 2X2 + 4 >= 12X1 + X2 + 4 = a__U71(mark(X1),X2) mark(U72(X)) = 2X + 4 >= 2X + 2 = a__U72(mark(X)) mark(isPal(X)) = 2X + 2 >= X + 1 = a__isPal(X) mark(U81(X)) = 2X >= 2X = a__U81(mark(X)) mark(isQid(X)) = 2X >= X = a__isQid(X) mark(isNePal(X)) = 2X >= X = a__isNePal(X) mark(nil()) = 4 >= 2 = nil() mark(tt()) = 6 >= 3 = tt() mark(a()) = 4 >= 2 = a() mark(e()) = 6 >= 3 = e() mark(i()) = 6 >= 3 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 2 >= 1 = u() a____(X1,X2) = 2X1 + X2 >= 2X1 + X2 = __(X1,X2) a__U11(X) = X >= X = U11(X) a__U21(X1,X2) = X1 + 4X2 >= X1 + 4X2 = U21(X1,X2) a__U22(X) = X + 3 >= X + 2 = U22(X) a__isList(X) = 4X >= 4X = isList(X) a__U31(X) = 4X >= 4X = U31(X) a__U41(X1,X2) = X1 + 2X2 >= X1 + X2 = U41(X1,X2) a__U42(X) = X >= X = U42(X) a__isNeList(X) = 4X >= 4X = isNeList(X) a__U51(X1,X2) = 2X1 + 2X2 >= 2X1 + X2 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X) = X >= X = U61(X) a__U71(X1,X2) = 6X1 + X2 + 4 >= 6X1 + X2 + 2 = U71(X1,X2) a__U72(X) = X + 2 >= X + 2 = U72(X) a__isPal(X) = X + 1 >= X + 1 = isPal(X) a__U81(X) = X >= X = U81(X) a__isQid(X) = X >= X = isQid(X) a__isNePal(X) = X >= X = isNePal(X) problem: a__U11(tt()) -> tt() a__U21(tt(),V2) -> a__U22(a__isList(V2)) a__U42(tt()) -> tt() a__U52(tt()) -> tt() a__U61(tt()) -> tt() a__isList(V) -> a__U11(a__isNeList(V)) a__isNeList(V) -> a__U31(a__isQid(V)) a__isNeList(__(V1,V2)) -> a__U41(a__isList(V1),V2) a__isNeList(__(V1,V2)) -> a__U51(a__isNeList(V1),V2) a__isNePal(V) -> a__U61(a__isQid(V)) a__isQid(e()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X)) -> a__U11(mark(X)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(isList(X)) -> a__isList(X) mark(U31(X)) -> a__U31(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U42(X)) -> a__U42(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U52(X)) -> a__U52(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U81(X)) -> a__U81(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(o()) -> o() a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) a__isList(X) -> isList(X) a__U31(X) -> U31(X) a__U41(X1,X2) -> U41(X1,X2) a__U42(X) -> U42(X) a__isNeList(X) -> isNeList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U72(X) -> U72(X) a__isPal(X) -> isPal(X) a__U81(X) -> U81(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [a__U72](x0) = 2x0 + 1, [tt] = 2, [a__U61](x0) = x0, [a__U22](x0) = x0 + 6, [a____](x0, x1) = 2x0 + x1, [a__U71](x0, x1) = 4x0 + 4x1 + 4, [a__isNePal](x0) = 2x0, [U52](x0) = x0 + 1, [a__U81](x0) = x0, [U41](x0, x1) = x0 + x1, [a__isPal](x0) = 4x0, [U11](x0) = 2x0, [isNeList](x0) = x0, [U21](x0, x1) = x0 + 2x1 + 4, [a__U11](x0) = 2x0, [U42](x0) = x0, [a__U41](x0, x1) = x0 + x1, [__](x0, x1) = 2x0 + x1, [U72](x0) = 2x0, [a__isList](x0) = 4x0, [a__isQid](x0) = x0, [o] = 0, [isList](x0) = 2x0, [a__U52](x0) = x0 + 1, [U31](x0) = 2x0, [a__U42](x0) = x0, [e] = 4, [a__isNeList](x0) = 2x0, [a__U31](x0) = 2x0, [a__U51](x0, x1) = 2x0 + x1, [isPal](x0) = x0, [a__U21](x0, x1) = x0 + 5x1 + 4, [U71](x0, x1) = 4x0 + x1 + 1, [U61](x0) = x0, [U81](x0) = x0, [isQid](x0) = x0, [U51](x0, x1) = 2x0 + x1, [isNePal](x0) = 2x0, [mark](x0) = 4x0 orientation: a__U11(tt()) = 4 >= 2 = tt() a__U21(tt(),V2) = 5V2 + 6 >= 4V2 + 6 = a__U22(a__isList(V2)) a__U42(tt()) = 2 >= 2 = tt() a__U52(tt()) = 3 >= 2 = tt() a__U61(tt()) = 2 >= 2 = tt() a__isList(V) = 4V >= 4V = a__U11(a__isNeList(V)) a__isNeList(V) = 2V >= 2V = a__U31(a__isQid(V)) a__isNeList(__(V1,V2)) = 4V1 + 2V2 >= 4V1 + V2 = a__U41(a__isList(V1),V2) a__isNeList(__(V1,V2)) = 4V1 + 2V2 >= 4V1 + V2 = a__U51(a__isNeList(V1),V2) a__isNePal(V) = 2V >= V = a__U61(a__isQid(V)) a__isQid(e()) = 4 >= 2 = tt() mark(__(X1,X2)) = 8X1 + 4X2 >= 8X1 + 4X2 = a____(mark(X1),mark(X2)) mark(U11(X)) = 8X >= 8X = a__U11(mark(X)) mark(U21(X1,X2)) = 4X1 + 8X2 + 16 >= 4X1 + 5X2 + 4 = a__U21(mark(X1),X2) mark(isList(X)) = 8X >= 4X = a__isList(X) mark(U31(X)) = 8X >= 8X = a__U31(mark(X)) mark(U41(X1,X2)) = 4X1 + 4X2 >= 4X1 + X2 = a__U41(mark(X1),X2) mark(U42(X)) = 4X >= 4X = a__U42(mark(X)) mark(isNeList(X)) = 4X >= 2X = a__isNeList(X) mark(U51(X1,X2)) = 8X1 + 4X2 >= 8X1 + X2 = a__U51(mark(X1),X2) mark(U52(X)) = 4X + 4 >= 4X + 1 = a__U52(mark(X)) mark(U61(X)) = 4X >= 4X = a__U61(mark(X)) mark(U71(X1,X2)) = 16X1 + 4X2 + 4 >= 16X1 + 4X2 + 4 = a__U71(mark(X1),X2) mark(U81(X)) = 4X >= 4X = a__U81(mark(X)) mark(isQid(X)) = 4X >= X = a__isQid(X) mark(isNePal(X)) = 8X >= 2X = a__isNePal(X) mark(o()) = 0 >= 0 = o() a____(X1,X2) = 2X1 + X2 >= 2X1 + X2 = __(X1,X2) a__U11(X) = 2X >= 2X = U11(X) a__U21(X1,X2) = X1 + 5X2 + 4 >= X1 + 2X2 + 4 = U21(X1,X2) a__isList(X) = 4X >= 2X = isList(X) a__U31(X) = 2X >= 2X = U31(X) a__U41(X1,X2) = X1 + X2 >= X1 + X2 = U41(X1,X2) a__U42(X) = X >= X = U42(X) a__isNeList(X) = 2X >= X = isNeList(X) a__U51(X1,X2) = 2X1 + X2 >= 2X1 + X2 = U51(X1,X2) a__U52(X) = X + 1 >= X + 1 = U52(X) a__U61(X) = X >= X = U61(X) a__U72(X) = 2X + 1 >= 2X = U72(X) a__isPal(X) = 4X >= X = isPal(X) a__U81(X) = X >= X = U81(X) a__isQid(X) = X >= X = isQid(X) a__isNePal(X) = 2X >= 2X = isNePal(X) problem: a__U21(tt(),V2) -> a__U22(a__isList(V2)) a__U42(tt()) -> tt() a__U61(tt()) -> tt() a__isList(V) -> a__U11(a__isNeList(V)) a__isNeList(V) -> a__U31(a__isQid(V)) a__isNeList(__(V1,V2)) -> a__U41(a__isList(V1),V2) a__isNeList(__(V1,V2)) -> a__U51(a__isNeList(V1),V2) a__isNePal(V) -> a__U61(a__isQid(V)) mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X)) -> a__U11(mark(X)) mark(isList(X)) -> a__isList(X) mark(U31(X)) -> a__U31(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U42(X)) -> a__U42(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U81(X)) -> a__U81(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(o()) -> o() a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) a__isList(X) -> isList(X) a__U31(X) -> U31(X) a__U41(X1,X2) -> U41(X1,X2) a__U42(X) -> U42(X) a__isNeList(X) -> isNeList(X) a__U51(X1,X2) -> U51(X1,X2) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__isPal(X) -> isPal(X) a__U81(X) -> U81(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [tt] = 2, [a__U61](x0) = 2x0, [a__U22](x0) = x0 + 4, [a____](x0, x1) = 2x0 + x1 + 5, [a__U71](x0, x1) = x0 + 2x1, [a__isNePal](x0) = 4x0, [U52](x0) = 2x0, [a__U81](x0) = 4x0 + 6, [U41](x0, x1) = 2x0 + x1, [a__isPal](x0) = 2x0, [U11](x0) = x0, [isNeList](x0) = x0, [U21](x0, x1) = 2x0 + x1, [a__U11](x0) = x0, [U42](x0) = 2x0, [a__U41](x0, x1) = 2x0 + x1, [__](x0, x1) = 2x0 + x1 + 5, [a__isList](x0) = x0, [a__isQid](x0) = x0, [o] = 2, [isList](x0) = x0, [a__U52](x0) = 4x0 + 1, [U31](x0) = x0, [a__U42](x0) = 2x0, [a__isNeList](x0) = x0, [a__U31](x0) = x0, [a__U51](x0, x1) = x0 + x1, [isPal](x0) = 2x0, [a__U21](x0, x1) = 2x0 + x1, [U71](x0, x1) = x0 + 2x1, [U61](x0) = 2x0, [U81](x0) = 4x0 + 6, [isQid](x0) = x0, [U51](x0, x1) = x0 + x1, [isNePal](x0) = 4x0, [mark](x0) = x0 orientation: a__U21(tt(),V2) = V2 + 4 >= V2 + 4 = a__U22(a__isList(V2)) a__U42(tt()) = 4 >= 2 = tt() a__U61(tt()) = 4 >= 2 = tt() a__isList(V) = V >= V = a__U11(a__isNeList(V)) a__isNeList(V) = V >= V = a__U31(a__isQid(V)) a__isNeList(__(V1,V2)) = 2V1 + V2 + 5 >= 2V1 + V2 = a__U41(a__isList(V1),V2) a__isNeList(__(V1,V2)) = 2V1 + V2 + 5 >= V1 + V2 = a__U51(a__isNeList(V1),V2) a__isNePal(V) = 4V >= 2V = a__U61(a__isQid(V)) mark(__(X1,X2)) = 2X1 + X2 + 5 >= 2X1 + X2 + 5 = a____(mark(X1),mark(X2)) mark(U11(X)) = X >= X = a__U11(mark(X)) mark(isList(X)) = X >= X = a__isList(X) mark(U31(X)) = X >= X = a__U31(mark(X)) mark(U41(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = a__U41(mark(X1),X2) mark(U42(X)) = 2X >= 2X = a__U42(mark(X)) mark(isNeList(X)) = X >= X = a__isNeList(X) mark(U51(X1,X2)) = X1 + X2 >= X1 + X2 = a__U51(mark(X1),X2) mark(U61(X)) = 2X >= 2X = a__U61(mark(X)) mark(U71(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = a__U71(mark(X1),X2) mark(U81(X)) = 4X + 6 >= 4X + 6 = a__U81(mark(X)) mark(isQid(X)) = X >= X = a__isQid(X) mark(isNePal(X)) = 4X >= 4X = a__isNePal(X) mark(o()) = 2 >= 2 = o() a____(X1,X2) = 2X1 + X2 + 5 >= 2X1 + X2 + 5 = __(X1,X2) a__U11(X) = X >= X = U11(X) a__U21(X1,X2) = 2X1 + X2 >= 2X1 + X2 = U21(X1,X2) a__isList(X) = X >= X = isList(X) a__U31(X) = X >= X = U31(X) a__U41(X1,X2) = 2X1 + X2 >= 2X1 + X2 = U41(X1,X2) a__U42(X) = 2X >= 2X = U42(X) a__isNeList(X) = X >= X = isNeList(X) a__U51(X1,X2) = X1 + X2 >= X1 + X2 = U51(X1,X2) a__U52(X) = 4X + 1 >= 2X = U52(X) a__U61(X) = 2X >= 2X = U61(X) a__isPal(X) = 2X >= 2X = isPal(X) a__U81(X) = 4X + 6 >= 4X + 6 = U81(X) a__isQid(X) = X >= X = isQid(X) a__isNePal(X) = 4X >= 4X = isNePal(X) problem: a__U21(tt(),V2) -> a__U22(a__isList(V2)) a__isList(V) -> a__U11(a__isNeList(V)) a__isNeList(V) -> a__U31(a__isQid(V)) a__isNePal(V) -> a__U61(a__isQid(V)) mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X)) -> a__U11(mark(X)) mark(isList(X)) -> a__isList(X) mark(U31(X)) -> a__U31(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U42(X)) -> a__U42(mark(X)) mark(isNeList(X)) -> a__isNeList(X) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U81(X)) -> a__U81(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(o()) -> o() a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) a__isList(X) -> isList(X) a__U31(X) -> U31(X) a__U41(X1,X2) -> U41(X1,X2) a__U42(X) -> U42(X) a__isNeList(X) -> isNeList(X) a__U51(X1,X2) -> U51(X1,X2) a__U61(X) -> U61(X) a__isPal(X) -> isPal(X) a__U81(X) -> U81(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [0] [tt] = [0] [1], [1] [a__U61](x0) = x0 + [1] [0], [1 0 0] [a__U22](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [a____](x0, x1) = [0 1 1]x0 + x1 + [0] [0 0 0] [0], [1 0 0] [1 0 0] [1] [a__U71](x0, x1) = [0 0 0]x0 + [1 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [1 0 0] [1] [a__isNePal](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [1] [a__U81](x0) = x0 + [1] [0], [1 0 0] [1] [U41](x0, x1) = x0 + [0 0 1]x1 + [0] [0 0 0] [0], [1 0 0] [a__isPal](x0) = [0 0 0]x0 [0 0 0] , [U11](x0) = x0 , [1 0 0] [0] [isNeList](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 0 1] [1 0 0] [U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 1] , [a__U11](x0) = x0 , [0] [U42](x0) = x0 + [1] [0], [1 0 0] [1 0 0] [1] [a__U41](x0, x1) = [0 1 1]x0 + [0 0 1]x1 + [0] [0 0 1] [0 0 0] [0], [1 0 0] [1] [__](x0, x1) = [0 1 1]x0 + x1 + [0] [0 0 0] [0], [1 0 0] [0] [a__isList](x0) = [0 1 0]x0 + [1] [0 0 0] [1], [1 0 0] [0] [a__isQid](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [o] = [0] [0], [1 0 0] [0] [isList](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [1 0 0] [0] [U31](x0) = [0 1 1]x0 + [0] [0 0 0] [1], [1] [a__U42](x0) = x0 + [1] [0], [1 0 0] [0] [a__isNeList](x0) = [0 1 0]x0 + [1] [0 0 0] [1], [1 0 0] [0] [a__U31](x0) = [0 1 1]x0 + [0] [0 0 0] [1], [1 0 1] [1 0 0] [0] [a__U51](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [1 0 0] [a__U21](x0, x1) = [0 0 1]x0 + [0 1 0]x1 [0 0 0] [1 1 1] , [1 1 0] [1 0 0] [1] [U71](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 1 1] [0], [0] [U61](x0) = x0 + [1] [0], [0] [U81](x0) = x0 + [1] [0], [1 0 0] [0] [isQid](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 1] [1 0 0] [0] [U51](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [1 0 0] [0] [isNePal](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 1 0] [0] [mark](x0) = [1 1 1]x0 + [0] [0 0 0] [1] orientation: [1 0 0] [1] [1 0 0] a__U21(tt(),V2) = [0 1 0]V2 + [1] >= [0 0 0]V2 = a__U22(a__isList(V2)) [1 1 1] [0] [0 0 0] [1 0 0] [0] [1 0 0] [0] a__isList(V) = [0 1 0]V + [1] >= [0 1 0]V + [1] = a__U11(a__isNeList(V)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] a__isNeList(V) = [0 1 0]V + [1] >= [0 0 0]V + [1] = a__U31(a__isQid(V)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] a__isNePal(V) = [0 0 0]V + [1] >= [0 0 0]V + [1] = a__U61(a__isQid(V)) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1 1 0] [1] [1 1 0] [1 1 0] [1] mark(__(X1,X2)) = [1 1 1]X1 + [1 1 1]X2 + [1] >= [1 1 1]X1 + [1 1 1]X2 + [1] = a____(mark(X1),mark(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 