/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____(__(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: [isNePal](x0) = x0, [isQid](x0) = x0, [U81](x0) = 2x0, [isPal](x0) = 2x0, [U72](x0) = x0, [U71](x0, x1) = 4x0 + 2x1, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = x0 + x1, [isNeList](x0) = x0, [U42](x0) = x0, [U41](x0, x1) = x0 + x1, [U31](x0) = x0, [isList](x0) = x0, [U22](x0) = x0, [U21](x0, x1) = x0 + x1, [U11](x0) = x0, [u] = 0, [o] = 7, [i] = 6, [e] = 0, [a] = 0, [a__isNePal](x0) = x0, [a__isQid](x0) = x0, [a__U81](x0) = 2x0, [a__U72](x0) = x0, [a__isPal](x0) = 2x0, [a__U71](x0, x1) = 4x0 + 2x1, [a__U61](x0) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = x0 + x1, [a__U42](x0) = x0, [a__isNeList](x0) = x0, [a__U41](x0, x1) = x0 + x1, [a__U31](x0) = x0, [a__U22](x0) = x0, [a__isList](x0) = x0, [a__U21](x0, x1) = x0 + x1, [a__U11](x0) = x0, [tt] = 0, [nil] = 4, [mark](x0) = x0, [a____](x0, x1) = 3x0 + x1, [__](x0, x1) = 3x0 + x1 orientation: a____(__(X,Y),Z) = 9X + 3Y + Z >= 3X + 3Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a____(X,nil()) = 3X + 4 >= X = mark(X) a____(nil(),X) = X + 12 >= 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) = 2P >= 2P = 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()) = 4 >= 0 = tt() a__isList(__(V1,V2)) = 3V1 + V2 >= V1 + V2 = a__U21(a__isList(V1),V2) a__isNeList(V) = V >= V = a__U31(a__isQid(V)) a__isNeList(__(V1,V2)) = 3V1 + V2 >= V1 + V2 = a__U41(a__isList(V1),V2) a__isNeList(__(V1,V2)) = 3V1 + V2 >= V1 + V2 = a__U51(a__isNeList(V1),V2) a__isNePal(V) = V >= V = a__U61(a__isQid(V)) a__isNePal(__(I,__(P,I))) = 4I + 3P >= 4I + 2P = a__U71(a__isQid(I),P) a__isPal(V) = 2V >= 2V = a__U81(a__isNePal(V)) a__isPal(nil()) = 8 >= 0 = tt() a__isQid(a()) = 0 >= 0 = tt() a__isQid(e()) = 0 >= 0 = tt() a__isQid(i()) = 6 >= 0 = tt() a__isQid(o()) = 7 >= 0 = tt() a__isQid(u()) = 0 >= 0 = tt() mark(__(X1,X2)) = 3X1 + X2 >= 3X1 + 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)) = X1 + X2 >= X1 + 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)) = X1 + X2 >= X1 + 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)) = 4X1 + 2X2 >= 4X1 + 2X2 = a__U71(mark(X1),X2) mark(U72(X)) = X >= X = 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()) = 0 >= 0 = tt() mark(a()) = 0 >= 0 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 6 >= 6 = i() mark(o()) = 7 >= 7 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = 3X1 + X2 >= 3X1 + 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) = X1 + X2 >= X1 + X2 = U41(X1,X2) a__U42(X) = X >= X = U42(X) a__isNeList(X) = X >= X = isNeList(X) a__U51(X1,X2) = X1 + X2 >= X1 + X2 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X) = X >= X = U61(X) a__U71(X1,X2) = 4X1 + 2X2 >= 4X1 + 2X2 = U71(X1,X2) a__U72(X) = X >= X = 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____(__(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(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) Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = 2x0, [isQid](x0) = 2x0, [U81](x0) = x0, [isPal](x0) = 3x0, [U72](x0) = x0 + 1, [U71](x0, x1) = x0 + 3x1, [U61](x0) = x0, [U52](x0) = x0, [U51](x0, x1) = 2x0 + 4x1, [isNeList](x0) = 4x0, [U42](x0) = x0, [U41](x0, x1) = 2x0 + 4x1, [U31](x0) = x0, [isList](x0) = 4x0, [U22](x0) = x0 + 6, [U21](x0, x1) = 3x0 + 4x1, [U11](x0) = x0, [u] = 4, [o] = 4, [i] = 0, [e] = 1, [a] = 4, [a__isNePal](x0) = 2x0, [a__isQid](x0) = 2x0, [a__U81](x0) = x0, [a__U72](x0) = x0 + 1, [a__isPal](x0) = 3x0, [a__U71](x0, x1) = x0 + 3x1, [a__U61](x0) = x0, [a__U52](x0) = x0, [a__U51](x0, x1) = 2x0 + 4x1, [a__U42](x0) = x0, [a__isNeList](x0) = 4x0, [a__U41](x0, x1) = 2x0 + 4x1, [a__U31](x0) = x0, [a__U22](x0) = x0 + 6, [a__isList](x0) = 4x0, [a__U21](x0, x1) = 3x0 + 4x1, [a__U11](x0) = x0, [tt] = 2, [nil] = 2, [mark](x0) = x0, [a____](x0, x1) = 3x0 + x1, [__](x0, x1) = 3x0 + x1 orientation: a____(__(X,Y),Z) = 9X + 3Y + Z >= 3X + 3Y + Z = a____(mark(X),a____(mark(Y),mark(Z))) a__U11(tt()) = 2 >= 2 = tt() a__U21(tt(),V2) = 4V2 + 6 >= 4V2 + 6 = a__U22(a__isList(V2)) a__U22(tt()) = 8 >= 2 = tt() a__U31(tt()) = 2 >= 2 = tt() a__U41(tt(),V2) = 4V2 + 4 >= 4V2 = a__U42(a__isNeList(V2)) a__U42(tt()) = 2 >= 2 = tt() a__U51(tt(),V2) = 4V2 + 4 >= 4V2 = a__U52(a__isList(V2)) a__U52(tt()) = 2 >= 2 = tt() a__U61(tt()) = 2 >= 2 = tt() a__U71(tt(),P) = 3P + 2 >= 3P + 1 = a__U72(a__isPal(P)) a__U72(tt()) = 3 >= 2 = tt() a__U81(tt()) = 2 >= 2 = tt() a__isList(V) = 4V >= 4V = a__U11(a__isNeList(V)) a__isList(__(V1,V2)) = 12V1 + 4V2 >= 12V1 + 4V2 = a__U21(a__isList(V1),V2) a__isNeList(V) = 4V >= 2V = a__U31(a__isQid(V)) a__isNeList(__(V1,V2)) = 12V1 + 4V2 >= 8V1 + 4V2 = a__U41(a__isList(V1),V2) a__isNeList(__(V1,V2)) = 12V1 + 4V2 >= 8V1 + 4V2 = a__U51(a__isNeList(V1),V2) a__isNePal(V) = 2V >= 2V = a__U61(a__isQid(V)) a__isNePal(__(I,__(P,I))) = 8I + 6P >= 2I + 3P = a__U71(a__isQid(I),P) a__isPal(V) = 3V >= 2V = a__U81(a__isNePal(V)) a__isQid(a()) = 8 >= 2 = tt() a__isQid(e()) = 2 >= 2 = tt() a__isQid(u()) = 8 >= 2 = tt() mark(__(X1,X2)) = 3X1 + X2 >= 3X1 + X2 = a____(mark(X1),mark(X2)) mark(U11(X)) = X >= X = a__U11(mark(X)) mark(U21(X1,X2)) = 3X1 + 4X2 >= 3X1 + 4X2 = a__U21(mark(X1),X2) mark(U22(X)) = X + 6 >= X + 6 = a__U22(mark(X)) mark(isList(X)) = 4X >= 4X = a__isList(X) mark(U31(X)) = X >= X = a__U31(mark(X)) mark(U41(X1,X2)) = 2X1 + 4X2 >= 2X1 + 4X2 = a__U41(mark(X1),X2) mark(U42(X)) = X >= X = a__U42(mark(X)) mark(isNeList(X)) = 4X >= 4X = a__isNeList(X) mark(U51(X1,X2)) = 2X1 + 4X2 >= 2X1 + 4X2 = 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 + 3X2 >= X1 + 3X2 = a__U71(mark(X1),X2) mark(U72(X)) = X + 1 >= X + 1 = a__U72(mark(X)) mark(isPal(X)) = 3X >= 3X = a__isPal(X) mark(U81(X)) = X >= X = a__U81(mark(X)) mark(isQid(X)) = 2X >= 2X = a__isQid(X) mark(isNePal(X)) = 2X >= 2X = a__isNePal(X) mark(nil()) = 2 >= 2 = nil() mark(tt()) = 2 >= 2 = tt() mark(a()) = 4 >= 4 = a() mark(e()) = 1 >= 1 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 4 >= 4 = o() mark(u()) = 4 >= 4 = u() a____(X1,X2) = 3X1 + X2 >= 3X1 + X2 = __(X1,X2) a__U11(X) = X >= X = U11(X) a__U21(X1,X2) = 3X1 + 4X2 >= 3X1 + 4X2 = U21(X1,X2) a__U22(X) = X + 6 >= X + 6 = U22(X) a__isList(X) = 4X >= 4X = isList(X) a__U31(X) = X >= X = U31(X) a__U41(X1,X2) = 2X1 + 4X2 >= 2X1 + 4X2 = U41(X1,X2) a__U42(X) = X >= X = U42(X) a__isNeList(X) = 4X >= 4X = isNeList(X) a__U51(X1,X2) = 2X1 + 4X2 >= 2X1 + 4X2 = U51(X1,X2) a__U52(X) = X >= X = U52(X) a__U61(X) = X >= X = U61(X) a__U71(X1,X2) = X1 + 3X2 >= X1 + 3X2 = U71(X1,X2) a__U72(X) = X + 1 >= X + 1 = U72(X) a__isPal(X) = 3X >= 3X = isPal(X) a__U81(X) = X >= X = U81(X) a__isQid(X) = 2X >= 2X = isQid(X) a__isNePal(X) = 2X >= 2X = 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__U31(tt()) -> tt() a__U42(tt()) -> tt() a__U52(tt()) -> tt() a__U61(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(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: [isNePal](x0) = 2x0 + 2, [isQid](x0) = x0, [U81](x0) = 2x0, [isPal](x0) = 4x0 + 4, [U72](x0) = x0, [U71](x0, x1) = x0 + x1, [U61](x0) = 2x0, [U52](x0) = x0, [U51](x0, x1) = 2x0 + x1, [isNeList](x0) = x0, [U42](x0) = x0, [U41](x0, x1) = x0 + x1, [U31](x0) = x0, [isList](x0) = x0, [U22](x0) = x0, [U21](x0, x1) = 2x0 + x1, [U11](x0) = x0, [u] = 0, [o] = 2, [i] = 3, [e] = 0, [a] = 1, [a__isNePal](x0) = 2x0 + 2, [a__isQid](x0) = x0, [a__U81](x0) = 2x0, [a__U72](x0) = x0, [a__isPal](x0) = 4x0 + 4, [a__U71](x0, x1) = x0 + x1, [a__U61](x0) = 2x0, [a__U52](x0) = x0, [a__U51](x0, x1) = 2x0 + x1, [a__U42](x0) = x0, [a__isNeList](x0) = x0, [a__U41](x0, x1) = x0 + x1, [a__U31](x0) = x0, [a__U22](x0) = x0, [a__isList](x0) = x0, [a__U21](x0, x1) = 2x0 + x1, [a__U11](x0) = x0, [tt] = 0, [nil] = 2, [mark](x0) = x0, [a____](x0, x1) = 2x0 + x1 + 1, [__](x0, x1) = 2x0 + x1 + 1 orientation: a____(__(X,Y),Z) = 4X + 2Y + Z + 3 >= 2X + 2Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z))) a__U11(tt()) = 0 >= 0 = tt() a__U21(tt(),V2) = V2 >= V2 = a__U22(a__isList(V2)) a__U31(tt()) = 0 >= 0 = tt() a__U42(tt()) = 0 >= 0 = tt() a__U52(tt()) = 0 >= 0 = tt() a__U61(tt()) = 0 >= 0 = tt() a__U81(tt()) = 0 >= 0 = tt() a__isList(V) = V >= V = a__U11(a__isNeList(V)) a__isList(__(V1,V2)) = 2V1 + V2 + 1 >= 2V1 + V2 = a__U21(a__isList(V1),V2) a__isNeList(V) = V >= V = a__U31(a__isQid(V)) a__isNeList(__(V1,V2)) = 2V1 + V2 + 1 >= V1 + V2 = a__U41(a__isList(V1),V2) a__isNeList(__(V1,V2)) = 2V1 + V2 + 1 >= 2V1 + V2 = a__U51(a__isNeList(V1),V2) a__isNePal(V) = 2V + 2 >= 2V = a__U61(a__isQid(V)) a__isNePal(__(I,__(P,I))) = 6I + 4P + 6 >= I + P = a__U71(a__isQid(I),P) a__isPal(V) = 4V + 4 >= 4V + 4 = a__U81(a__isNePal(V)) a__isQid(e()) = 0 >= 0 = tt() mark(__(X1,X2)) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = a____(mark(X1),mark(X2)) mark(U11(X)) = X >= X = a__U11(mark(X)) mark(U21(X1,X2)) = 2X1 + X2 >= 2X1 + 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)) = X1 + X2 >= X1 + 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)) = 2X >= 2X = a__U61(mark(X)) mark(U71(X1,X2)) = X1 + X2 >= X1 + X2 = a__U71(mark(X1),X2) mark(U72(X)) = X >= X = a__U72(mark(X)) mark(isPal(X)) = 4X + 4 >= 4X + 4 = a__isPal(X) mark(U81(X)) = 2X >= 2X = a__U81(mark(X)) mark(isQid(X)) = X >= X = a__isQid(X) mark(isNePal(X)) = 2X + 2 >= 2X + 2 = a__isNePal(X) mark(nil()) = 2 >= 2 = nil() mark(tt()) = 0 >= 0 = tt() mark(a()) = 1 >= 1 = a() mark(e()) = 0 >= 0 = e() mark(i()) = 3 >= 3 = i() mark(o()) = 2 >= 2 = o() mark(u()) = 0 >= 0 = u() a____(X1,X2) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = __(X1,X2) a__U11(X) = X >= X = U11(X) a__U21(X1,X2) = 2X1 + X2 >= 2X1 + 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) = X1 + X2 >= X1 + 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) = 2X >= 2X = U61(X) a__U71(X1,X2) = X1 + X2 >= X1 + X2 = U71(X1,X2) a__U72(X) = X >= X = U72(X) a__isPal(X) = 4X + 4 >= 4X + 4 = isPal(X) a__U81(X) = 2X >= 2X = U81(X) a__isQid(X) = X >= X = isQid(X) a__isNePal(X) = 2X + 2 >= 2X + 2 = isNePal(X) problem: a__U11(tt()) -> tt() a__U21(tt(),V2) -> a__U22(a__isList(V2)) a__U31(tt()) -> tt() a__U42(tt()) -> tt() a__U52(tt()) -> tt() a__U61(tt()) -> tt() a__U81(tt()) -> tt() a__isList(V) -> a__U11(a__isNeList(V)) a__isNeList(V) -> a__U31(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: [isNePal](x0) = x0 + 2, [isQid](x0) = x0, [U81](x0) = x0 + 2, [isPal](x0) = x0 + 2, [U72](x0) = x0 + 1, [U71](x0, x1) = 4x0 + x1 + 2, [U61](x0) = x0, [U52](x0) = 4x0 + 4, [U51](x0, x1) = x0 + 5x1 + 2, [isNeList](x0) = x0 + 1, [U42](x0) = x0, [U41](x0, x1) = x0 + 2x1 + 3, [U31](x0) = x0 + 1, [isList](x0) = x0 + 1, [U22](x0) = x0 + 4, [U21](x0, x1) = 4x0 + x1, [U11](x0) = x0 + 1, [u] = 4, [o] = 0, [i] = 0, [e] = 3, [a] = 2, [a__isNePal](x0) = x0 + 2, [a__isQid](x0) = x0, [a__U81](x0) = x0 + 2, [a__U72](x0) = x0 + 1, [a__isPal](x0) = 4x0 + 4, [a__U71](x0, x1) = 4x0 + x1 + 3, [a__U61](x0) = x0, [a__U52](x0) = 4x0 + 4, [a__U51](x0, x1) = x0 + 5x1 + 3, [a__U42](x0) = x0, [a__isNeList](x0) = x0 + 1, [a__U41](x0, x1) = x0 + 3x1 + 3, [a__U31](x0) = x0 + 1, [a__U22](x0) = x0 + 5, [a__isList](x0) = x0 + 2, [a__U21](x0, x1) = 4x0 + x1, [a__U11](x0) = x0 + 1, [tt] = 3, [nil] = 4, [mark](x0) = 4x0, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 orientation: a__U11(tt()) = 4 >= 3 = tt() a__U21(tt(),V2) = V2 + 12 >= V2 + 7 = a__U22(a__isList(V2)) a__U31(tt()) = 4 >= 3 = tt() a__U42(tt()) = 3 >= 3 = tt() a__U52(tt()) = 16 >= 3 = tt() a__U61(tt()) = 3 >= 3 = tt() a__U81(tt()) = 5 >= 3 = tt() a__isList(V) = V + 2 >= V + 2 = a__U11(a__isNeList(V)) a__isNeList(V) = V + 1 >= V + 1 = a__U31(a__isQid(V)) a__isPal(V) = 4V + 4 >= V + 4 = a__U81(a__isNePal(V)) a__isQid(e()) = 3 >= 3 = tt() mark(__(X1,X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = a____(mark(X1),mark(X2)) mark(U11(X)) = 4X + 4 >= 4X + 1 = a__U11(mark(X)) mark(U21(X1,X2)) = 16X1 + 4X2 >= 16X1 + X2 = a__U21(mark(X1),X2) mark(U22(X)) = 4X + 16 >= 4X + 5 = a__U22(mark(X)) mark(isList(X)) = 4X + 4 >= X + 2 = a__isList(X) mark(U31(X)) = 4X + 4 >= 4X + 1 = a__U31(mark(X)) mark(U41(X1,X2)) = 4X1 + 8X2 + 12 >= 4X1 + 3X2 + 3 = a__U41(mark(X1),X2) mark(U42(X)) = 