/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- failure 'Failure("No result of SMT solver - maybe due to some flag of the solver? or the solver was not found in PATH?")' in subprocess 62367 NO Problem: zeros() -> cons(0(),n__zeros()) U11(tt()) -> tt() U21(tt()) -> tt() U31(tt()) -> tt() U41(tt(),V2) -> U42(isNatIList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isNatList(activate(V2))) U52(tt()) -> tt() U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L)) U62(tt(),L) -> s(length(activate(L))) isNat(n__0()) -> tt() isNat(n__length(V1)) -> U11(isNatList(activate(V1))) isNat(n__s(V1)) -> U21(isNat(activate(V1))) isNatIList(V) -> U31(isNatList(activate(V))) isNatIList(n__zeros()) -> tt() isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatList(n__nil()) -> tt() isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) length(nil()) -> 0() length(cons(N,L)) -> U61(isNatList(activate(L)),activate(L),N) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) nil() -> n__nil() activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__nil()) -> nil() activate(X) -> X Proof: Matrix Interpretation Processor: dim=1 interpretation: [length](x0) = x0, [tt] = 0, [U61](x0, x1, x2) = x0 + 2x1 + 3x2, [U41](x0, x1) = 4x0 + 4x1 + 1, [0] = 0, [cons](x0, x1) = 4x0 + 4x1, [isNat](x0) = x0, [n__length](x0) = x0, [s](x0) = 2x0, [U62](x0, x1) = 2x0 + 2x1, [n__s](x0) = 2x0, [U11](x0) = x0, [isNatIList](x0) = x0 + 1, [zeros] = 0, [U31](x0) = x0 + 1, [n__0] = 0, [nil] = 4, [U52](x0) = x0, [U51](x0, x1) = 4x0 + x1, [n__cons](x0, x1) = 4x0 + 4x1, [n__nil] = 4, [U42](x0) = x0, [activate](x0) = x0, [isNatList](x0) = x0, [U21](x0) = x0, [n__zeros] = 0 orientation: zeros() = 0 >= 0 = cons(0(),n__zeros()) U11(tt()) = 0 >= 0 = tt() U21(tt()) = 0 >= 0 = tt() U31(tt()) = 1 >= 0 = tt() U41(tt(),V2) = 4V2 + 1 >= V2 + 1 = U42(isNatIList(activate(V2))) U42(tt()) = 0 >= 0 = tt() U51(tt(),V2) = V2 >= V2 = U52(isNatList(activate(V2))) U52(tt()) = 0 >= 0 = tt() U61(tt(),L,N) = 2L + 3N >= 2L + 2N = U62(isNat(activate(N)),activate(L)) U62(tt(),L) = 2L >= 2L = s(length(activate(L))) isNat(n__0()) = 0 >= 0 = tt() isNat(n__length(V1)) = V1 >= V1 = U11(isNatList(activate(V1))) isNat(n__s(V1)) = 2V1 >= V1 = U21(isNat(activate(V1))) isNatIList(V) = V + 1 >= V + 1 = U31(isNatList(activate(V))) isNatIList(n__zeros()) = 1 >= 0 = tt() isNatIList(n__cons(V1,V2)) = 4V1 + 4V2 + 1 >= 4V1 + 4V2 + 1 = U41(isNat(activate(V1)),activate(V2)) isNatList(n__nil()) = 4 >= 0 = tt() isNatList(n__cons(V1,V2)) = 4V1 + 4V2 >= 4V1 + V2 = U51(isNat(activate(V1)),activate(V2)) length(nil()) = 4 >= 0 = 0() length(cons(N,L)) = 4L + 4N >= 3L + 3N = U61(isNatList(activate(L)),activate(L),N) zeros() = 0 >= 0 = n__zeros() 0() = 0 >= 0 = n__0() length(X) = X >= X = n__length(X) s(X) = 2X >= 2X = n__s(X) cons(X1,X2) = 4X1 + 4X2 >= 4X1 + 4X2 = n__cons(X1,X2) nil() = 4 >= 4 = n__nil() activate(n__zeros()) = 0 >= 0 = zeros() activate(n__0()) = 0 >= 0 = 0() activate(n__length(X)) = X >= X = length(activate(X)) activate(n__s(X)) = 2X >= 2X = s(activate(X)) activate(n__cons(X1,X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(activate(X1),X2) activate(n__nil()) = 4 >= 4 = nil() activate(X) = X >= X = X problem: zeros() -> cons(0(),n__zeros()) U11(tt()) -> tt() U21(tt()) -> tt() U41(tt(),V2) -> U42(isNatIList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isNatList(activate(V2))) U52(tt()) -> tt() U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L)) U62(tt(),L) -> s(length(activate(L))) isNat(n__0()) -> tt() isNat(n__length(V1)) -> U11(isNatList(activate(V1))) isNat(n__s(V1)) -> U21(isNat(activate(V1))) isNatIList(V) -> U31(isNatList(activate(V))) isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) length(cons(N,L)) -> U61(isNatList(activate(L)),activate(L),N) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) nil() -> n__nil() activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__nil()) -> nil() activate(X) -> X Matrix Interpretation Processor: dim=1 interpretation: [length](x0) = x0 + 5, [tt] = 0, [U61](x0, x1, x2) = x0 + x1 + 2x2 + 5, [U41](x0, x1) = 2x0 + 4x1, [0] = 0, [cons](x0, x1) = 2x0 + 3x1, [isNat](x0) = 2x0, [n__length](x0) = x0 + 5, [s](x0) = x0, [U62](x0, x1) = x0 + x1 + 5, [n__s](x0) = x0, [U11](x0) = x0 + 1, [isNatIList](x0) = 2x0, [zeros] = 0, [U31](x0) = x0, [n__0] = 0, [nil] = 0, [U52](x0) = x0, [U51](x0, x1) = x0 + 4x1, [n__cons](x0, x1) = 2x0 + 3x1, [n__nil] = 0, [U42](x0) = 2x0, [activate](x0) = x0, [isNatList](x0) = 2x0, [U21](x0) = x0, [n__zeros] = 0 orientation: zeros() = 0 >= 0 = cons(0(),n__zeros()) U11(tt()) = 1 >= 0 = tt() U21(tt()) = 0 >= 0 = tt() U41(tt(),V2) = 4V2 >= 4V2 = U42(isNatIList(activate(V2))) U42(tt()) = 0 >= 0 = tt() U51(tt(),V2) = 4V2 >= 2V2 = U52(isNatList(activate(V2))) U52(tt()) = 0 >= 0 = tt() U61(tt(),L,N) = L + 2N + 5 >= L + 2N + 5 = U62(isNat(activate(N)),activate(L)) U62(tt(),L) = L + 5 >= L + 5 = s(length(activate(L))) isNat(n__0()) = 0 >= 0 = tt() isNat(n__length(V1)) = 2V1 + 10 >= 2V1 + 1 = U11(isNatList(activate(V1))) isNat(n__s(V1)) = 2V1 >= 2V1 = U21(isNat(activate(V1))) isNatIList(V) = 2V >= 2V = U31(isNatList(activate(V))) isNatIList(n__cons(V1,V2)) = 4V1 + 6V2 >= 4V1 + 4V2 = U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) = 4V1 + 6V2 >= 2V1 + 4V2 = U51(isNat(activate(V1)),activate(V2)) length(cons(N,L)) = 3L + 2N + 5 >= 3L + 2N + 5 = U61(isNatList(activate(L)),activate(L),N) zeros() = 0 >= 0 = n__zeros() 0() = 0 >= 0 = n__0() length(X) = X + 5 >= X + 5 = n__length(X) s(X) = X >= X = n__s(X) cons(X1,X2) = 2X1 + 3X2 >= 2X1 + 3X2 = n__cons(X1,X2) nil() = 0 >= 0 = n__nil() activate(n__zeros()) = 0 >= 0 = zeros() activate(n__0()) = 0 >= 0 = 0() activate(n__length(X)) = X + 5 >= X + 5 = length(activate(X)) activate(n__s(X)) = X >= X = s(activate(X)) activate(n__cons(X1,X2)) = 2X1 + 3X2 >= 2X1 + 3X2 = cons(activate(X1),X2) activate(n__nil()) = 0 >= 0 = nil() activate(X) = X >= X = X problem: zeros() -> cons(0(),n__zeros()) U21(tt()) -> tt() U41(tt(),V2) -> U42(isNatIList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isNatList(activate(V2))) U52(tt()) -> tt() U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L)) U62(tt(),L) -> s(length(activate(L))) isNat(n__0()) -> tt() isNat(n__s(V1)) -> U21(isNat(activate(V1))) isNatIList(V) -> U31(isNatList(activate(V))) isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) length(cons(N,L)) -> U61(isNatList(activate(L)),activate(L),N) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) nil() -> n__nil() activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__nil()) -> nil() activate(X) -> X