1 0] [0] [1 1 0] [0] mark(U11(X)) = [1 1 1]X + [0] >= [1 1 1]X + [0] = a__U11(mark(X)) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 0 0] [0] mark(isList(X)) = [1 1 0]X + [1] >= [0 1 0]X + [1] = a__isList(X) [0 0 0] [1] [0 0 0] [1] [1 1 1] [0] [1 1 0] [0] mark(U31(X)) = [1 1 1]X + [1] >= [1 1 1]X + [1] = a__U31(mark(X)) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1 0 1] [1] [1 1 0] [1 0 0] [1] mark(U41(X1,X2)) = [1 1 1]X1 + [1 0 1]X2 + [1] >= [1 1 1]X1 + [0 0 1]X2 + [1] = a__U41(mark(X1),X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 1 0] [1] [1 1 0] [1] mark(U42(X)) = [1 1 1]X + [1] >= [1 1 1]X + [1] = a__U42(mark(X)) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1] [1 0 0] [0] mark(isNeList(X)) = [1 1 0]X + [1] >= [0 1 0]X + [1] = a__isNeList(X) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1 0 0] [1] [1 1 0] [1 0 0] [1] mark(U51(X1,X2)) = [1 1 1]X1 + [1 0 0]X2 + [1] >= [1 1 1]X1 + [0 0 0]X2 + [1] = a__U51(mark(X1),X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [1 1 0] [1] [1 1 0] [1] mark(U61(X)) = [1 1 1]X + [1] >= [1 1 1]X + [1] = a__U61(mark(X)) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] mark(U71(X1,X2)) = [1 1 0]X1 + [1 1 1]X2 + [1] >= [0 0 0]X1 + [1 0 0]X2 + [0] = a__U71(mark(X1),X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [1 1 0] [1] [1 1 0] [1] mark(U81(X)) = [1 1 1]X + [1] >= [1 1 1]X + [1] = a__U81(mark(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] mark(isQid(X)) = [1 0 0]X + [1] >= [0 0 0]X + [0] = a__isQid(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] mark(isNePal(X)) = [1 0 0]X + [1] >= [0 0 0]X + [1] = a__isNePal(X) [0 0 0] [1] [0 0 0] [1] [0] [0] mark(o()) = [0] >= [0] = o() [1] [0] [1 0 0] [1] [1 0 0] [1] a____(X1,X2) = [0 1 1]X1 + X2 + [0] >= [0 1 1]X1 + X2 + [0] = __(X1,X2) [0 0 0] [0] [0 0 0] [0] a__U11(X) = X >= X = U11(X) [1 0 1] [1 0 0] [1 0 1] [1 0 0] a__U21(X1,X2) = [0 0 1]X1 + [0 1 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(X1,X2) [0 0 0] [1 1 1] [0 0 0] [0 0 1] [1 0 0] [0] [1 0 0] [0] a__isList(X) = [0 1 0]X + [1] >= [0 1 0]X + [0] = isList(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] a__U31(X) = [0 1 1]X + [0] >= [0 1 1]X + [0] = U31(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] [1] [1 0 0] [1] a__U41(X1,X2) = [0 1 1]X1 + [0 0 1]X2 + [0] >= X1 + [0 0 1]X2 + [0] = U41(X1,X2) [0 0 1] [0 0 0] [0] [0 0 0] [0] [1] [0] a__U42(X) = X + [1] >= X + [1] = U42(X) [0] [0] [1 0 0] [0] [1 0 0] [0] a__isNeList(X) = [0 1 0]X + [1] >= [0 1 0]X + [1] = isNeList(X) [0 0 0] [1] [0 0 0] [0] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] a__U51(X1,X2) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [0 0 0]X2 + [1] = U51(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1] [0] a__U61(X) = X + [1] >= X + [1] = U61(X) [0] [0] [1 0 0] [1 0 0] a__isPal(X) = [0 0 0]X >= [0 0 0]X = isPal(X) [0 0 0] [0 0 0] [1] [0] a__U81(X) = X + [1] >= X + [1] = U81(X) [0] [0] [1 0 0] [0] [1 0 0] [0] a__isQid(X) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isQid(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [0] a__isNePal(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNePal(X) [0 0 0] [1] [0 0 0] [0] problem: a__isList(V) -> a__U11(a__isNeList(V)) a__isNeList(V) -> a__U31(a__isQid(V)) a__isNePal(V) -> a__U61(a__isQid(V)) mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U11(X)) -> a__U11(mark(X)) mark(isList(X)) -> a__isList(X) mark(U31(X)) -> a__U31(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U42(X)) -> a__U42(mark(X)) mark(U51(X1,X2)) -> a__U51(mark(X1),X2) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1,X2)) -> a__U71(mark(X1),X2) mark(U81(X)) -> a__U81(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(o()) -> o() a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) a__isList(X) -> isList(X) a__U31(X) -> U31(X) a__U41(X1,X2) -> U41(X1,X2) a__isNeList(X) -> isNeList(X) a__U51(X1,X2) -> U51(X1,X2) a__isPal(X) -> isPal(X) a__isQid(X) -> isQid(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [a__U61](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [0] [a____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 