4X >= 4X = a__U42(mark(X)) mark(isNeList(X)) = 4X + 4 >= X + 1 = a__isNeList(X) mark(U51(X1,X2)) = 4X1 + 20X2 + 8 >= 4X1 + 5X2 + 3 = a__U51(mark(X1),X2) mark(U52(X)) = 16X + 16 >= 16X + 4 = a__U52(mark(X)) mark(U61(X)) = 4X >= 4X = a__U61(mark(X)) mark(U71(X1,X2)) = 16X1 + 4X2 + 8 >= 16X1 + X2 + 3 = a__U71(mark(X1),X2) mark(U72(X)) = 4X + 4 >= 4X + 1 = a__U72(mark(X)) mark(isPal(X)) = 4X + 8 >= 4X + 4 = a__isPal(X) mark(U81(X)) = 4X + 8 >= 4X + 2 = a__U81(mark(X)) mark(isQid(X)) = 4X >= X = a__isQid(X) mark(isNePal(X)) = 4X + 8 >= X + 2 = a__isNePal(X) mark(nil()) = 16 >= 4 = nil() mark(tt()) = 12 >= 3 = tt() mark(a()) = 8 >= 2 = a() mark(e()) = 12 >= 3 = e() mark(i()) = 0 >= 0 = i() mark(o()) = 0 >= 0 = o() mark(u()) = 16 >= 4 = u() a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2) a__U11(X) = X + 1 >= X + 1 = U11(X) a__U21(X1,X2) = 4X1 + X2 >= 4X1 + X2 = U21(X1,X2) a__U22(X) = X + 5 >= X + 4 = U22(X) a__isList(X) = X + 2 >= X + 1 = isList(X) a__U31(X) = X + 1 >= X + 1 = U31(X) a__U41(X1,X2) = X1 + 3X2 + 3 >= X1 + 2X2 + 3 = U41(X1,X2) a__U42(X) = X >= X = U42(X) a__isNeList(X) = X + 1 >= X + 1 = isNeList(X) a__U51(X1,X2) = X1 + 5X2 + 3 >= X1 + 5X2 + 2 = U51(X1,X2) a__U52(X) = 4X + 4 >= 4X + 4 = U52(X) a__U61(X) = X >= X = U61(X) a__U71(X1,X2) = 4X1 + X2 + 3 >= 4X1 + X2 + 2 = U71(X1,X2) a__U72(X) = X + 1 >= X + 1 = U72(X) a__isPal(X) = 4X + 4 >= X + 2 = isPal(X) a__U81(X) = X + 2 >= X + 2 = U81(X) a__isQid(X) = X >= X = isQid(X) a__isNePal(X) = X + 2 >= X + 2 = isNePal(X) problem: 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__isPal(V) -> a__U81(a__isNePal(V)) a__isQid(e()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U42(X)) -> a__U42(mark(X)) mark(U61(X)) -> a__U61(mark(X)) mark(isQid(X)) -> a__isQid(X) mark(i()) -> i() 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__U42(X) -> U42(X) a__isNeList(X) -> isNeList(X) a__U52(X) -> U52(X) a__U61(X) -> U61(X) a__U72(X) -> U72(X) a__U81(X) -> U81(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = x0, [isQid](x0) = x0, [U81](x0) = x0, [U72](x0) = 2x0, [U61](x0) = x0 + 2, [U52](x0) = 2x0, [isNeList](x0) = x0, [U42](x0) = x0, [U41](x0, x1) = 2x0 + 4x1, [U31](x0) = x0, [U21](x0, x1) = x0 + 4x1, [U11](x0) = 2x0, [o] = 2, [i] = 4, [e] = 0, [a__isNePal](x0) = 2x0, [a__isQid](x0) = 2x0, [a__U81](x0) = 2x0, [a__U72](x0) = 2x0, [a__isPal](x0) = 4x0, [a__U61](x0) = x0 + 2, [a__U52](x0) = 2x0 + 4, [a__U42](x0) = x0, [a__isNeList](x0) = 2x0, [a__U41](x0, x1) = 2x0 + 4x1 + 2, [a__U31](x0) = x0, [a__isList](x0) = 6x0, [a__U21](x0, x1) = x0 + 4x1, [a__U11](x0) = 2x0, [tt] = 0, [mark](x0) = 4x0, [a____](x0, x1) = x0 + x1 + 4, [__](x0, x1) = x0 + x1 + 1 orientation: a__U42(tt()) = 0 >= 0 = tt() a__U61(tt()) = 2 >= 0 = tt() a__isList(V) = 6V >= 4V = a__U11(a__isNeList(V)) a__isNeList(V) = 2V >= 2V = a__U31(a__isQid(V)) a__isPal(V) = 4V >= 4V = a__U81(a__isNePal(V)) a__isQid(e()) = 0 >= 0 = tt() mark(__(X1,X2)) = 4X1 + 4X2 + 4 >= 4X1 + 4X2 + 4 = a____(mark(X1),mark(X2)) mark(U21(X1,X2)) = 4X1 + 16X2 >= 4X1 + 4X2 = a__U21(mark(X1),X2) mark(U42(X)) = 4X >= 4X = a__U42(mark(X)) mark(U61(X)) = 4X + 8 >= 4X + 2 = a__U61(mark(X)) mark(isQid(X)) = 4X >= 2X = a__isQid(X) mark(i()) = 16 >= 4 = i() mark(o()) = 8 >= 2 = o() a____(X1,X2) = X1 + X2 + 4 >= X1 + X2 + 1 = __(X1,X2) a__U11(X) = 2X >= 2X = U11(X) a__U21(X1,X2) = X1 + 4X2 >= X1 + 4X2 = U21(X1,X2) a__U31(X) = X >= X = U31(X) a__U41(X1,X2) = 2X1 + 4X2 + 2 >= 2X1 + 4X2 = U41(X1,X2) a__U42(X) = X >= X = U42(X) a__isNeList(X) = 2X >= X = isNeList(X) a__U52(X) = 2X + 4 >= 2X = U52(X) a__U61(X) = X + 2 >= X + 2 = U61(X) a__U72(X) = 2X >= 2X = U72(X) a__U81(X) = 2X >= X = U81(X) a__isQid(X) = 2X >= X = isQid(X) a__isNePal(X) = 2X >= X = isNePal(X) problem: a__U42(tt()) -> tt() a__isList(V) -> a__U11(a__isNeList(V)) a__isNeList(V) -> a__U31(a__isQid(V)) a__isPal(V) -> a__U81(a__isNePal(V)) a__isQid(e()) -> tt() mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U42(X)) -> a__U42(mark(X)) mark(isQid(X)) -> a__isQid(X) a__U11(X) -> U11(X) a__U21(X1,X2) -> U21(X1,X2) a__U31(X) -> U31(X) a__U42(X) -> U42(X) a__isNeList(X) -> isNeList(X) a__U61(X) -> U61(X) a__U72(X) -> U72(X) a__U81(X) -> U81(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = x0, [isQid](x0) = x0, [U81](x0) = x0, [U72](x0) = 4x0, [U61](x0) = x0, [isNeList](x0) = x0, [U42](x0) = 2x0 + 2, [U31](x0) = x0, [U21](x0, x1) = 2x0 + 2x1 + 1, [U11](x0) = x0, [e] = 2, [a__isNePal](x0) = x0, [a__isQid](x0) = x0, [a__U81](x0) = x0, [a__U72](x0) = 4x0, [a__isPal](x0) = 2x0, [a__U61](x0) = x0, [a__U42](x0) = 2x0 + 5, [a__isNeList](x0) = x0 + 1, [a__U31](x0) = x0, [a__isList](x0) = 4x0 + 4, [a__U21](x0, x1) = 2x0 + 4x1 + 2, [a__U11](x0) = 4x0, [tt] = 1, [mark](x0) = 4x0, [a____](x0, x1) = x0 + 4x1, [__](x0, x1) = x0 + 4x1 orientation: a__U42(tt()) = 7 >= 1 = tt() a__isList(V) = 4V + 4 >= 4V + 4 = a__U11(a__isNeList(V)) a__isNeList(V) = V + 1 >= V = a__U31(a__isQid(V)) a__isPal(V) = 2V >= V = a__U81(a__isNePal(V)) a__isQid(e()) = 2 >= 1 = tt() mark(__(X1,X2)) = 4X1 + 16X2 >= 4X1 + 16X2 = a____(mark(X1),mark(X2)) mark(U21(X1,X2)) = 8X1 + 8X2 + 4 >= 8X1 + 4X2 + 2 = a__U21(mark(X1),X2) mark(U42(X)) = 8X + 8 >= 8X + 5 = a__U42(mark(X)) mark(isQid(X)) = 4X >= X = a__isQid(X) a__U11(X) = 4X >= X = U11(X) a__U21(X1,X2) = 2X1 + 4X2 + 2 >= 2X1 + 2X2 + 1 = U21(X1,X2) a__U31(X) = X >= X = U31(X) a__U42(X) = 2X + 5 >= 2X + 2 = U42(X) a__isNeList(X) = X + 1 >= X = isNeList(X) a__U61(X) = X >= X = U61(X) a__U72(X) = 4X >= 4X = U72(X) a__U81(X) = X >= X = U81(X) a__isQid(X) = X >= X = isQid(X) a__isNePal(X) = X >= X = isNePal(X) problem: a__isList(V) -> a__U11(a__isNeList(V)) a__isPal(V) -> a__U81(a__isNePal(V)) mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) mark(isQid(X)) -> a__isQid(X) a__U11(X) -> U11(X) a__U31(X) -> U31(X) a__U61(X) -> U61(X) a__U72(X) -> U72(X) a__U81(X) -> U81(X) a__isQid(X) -> isQid(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = x0, [isQid](x0) = 2x0 + 1, [U81](x0) = x0, [U72](x0) = x0, [U61](x0) = x0, [U31](x0) = x0, [U11](x0) = x0, [a__isNePal](x0) = 