Matrix Interpretation Processor: dim=1 interpretation: [length](x0) = 2x0, [tt] = 0, [U61](x0, x1, x2) = 2x0 + 2x1 + 4x2, [U41](x0, x1) = x0 + x1 + 6, [0] = 0, [cons](x0, x1) = 2x0 + 2x1, [isNat](x0) = x0, [n__length](x0) = 2x0, [s](x0) = x0, [U62](x0, x1) = x0 + 2x1, [n__s](x0) = x0, [isNatIList](x0) = x0 + 6, [zeros] = 0, [U31](x0) = x0, [n__0] = 0, [nil] = 4, [U52](x0) = 2x0, [U51](x0, x1) = x0 + 2x1, [n__cons](x0, x1) = 2x0 + 2x1, [n__nil] = 4, [U42](x0) = x0, [activate](x0) = x0, [isNatList](x0) = x0, [U21](x0) = x0, [n__zeros] = 0 orientation: zeros() = 0 >= 0 = cons(0(),n__zeros()) U21(tt()) = 0 >= 0 = tt() U41(tt(),V2) = V2 + 6 >= V2 + 6 = U42(isNatIList(activate(V2))) U42(tt()) = 0 >= 0 = tt() U51(tt(),V2) = 2V2 >= 2V2 = U52(isNatList(activate(V2))) U52(tt()) = 0 >= 0 = tt() U61(tt(),L,N) = 2L + 4N >= 2L + N = U62(isNat(activate(N)),activate(L)) U62(tt(),L) = 2L >= 2L = s(length(activate(L))) isNat(n__0()) = 0 >= 0 = tt() isNat(n__s(V1)) = V1 >= V1 = U21(isNat(activate(V1))) isNatIList(V) = V + 6 >= V = U31(isNatList(activate(V))) isNatIList(n__cons(V1,V2)) = 2V1 + 2V2 + 6 >= V1 + V2 + 6 = U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) = 2V1 + 2V2 >= V1 + 2V2 = U51(isNat(activate(V1)),activate(V2)) length(cons(N,L)) = 4L + 4N >= 4L + 4N = U61(isNatList(activate(L)),activate(L),N) zeros() = 0 >= 0 = n__zeros() 0() = 0 >= 0 = n__0() length(X) = 2X >= 2X = n__length(X) s(X) = X >= X = n__s(X) cons(X1,X2) = 2X1 + 2X2 >= 2X1 + 2X2 = n__cons(X1,X2) nil() = 4 >= 4 = n__nil() activate(n__zeros()) = 0 >= 0 = zeros() activate(n__0()) = 0 >= 0 = 0() activate(n__length(X)) = 2X >= 2X = length(activate(X)) activate(n__s(X)) = X >= X = s(activate(X)) activate(n__cons(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = cons(activate(X1),X2) activate(n__nil()) = 4 >= 4 = nil() activate(X) = X >= X = X problem: zeros() -> cons(0(),n__zeros()) U21(tt()) -> tt() U41(tt(),V2) -> U42(isNatIList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isNatList(activate(V2))) U52(tt()) -> tt() U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L)) U62(tt(),L) -> s(length(activate(L))) isNat(n__0()) -> tt() isNat(n__s(V1)) -> U21(isNat(activate(V1))) isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) length(cons(N,L)) -> U61(isNatList(activate(L)),activate(L),N) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) nil() -> n__nil() activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__nil()) -> nil() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [0] [length](x0) = [0 1 0]x0 + [1] [0 1 1] [1], [0] [tt] = [1] [0], [1 0 0] [1 1 0] [1 0 0] [0] [U61](x0, x1, x2) = [0 0 0]x0 + [1 1 0]x1 + [1 0 0]x2 + [1] [0 0 0] [1 1 0] [1 0 0] [1], [1 0 0] [1 0 0] [1] [U41](x0, x1) = [1 0 0]x0 + [1 1 0]x1 + [0] [0 0 0] [1 1 0] [0], [0] [0] = [0] [1], [1 0 0] [1 0 1] [cons](x0, x1) = [1 0 0]x0 + [1 1 0]x1 [1 0 0] [0 0 0] , [1 0 0] [0] [isNat](x0) = [1 1 1]x0 + [0] [0 