1] [0 0 1] [1], [1 1 0] [1 0 0] [a__U71](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 1 0] [0 0 0] , [1 0 0] [1] [a__isNePal](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [a__U81](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 1] [0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 1] [0 1 0] [1], [1 0 0] [a__isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U11](x0) = [0 0 0]x0 [0 1 1] , [0] [isNeList](x0) = x0 + [0] [1], [1 0 0] [1 0 0] [U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 1 0] [a__U11](x0) = [0 0 0]x0 [0 1 1] , [1 0 1] [1] [U42](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1 1 1] [0] [a__U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 1] [0 1 0] [1], [1 0 0] [1 0 0] [0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 1] [0 0 1] [1], [1 1 1] [1] [a__isList](x0) = [0 0 0]x0 + [1] [0 1 1] [1], [1 0 0] [0] [a__isQid](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [0] [o] = [0] [0], [1 0 0] [0] [isList](x0) = [0 0 0]x0 + [1] [0 1 1] [1], [1 0 0] [U31](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [a__U42](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [0] [a__isNeList](x0) = [0 1 0]x0 + [0] [0 0 1] [1], [1 0 0] [a__U31](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [1 0 0] [0] [a__U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 1] [0 0 0] [1], [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__U21](x0, x1) = [0 0 1]x0 + [0 0 0]x1 [1 0 0] [1 0 1] , [1 0 1] [1 0 0] [1] [U71](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 1 0] [0 0 0] [0], [1 0 1] [1] [U61](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [U81](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [0] [isQid](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [1 0 0] [1 0 0] [0] [U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 1] [0 0 0] [1], [1 0 0] [0] [isNePal](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 1] [mark](x0) = [0 1 0]x0 [0 0 1] orientation: [1 1 1] [1] [1 1 1] [0] a__isList(V) = [0 0 0]V + [1] >= [0 0 0]V + [0] = a__U11(a__isNeList(V)) [0 1 1] [1] [0 1 1] [1] [1 0 1] [0] [1 0 0] a__isNeList(V) = [0 1 0]V + [0] >= [0 0 0]V = a__U31(a__isQid(V)) [0 0 1] [1] [0 0 1] [1 0 0] [1] [1 0 0] a__isNePal(V) = [0 0 0]V + [0] >= [0 0 0]V = a__U61(a__isQid(V)) [0 0 0] [0] [0 0 0] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [0] mark(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = a____(mark(X1),mark(X2)) [0 0 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] [1 1 1] [1 1 1] mark(U11(X)) = [0 0 0]X >= [0 0 0]X = a__U11(mark(X)) [0 1 1] [0 1 1] [1 1 1] [1] [1 1 1] [1] mark(isList(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__isList(X) [0 1 1] [1] [0 1 1] [1] [1 0 1] [1 0 1] mark(U31(X)) = [0 0 0]X >= [0 0 0]X = a__U31(mark(X)) [0 0 1] [0 0 1] [1 0 1] [1 1 1] [1] [1 0 1] [1 1 1] [0] mark(U41(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = a__U41(mark(X1),X2) [0 0 1] [0 1 0] [1] [0 0 1] [0 1 0] [1] [1 0 1] [1] [1 0 1] mark(U42(X)) = [0 0 0]X + [0] >= [0 0 0]X = a__U42(mark(X)) [0 0 0] [0] [0 0 0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [0] mark(U51(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = a__U51(mark(X1),X2) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 0 1] [1] [1 0 1] mark(U61(X)) = [0 0 0]X + [0] >= [0 0 0]X = a__U61(mark(X)) [0 0 0] [0] [0 0 0] [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] mark(U71(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = a__U71(mark(X1),X2) [0 1 0] [0 0 0] [0] [0 1 0] [0 0 0] [1 0 1] [1 0 1] mark(U81(X)) = [0 0 0]X >= [0 0 0]X = a__U81(mark(X)) [0 0 1] [0 0 0] [1 0 1] [0] [1 0 0] [0] mark(isQid(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__isQid(X) [0 0 1] [0] [0 0 1] [0] [1 0 0] [1] [1 