2x0, [a__isQid](x0) = 4x0 + 4, [a__U81](x0) = x0 + 2, [a__U72](x0) = x0, [a__isPal](x0) = 3x0 + 2, [a__U61](x0) = x0, [a__isNeList](x0) = 2x0, [a__U31](x0) = x0 + 4, [a__isList](x0) = 4x0, [a__U11](x0) = 2x0, [mark](x0) = 4x0 + 4, [a____](x0, x1) = x0 + 4x1 + 4, [__](x0, x1) = 2x0 + 4x1 + 5 orientation: a__isList(V) = 4V >= 4V = a__U11(a__isNeList(V)) a__isPal(V) = 3V + 2 >= 2V + 2 = a__U81(a__isNePal(V)) mark(__(X1,X2)) = 8X1 + 16X2 + 24 >= 4X1 + 16X2 + 24 = a____(mark(X1),mark(X2)) mark(isQid(X)) = 8X + 8 >= 4X + 4 = a__isQid(X) a__U11(X) = 2X >= X = U11(X) a__U31(X) = X + 4 >= X = U31(X) a__U61(X) = X >= X = U61(X) a__U72(X) = X >= X = U72(X) a__U81(X) = X + 2 >= X = U81(X) a__isQid(X) = 4X + 4 >= 2X + 1 = isQid(X) a__isNePal(X) = 2X >= X = isNePal(X) problem: a__isList(V) -> a__U11(a__isNeList(V)) a__isPal(V) -> a__U81(a__isNePal(V)) mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) a__U11(X) -> U11(X) a__U61(X) -> U61(X) a__U72(X) -> U72(X) a__isNePal(X) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = x0, [U72](x0) = x0, [U61](x0) = x0, [U11](x0) = x0, [a__isNePal](x0) = x0 + 1, [a__U81](x0) = x0, [a__U72](x0) = x0, [a__isPal](x0) = x0 + 1, [a__U61](x0) = x0, [a__isNeList](x0) = x0, [a__isList](x0) = x0, [a__U11](x0) = x0, [mark](x0) = 4x0 + 4, [a____](x0, x1) = x0 + x1, [__](x0, x1) = x0 + x1 + 1 orientation: a__isList(V) = V >= V = a__U11(a__isNeList(V)) a__isPal(V) = V + 1 >= V + 1 = a__U81(a__isNePal(V)) mark(__(X1,X2)) = 4X1 + 4X2 + 8 >= 4X1 + 4X2 + 8 = a____(mark(X1),mark(X2)) a__U11(X) = X >= X = U11(X) a__U61(X) = X >= X = U61(X) a__U72(X) = X >= X = U72(X) a__isNePal(X) = X + 1 >= X = isNePal(X) problem: a__isList(V) -> a__U11(a__isNeList(V)) a__isPal(V) -> a__U81(a__isNePal(V)) mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) a__U11(X) -> U11(X) a__U61(X) -> U61(X) a__U72(X) -> U72(X) Matrix Interpretation Processor: dim=1 interpretation: [U72](x0) = x0, [U61](x0) = x0, [U11](x0) = x0, [a__isNePal](x0) = x0, [a__U81](x0) = x0, [a__U72](x0) = x0 + 1, [a__isPal](x0) = x0, [a__U61](x0) = x0, [a__isNeList](x0) = x0, [a__isList](x0) = x0, [a__U11](x0) = x0, [mark](x0) = x0, [a____](x0, x1) = 4x0 + 2x1 + 2, [__](x0, x1) = 4x0 + 2x1 + 2 orientation: a__isList(V) = V >= V = a__U11(a__isNeList(V)) a__isPal(V) = V >= V = a__U81(a__isNePal(V)) mark(__(X1,X2)) = 4X1 + 2X2 + 2 >= 4X1 + 2X2 + 2 = a____(mark(X1),mark(X2)) a__U11(X) = X >= X = U11(X) a__U61(X) = X >= X = U61(X) a__U72(X) = X + 1 >= X = U72(X) problem: a__isList(V) -> a__U11(a__isNeList(V)) a__isPal(V) -> a__U81(a__isNePal(V)) mark(__(X1,X2)) -> a____(mark(X1),mark(X2)) a__U11(X) -> U11(X) a__U61(X) -> U61(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [U61](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__U81](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__isPal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__U61](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__isList](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [a__U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [mark](x0) = [0 