0 0] [1], [1 1 0] [0] [n__length](x0) = [0 1 0]x0 + [1] [0 0 1] [1], [1 0 0] [0] [s](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [1 1 0] [0] [U62](x0, x1) = [0 0 1]x0 + [1 1 0]x1 + [0] [0 0 0] [0 0 0] [1], [1 0 0] [0] [n__s](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [1] [isNatIList](x0) = [1 1 0]x0 + [0] [0 1 0] [0], [0] [zeros] = [1] [1], [0] [n__0] = [0] [1], [0] [nil] = [0] [0], [1 1 0] [U52](x0) = [0 1 0]x0 [0 0 1] , [1 0 0] [1 0 0] [0] [U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [1], [1 0 0] [1 0 1] [n__cons](x0, x1) = [1 0 0]x0 + [1 1 0]x1 [0 0 0] [0 0 0] , [0] [n__nil] = [0] [0], [1 0 0] [U42](x0) = [0 1 0]x0 [0 1 0] , [1 0 0] [activate](x0) = [0 1 0]x0 [1 1 1] , [1 0 0] [0] [isNatList](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [0] [U21](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [0] [n__zeros] = [1] [0] orientation: [0] [0] zeros() = [1] >= [1] = cons(0(),n__zeros()) [1] [0] [0] [0] U21(tt()) = [1] >= [1] = tt() [0] [0] [1 0 0] [1] [1 0 0] [1] U41(tt(),V2) = [1 1 0]V2 + [0] >= [1 1 0]V2 + [0] = U42(isNatIList(activate(V2))) [1 1 0] [0] [1 1 0] [0] [0] [0] U42(tt()) = [1] >= [1] = tt() [1] [0] [1 0 0] [0] [1 0 0] [0] U51(tt(),V2) = [0 0 0]V2 + [0] >= [0 0 0]V2 + [0] = U52(isNatList(activate(V2))) [0 0 0] [1] [0 0 0] [1] [1] [0] U52(tt()) = [1] >= [1] = tt() [0] [0] [1 1 0] [1 0 0] [0] [1 1 0] [1 0 0] [0] U61(tt(),L,N) = [1 1 0]L + [1 0 0]N + [1] >= [1 1 0]L + [0 0 0]N + [1] = U62(isNat(activate(N)),activate(L)) [1 1 0] [1 0 0] [1] [0 0 0] [0 0 0] [1] [1 1 0] [0] [1 1 0] [0] U62(tt(),L) = [1 1 0]L + [0] >= [0 0 0]L + [0] = s(length(activate(L))) [0 0 0] [1] [0 0 0] [1] [0] [0] isNat(n__0()) = [1] >= [1] = tt() [1] [0] [1 0 0] [0] [1 0 0] [0] isNat(n__s(V1)) = [1 0 0]V1 + [1] >= [0 0 0]V1 + [1] = U21(isNat(activate(V1))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 0] [1] isNatIList(n__cons(V1,V2)) = [2 0 0]V1 + [2 1 1]V2 + [0] >= [1 0 0]V1 + [1 1 0]V2 + [0] = U41(isNat(activate(V1)),activate(V2)) [1 0 0] [1 1 0] [0] [0 0 0] [1 1 0] [0] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 0] [0] isNatList(n__cons(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 + [0] = U51(isNat(activate(V1)),activate(V2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [2 1 1] [2 0 0] [0] [2 1 0] [1 0 0] [0] length(cons(N,L)) = [1 1 0]L + [1 0 0]N + [1] >= [1 1 0]L + [1 0 0]N + [1] = U61(isNatList(activate(L)),activate(L),N) [1 1 0] [2 0 0] [1] [1 1 0] [1 0 0] [1] [0] [0] zeros() = [1] >= [1] = n__zeros() [1] [0] [0] [0] 0() = [0] >= [0] = n__0() [1] [1] [1 1 0] [0] [1 1 0] [0] length(X) = [0 1 0]X + [1] >= [0 1 0]X + [1] = n__length(X) [0 1 1] [1] [0 0 1] [1] [1 0 0] [0] [1 0 0] [0] s(X) = [0 0 0]X + [0] >= [0 0 0]X + [0] = n__s(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 1] [1 0 0] [1 0 1] cons(X1,X2) = [1 0 0]X1 + [1 1 0]X2 >= [1 0 0]X1 + [1 1 0]X2 = n__cons(X1,X2) [1 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] nil() = [0] >= [0] = n__nil() [0] [0] [0] [0] activate(n__zeros()) = [1] >= [1] = zeros() [1] [1] [0] [0] activate(n__0()) = [0] >= [0] = 0() [1] [1] [1 1 0] [0] [1 1 0] [0] activate(n__length(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = length(activate(X)) [1 