0 0] [1] mark(isNePal(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = a__isNePal(X) [0 0 0] [1] [0 0 0] [0] [0] [0] mark(o()) = [0] >= [0] = o() [0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] a____(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = __(X1,X2) [0 0 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] [1 1 0] [1 0 0] a__U11(X) = [0 0 0]X >= [0 0 0]X = U11(X) [0 1 1] [0 1 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U21(X1,X2) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(X1,X2) [1 0 0] [1 0 1] [0 0 0] [0 0 0] [1 1 1] [1] [1 0 0] [0] a__isList(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isList(X) [0 1 1] [1] [0 1 1] [1] [1 0 0] [1 0 0] a__U31(X) = [0 0 0]X >= [0 0 0]X = U31(X) [0 0 1] [0 0 1] [1 0 0] [1 1 1] [0] [1 0 0] [1 0 1] [0] a__U41(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U41(X1,X2) [0 0 1] [0 1 0] [1] [0 0 1] [0 1 0] [1] [1 0 1] [0] [0] a__isNeList(X) = [0 1 0]X + [0] >= X + [0] = isNeList(X) [0 0 1] [1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] a__U51(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U51(X1,X2) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 0 0] [1 0 0] a__isPal(X) = [0 0 0]X >= [0 0 0]X = isPal(X) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] a__isQid(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isQid(X) [0 0 1] [0] [0 0 1] [0] problem: a__isNeList(V) -> a__U31(a__isQid(V)) mark(U11(X)) -> a__U11(mark(X)) mark(isList(X)) -> a__isList(X) mark(U31(X)) -> a__U31(mark(X)) mark(U81(X)) -> a__U81(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(isNePal(X)) -> a__isNePal(X) mark(o()) -> o() a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) a__U31(X) -> U31(X) a__U41(X1,X2) -> U41(X1,X2) a__isNeList(X) -> isNeList(X) a__U51(X1,X2) -> U51(X1,X2) a__isPal(X) -> isPal(X) a__isQid(X) -> isQid(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [0] [a____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [1], [1 0 0] [0] [a__isNePal](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [1 0 0] [1 0 0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [0] [a__U81](x0) = [0 0 1]x0 + [0] [0 0 0] [1], [1 0 0] [a__isPal](x0) = [0 0 0]x0 [0 0 0] , [0] [U11](x0) = x0 + [1] [0], [1 0 0] [0] [isNeList](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [1 0 0] [1 0 0] [U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [a__U11](x0) = x0 + [1] [0], [1 0 0] [1 0 0] [a__U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [a__isList](x0) = [0 0 1]x0 [0 0 0] , [1 0 0] [0] [a__isQid](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [0] [o] = [1] [0], [1 1 0] [1] [isList](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 0 0] [0] [U31](x0) = [0 1 1]x0 + [0] [0 0 0] [1], [1 0 0] [1] [a__isNeList](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [1 0 0] [0] [a__U31](x0) = [0 1 1]x0 + [0] [0 0 0] [1], [1 0 0] [1 0 0] [a__U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 1 1] [0] [U81](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [0] [isQid](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [1 0 0] [U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [isNePal](x0) = [0 1 0]x0 [0 0 0] , [1 1 1] [0] [mark](x0) = [0 1 1]x0 + [0] [0 0 0] [1] orientation: [1 0 0] [1] [1 0 0] [0] a__isNeList(V) = [0 0 0]V + [1] >= [0 0 0]V + [1] = a__U31(a__isQid(V)) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 1] [0] mark(U11(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = a__U11(mark(X)) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 0 0] mark(isList(X)) = [0 0 1]X + [0] >= [0 0 1]X = a__isList(X) [0 0 0] [1] [0 0 0] [1 1 1] [1] [1 1 1] [0] mark(U31(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = a__U31(mark(X)) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 1] [0] mark(U81(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__U81(mark(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [0] mark(isQid(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = a__isQid(X) [0 