0 0]x0 [0 0 0] , [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] [1] [__](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] a__isList(V) = [0 0 0]V >= [0 0 0]V = a__U11(a__isNeList(V)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] a__isPal(V) = [0 0 0]V >= [0 0 0]V = a__U81(a__isNePal(V)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] mark(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = a____(mark(X1),mark(X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 1 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] a__U61(X) = [0 0 0]X >= [0 0 0]X = U61(X) [0 0 0] [0 0 0] problem: a__isList(V) -> a__U11(a__isNeList(V)) a__isPal(V) -> a__U81(a__isNePal(V)) a__U11(X) -> U11(X) a__U61(X) -> U61(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [U61](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__U81](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [a__isPal](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [a__U61](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__isList](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [a__U11](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 0] [1 0 0] a__isList(V) = [0 0 0]V >= [0 0 0]V = a__U11(a__isNeList(V)) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] a__isPal(V) = [0 0 0]V + [0] >= [0 0 0]V = a__U81(a__isNePal(V)) [0 0 0] [0] [0 0 0] [1 1 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] a__U61(X) = [0 0 0]X >= [0 0 0]X = U61(X) [0 0 0] [0 0 0] problem: a__isList(V) -> a__U11(a__isNeList(V)) a__U11(X) -> U11(X) a__U61(X) -> U61(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [U61](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U11](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [1] [a__U61](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [a__isNeList](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [a__isList](x0) = [0 1 0]x0 [1 0 0] , [1 0 0] [a__U11](x0) = [0 1 0]x0 [0 0 0] orientation: [1 0 0] [1 0 0] a__isList(V) = [0 1 0]V >= [0 1 0]V = a__U11(a__isNeList(V)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] a__U11(X) = [0 1 0]X >= [0 1 0]X = U11(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] a__U61(X) = [0 0 0]X + [0] >= [0 0 0]X = U61(X) [0 0 0] [0] [0 0 0] problem: a__isList(V) -> a__U11(a__isNeList(V)) a__U11(X) -> U11(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [a__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [1] [a__isList](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [a__U11](x0) = [0 0 0]x0 [0 0 0] orientation: [1 1 0] [1] [1 0 0] a__isList(V) = [0 0 0]V + [0] >= [0 0 0]V = a__U11(a__isNeList(V)) [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] problem: a__U11(X) -> U11(X) Matrix Interpretation Processor: dim=3 interpretation: [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 1] [0] orientation: [1 0 0] [1] [1 0 0] a__U11(X) = [0 0 0]X + [0] >= [0 0 0]X = U11(X) [0 0 1] [0] [0 0 0] problem: Qed