2 1] [2] [1 2 1] [1] [1 0 0] [0] [1 0 0] [0] activate(n__s(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = s(activate(X)) [1 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 1] [1 0 0] [1 0 1] activate(n__cons(X1,X2)) = [1 0 0]X1 + [1 1 0]X2 >= [1 0 0]X1 + [1 1 0]X2 = cons(activate(X1),X2) [2 0 0] [2 1 1] [1 0 0] [0 0 0] [0] [0] activate(n__nil()) = [0] >= [0] = nil() [0] [0] [1 0 0] activate(X) = [0 1 0]X >= X = X [1 1 1] problem: zeros() -> cons(0(),n__zeros()) U21(tt()) -> tt() U41(tt(),V2) -> U42(isNatIList(activate(V2))) U42(tt()) -> tt() U51(tt(),V2) -> U52(isNatList(activate(V2))) U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L)) U62(tt(),L) -> s(length(activate(L))) isNat(n__0()) -> tt() isNat(n__s(V1)) -> U21(isNat(activate(V1))) isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) length(cons(N,L)) -> U61(isNatList(activate(L)),activate(L),N) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) nil() -> n__nil() activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__nil()) -> nil() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [0] [length](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [0] [tt] = [0] [1], [1 0 1] [1 1 0] [1 0 0] [0] [U61](x0, x1, x2) = [0 0 1]x0 + [0 0 0]x1 + [0 0 0]x2 + [0] [0 0 1] [0 0 0] [0 0 0] [1], [1 0 0] [1 1 0] [U41](x0, x1) = [0 0 0]x0 + [1 0 0]x1 [0 0 0] [0 0 0] , [0] [0] = [0] [0], [1 0 0] [1 1 0] [cons](x0, x1) = [0 0 0]x0 + [1 0 0]x1 [0 0 0] [0 1 1] , [1 0 0] [0] [isNat](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 1 0] [0] [n__length](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [1 1 0] [0] [s](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [1 1 0] [1] [U62](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [0] [0 0 1] [0 0 0] [1], [1 1 0] [0] [n__s](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [isNatIList](x0) = [0 1 0]x0 [0 0 0] , [0] [zeros] = [0] [1], [0] [n__0] = [0] [0], [0] [nil] = [0] [0], [1 0 0] [U52](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U51](x0, x1) = [1 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 1 0] [n__cons](x0, x1) = [0 0 0]x0 + [1 0 0]x1 [0 0 0] [0 0 1] , [0] [n__nil] = [0] [0], [1 1 1] [U42](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [activate](x0) = [0 1 0]x0 [1 0 1] , [1 0 0] [isNatList](x0) = [1 0 0]x0 [0 0 0] , [1 0 0] [0] [U21](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [n__zeros] = [0] [1] orientation: [0] [0] zeros() = [0] >= [0] = cons(0(),n__zeros()) [1] [1] [0] [0] U21(tt()) = [0] >= [0] = tt() [1] [1] [1 1 0] [1 1 0] U41(tt(),V2) = [1 0 0]V2 >= [0 0 0]V2 = U42(isNatIList(activate(V2))) [0 0 0] [0 0 0] [1] [0] U42(tt()) = [0] >= [0] = tt() [1] [1] [1 0 0] [1 0 0] U51(tt(),V2) = [0 0 0]V2 >= [0 0 0]V2 = U52(isNatList(activate(V2))) [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] U61(tt(),L,N) = [0 0 0]L + [0 0 0]N + [1] >= [0 0 0]L + [0 0 0]N + [1] = U62(isNat(activate(N)),activate(L)) [0 0 0] [0 0 0] [2] [0 0 0] [0 0 0] [2] [1 1 0] [1] [1 1 0] [1] U62(tt(),L) = [0 0 0]L + [1] >= [0 0 0]L + [1] = s(length(activate(L))) [0 0 0] [2] [0 0 0] [0] [0] [0] isNat(n__0()) = [0] >= [0] = tt() [1] [1] [1 