0 0] [1] [0 0 0] [0] [1 1 0] [0] [1 0 0] [0] mark(isNePal(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = a__isNePal(X) [0 0 0] [1] [0 0 0] [1] [1] [0] mark(o()) = [1] >= [1] = o() [1] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] a____(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [0] a__U11(X) = X + [1] >= X + [1] = U11(X) [0] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U21(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] a__U31(X) = [0 1 1]X + [0] >= [0 1 1]X + [0] = U31(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U41(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [0] a__isNeList(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNeList(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U51(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__isPal(X) = [0 0 0]X >= [0 0 0]X = isPal(X) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] a__isQid(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isQid(X) [0 0 0] [0] [0 0 0] [0] problem: mark(isNePal(X)) -> a__isNePal(X) a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) a__U31(X) -> U31(X) a__U41(X1,X2) -> U41(X1,X2) a__U51(X1,X2) -> U51(X1,X2) a__isPal(X) -> isPal(X) a__isQid(X) -> isQid(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [a____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [a__isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [a__isPal](x0) = [0 0 0]x0 [1 0 0] , [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [a__U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [a__isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [mark](x0) = [0 0 0]x0 + [0] [0 0 0] [0] orientation: [1 0 0] [1] [1 0 0] mark(isNePal(X)) = [0 0 0]X + [0] >= [0 0 0]X = a__isNePal(X) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a____(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U11(X) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U21(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U31(X) = [0 0 0]X >= [0 0 0]X = U31(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U41(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U51(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__isPal(X) = [0 0 0]X >= [0 0 0]X = isPal(X) [1 0 0] [0 0 0] [1 0 0] [1 0 0] a__isQid(X) = [0 0 0]X >= [0 0 0]X = isQid(X) [0 0 0] [0 0 0] problem: a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) a__U31(X) -> U31(X) a__U41(X1,X2) -> U41(X1,X2) a__U51(X1,X2) -> U51(X1,X2) a__isPal(X) -> isPal(X) a__isQid(X) -> isQid(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [a____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [a__isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [a__U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1] [a__isQid](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 1 0] , [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [isQid](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] a____(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U11(X) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U21(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U31(X) = [0 0 0]X >= [0 0 0]X = U31(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U41(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U51(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 0] [0 1 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__isPal(X) = [0 0 0]X >= [0 0 0]X = isPal(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] a__isQid(X) = [0 0 0]X + [0] >= [0 0 0]X = isQid(X) [0 0 0] [0] [0 0 0] problem: a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) a__U31(X) -> U31(X) a__U41(X1,X2) -> U41(X1,X2) a__U51(X1,X2) -> U51(X1,X2) a__isPal(X) -> isPal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [a____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1] [a__isPal](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [a__U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [1 0 