1 0] [0] [1 0 0] [0] isNat(n__s(V1)) = [0 0 0]V1 + [0] >= [0 0 0]V1 + [0] = U21(isNat(activate(V1))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 1 0] [1 0 0] [1 1 0] isNatIList(n__cons(V1,V2)) = [0 0 0]V1 + [1 0 0]V2 >= [0 0 0]V1 + [1 0 0]V2 = U41(isNat(activate(V1)),activate(V2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] isNatList(n__cons(V1,V2)) = [1 0 0]V1 + [1 1 0]V2 >= [1 0 0]V1 + [0 0 0]V2 = U51(isNat(activate(V1)),activate(V2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [2 1 0] [1 0 0] [0] [2 1 0] [1 0 0] [0] length(cons(N,L)) = [0 0 0]L + [0 0 0]N + [1] >= [0 0 0]L + [0 0 0]N + [0] = U61(isNatList(activate(L)),activate(L),N) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] zeros() = [0] >= [0] = n__zeros() [1] [1] [0] [0] 0() = [0] >= [0] = n__0() [0] [0] [1 1 0] [0] [1 1 0] [0] length(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = n__length(X) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 1 0] [0] s(X) = [0 0 0]X + [1] >= [0 0 0]X + [1] = n__s(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] cons(X1,X2) = [0 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = n__cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 0 1] [0] [0] nil() = [0] >= [0] = n__nil() [0] [0] [0] [0] activate(n__zeros()) = [0] >= [0] = zeros() [1] [1] [0] [0] activate(n__0()) = [0] >= [0] = 0() [0] [0] [1 1 0] [0] [1 1 0] [0] activate(n__length(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = length(activate(X)) [1 1 0] [1] [0 0 0] [1] [1 1 0] [0] [1 1 0] [0] activate(n__s(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = s(activate(X)) [1 1 0] [0] [0 0 0] [0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] activate(n__cons(X1,X2)) = [0 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = cons(activate(X1),X2) [1 0 0] [1 1 1] [0 0 0] [0 1 1] [0] [0] activate(n__nil()) = [0] >= [0] = nil() [0] [0] [1 0 0] activate(X) = [0 1 0]X >= X = X [1 0 1] problem: zeros() -> cons(0(),n__zeros()) U21(tt()) -> tt() U41(tt(),V2) -> U42(isNatIList(activate(V2))) U51(tt(),V2) -> U52(isNatList(activate(V2))) U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L)) U62(tt(),L) -> s(length(activate(L))) isNat(n__0()) -> tt() isNat(n__s(V1)) -> U21(isNat(activate(V1))) isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) length(cons(N,L)) -> U61(isNatList(activate(L)),activate(L),N) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) nil() -> n__nil() activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__nil()) -> nil() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [1] [length](x0) = [0 0 0]x0 + [0] [1 0 1] [0], [0] [tt] = [1] [0], [1 1 0] [1 1 0] [1 0 1] [U61](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 [0 1 0] [1 0 0] [0 1 1] , [1 0 0] [1 0 0] [0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [1], [0] [0] = [0] [0], [1 0 1] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [1 1 0]x1 [0 1 0] [0 0 0] , [1 0 0] [0] [isNat](x0) = [0 0 1]x0 + [1] [0 1 0] [0], [1 1 0] [1] [n__length](x0) = [0 0 0]x0 + [0] [1 0 1] [0], [1 1 0] [s](x0) = [0 0 0]x0 [0 1 0] , [1 0 0] [1 1 0] [1] [U62](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 