0] [isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] a____(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U11(X) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U21(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U31(X) = [0 0 0]X >= [0 0 0]X = U31(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U41(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U51(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 1] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] a__isPal(X) = [0 0 0]X + [0] >= [0 0 0]X = isPal(X) [0 0 1] [0] [0 0 0] problem: a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) a__U31(X) -> U31(X) a__U41(X1,X2) -> U41(X1,X2) a__U51(X1,X2) -> U51(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [a____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [a__U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [1] [a__U51](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [1 0 0] [1 0 0] [a__U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] a____(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U11(X) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U21(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U31(X) = [0 0 0]X >= [0 0 0]X = U31(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U41(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] a__U51(X1,X2) = [0 0 1]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] problem: a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) a__U31(X) -> U31(X) a__U41(X1,X2) -> U41(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [a____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [a__U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [1] [a__U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [a__U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] a____(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U11(X) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U21(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U31(X) = [0 0 0]X >= [0 0 0]X = U31(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] a__U41(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] problem: a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) a__U31(X) -> U31(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [a____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [a__U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [a__U31](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1 0 0] [a__U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] a____(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U11(X) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] a__U21(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U21(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] a__U31(X) = [0 0 0]X + [0] >= [0 0 0]X = U31(X) [0 0 0] [0] [0 0 0] problem: a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [a____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [a__U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [1] [a__U21](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] a____(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__U11(X) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] a__U21(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = U21(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] problem: a____(X1,X2) -> __(X1,X2) a__U11(X) -> U11(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [a____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [a__U11](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] a____(X1,X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] a__U11(X) = [0 0 0]X + [0] >= [0 0 0]X = U11(X) [0 0 0] [0] [0 0 0] problem: a____(X1,X2) -> __(X1,X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [1] [a____](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 1] [0], [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] a____(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 1] [0] [0 0 0] [0 0 0] problem: Qed