1 1] [1 0 0] [0], [1 1 0] [n__s](x0) = [0 0 0]x0 [0 1 0] , [1 0 0] [0] [isNatIList](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [0] [zeros] = [1] [0], [0] [n__0] = [0] [0], [0] [nil] = [0] [0], [1 0 0] [U52](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] [1 1 0] , [1 0 1] [1 0 0] [n__cons](x0, x1) = [0 0 0]x0 + [1 1 0]x1 [0 1 0] [0 0 0] , [0] [n__nil] = [0] [0], [1 0 0] [U42](x0) = [0 0 0]x0 [0 0 0] , [activate](x0) = x0 , [1 0 0] [isNatList](x0) = [0 0 0]x0 [1 1 0] , [1 0 1] [0] [U21](x0) = [0 0 1]x0 + [1] [0 0 0] [0], [0] [n__zeros] = [1] [0] orientation: [0] [0] zeros() = [1] >= [1] = cons(0(),n__zeros()) [0] [0] [0] [0] U21(tt()) = [1] >= [1] = tt() [0] [0] [1 0 0] [0] [1 0 0] U41(tt(),V2) = [0 0 0]V2 + [0] >= [0 0 0]V2 = U42(isNatIList(activate(V2))) [0 0 0] [1] [0 0 0] [1 0 0] [1 0 0] U51(tt(),V2) = [0 0 0]V2 >= [0 0 0]V2 = U52(isNatList(activate(V2))) [1 1 0] [0 0 0] [1 1 0] [1 0 1] [1] [1 1 0] [1 0 0] [1] U61(tt(),L,N) = [0 0 0]L + [0 0 0]N + [0] >= [0 0 0]L + [0 0 0]N + [0] = U62(isNat(activate(N)),activate(L)) [1 0 0] [0 1 1] [1] [1 0 0] [0 1 1] [1] [1 1 0] [1] [1 1 0] [1] U62(tt(),L) = [0 0 0]L + [0] >= [0 0 0]L + [0] = s(length(activate(L))) [1 0 0] [1] [0 0 0] [0] [0] [0] isNat(n__0()) = [1] >= [1] = tt() [0] [0] [1 1 0] [0] [1 1 0] [0] isNat(n__s(V1)) = [0 1 0]V1 + [1] >= [0 1 0]V1 + [1] = U21(isNat(activate(V1))) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 0 0] [0] [1 0 0] [1 0 0] [0] isNatIList(n__cons(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 + [1] >= [0 0 0]V1 + [0 0 0]V2 + [0] = U41(isNat(activate(V1)),activate(V2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 1] [1 0 0] [1 0 0] [1 0 0] isNatList(n__cons(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = U51(isNat(activate(V1)),activate(V2)) [1 0 1] [2 1 0] [0 0 0] [1 1 0] [2 1 0] [1 0 1] [1] [2 1 0] [1 0 1] length(cons(N,L)) = [0 0 0]L + [0 0 0]N + [0] >= [0 0 0]L + [0 0 0]N = U61(isNatList(activate(L)),activate(L),N) [1 0 0] [1 1 1] [0] [1 0 0] [0 1 1] [0] [0] zeros() = [1] >= [1] = n__zeros() [0] [0] [0] [0] 0() = [0] >= [0] = n__0() [0] [0] [1 1 0] [1] [1 1 0] [1] length(X) = [0 0 0]X + [0] >= [0 0 0]X + [0] = n__length(X) [1 0 1] [0] [1 0 1] [0] [1 1 0] [1 1 0] s(X) = [0 0 0]X >= [0 0 0]X = n__s(X) [0 1 0] [0 1 0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] cons(X1,X2) = [0 0 0]X1 + [1 1 0]X2 >= [0 0 0]X1 + [1 1 0]X2 = n__cons(X1,X2) [0 1 0] [0 0 0] [0 1 0] [0 0 0] [0] [0] nil() = [0] >= [0] = n__nil() [0] [0] [0] [0] activate(n__zeros()) = [1] >= [1] = zeros() [0] [0] [0] [0] activate(n__0()) = [0] >= [0] = 0() [0] [0] [1 1 0] [1] [1 1 0] [1] activate(n__length(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = length(activate(X)) [1 0 1] [0] [1 0 1] [0] [1 1 0] [1 1 0] activate(n__s(X)) = [0 0 0]X >= [0 0 0]X = s(activate(X)) [0 1 0] [0 1 0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] activate(n__cons(X1,X2)) = [0 0 0]X1 + [1 1 0]X2 >= [0 0 0]X1 + [1 1 0]X2 = cons(activate(X1),X2) [0 1 0] [0 0 0] [0 1 0] [0 0 0] [0] [0] activate(n__nil()) = [0] >= [0] = nil() [0] [0] activate(X) = X >= X = X problem: zeros() -> cons(0(),n__zeros()) U21(tt()) -> tt() U41(tt(),V2) -> U42(isNatIList(activate(V2))) U51(tt(),V2) -> U52(isNatList(activate(V2))) U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L)) U62(tt(),L) -> s(length(activate(L))) isNat(n__0()) -> tt() isNat(n__s(V1)) -> U21(isNat(activate(V1))) isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) nil() -> n__nil() activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__nil()) -> nil() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [0] [length](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [tt] = [0] [1], [1 0 0] [1 1 1] [1 0 1] [0] [U61](x0, x1, x2) = [0 0 0]x0 + [0 1 1]x1 + [1 0 0]x2 + [0] [0 0 0] [1 0 1] [1 1 1] [1], [1 0 0] [1 0 0] [0] [U41](x0, x1) = [0 0 0]x0 + [1 0 0]x1 + [1] [0 0 0] [0 0 0] [1], [0] [0] = [0] [1], [1 0 0] [1 0 0] [cons](x0, x1) = [1 0 1]x0 + [0 1 0]x1 [0 0 0] [0 1 1] , [1 0 0] [isNat](x0) = [0 0 1]x0 [0 0 1] , [1 0 1] [0] [n__length](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [1] [s](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 0 1] [1 0 1] [0] [U62](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [1], [1 0 0] [1] [n__s](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 0 0] [0] [isNatIList](x0) = [1 0 0]x0 + [1] [0 0 0] [1], [0] [zeros] = [1] [0], [0] [n__0] = [0] [1], [1] [nil] = [0] [0], [1 0 0] [U52](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 1] [U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [n__cons](x0, x1) = [1 0 1]x0 + [0 1 0]x1 [0 0 0] [0 1 1] , [1] [n__nil] = [0] [0], [1 0 0] [0] [U42](x0) = [1 0 1]x0 + [0] [0 0 0] [1], [0] [activate](x0) = x0 + [1] [0], [1 0 1] [isNatList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [U21](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [0] [n__zeros] = [0] [0] orientation: [0] [0] zeros() = [1] >= [1] = cons(0(),n__zeros()) [0] [0] [1] [0] U21(tt()) = [0] >= [0] = tt() [1] [1] [1 0 0] [0] [1 0 0] [0] U41(tt(),V2) = [1 0 0]V2 + [1] >= [1 0 0]V2 + [1] = U42(isNatIList(activate(V2))) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1 0 1] U51(tt(),V2) = [0 0 0]V2 >= [0 0 0]V2 = U52(isNatList(activate(V2))) [0 0 0] [0 0 0] [1 1 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] U61(tt(),L,N) = [0 1 1]L + [1 0 0]N + [0] >= [0 0 0]L + [0 0 0]N + [0] = U62(isNat(activate(N)),activate(L)) [1 0 1] [1 1 1] [1] [0 0 0] [0 0 0] [1] [1 0 1] [1] [1 0 1] [1] U62(tt(),L) = [0 0 0]L + [0] >= [0 0 0]L + [0] = s(length(activate(L))) [0 0 0] [1] [0 0 0] [1] [0] [0] isNat(n__0()) = [1] >= [0] = tt() [1] [1] [1 0 0] [1] [1 0 0] [1] isNat(n__s(V1)) = [0 0 1]V1 + [0] >= [0 0 0]V1 + [0] = U21(isNat(activate(V1))) [0 0 1] [0] [0 0 1] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] isNatIList(n__cons(V1,V2)) = [1 0 0]V1 + [1 0 0]V2 + [1] >= [0 0 0]V1 + [1 0 0]V2 + [1] = U41(isNat(activate(V1)),activate(V2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 1 1] [1 0 0] [1 0 1] isNatList(n__cons(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = U51(isNat(activate(V1)),activate(V2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] zeros() = [1] >= [0] = n__zeros() [0] [0] [0] [0] 0() = [0] >= [0] = n__0() [1] [1] [1 0 1] [0] [1 0 1] [0] length(X) = [0 0 0]X + [0] >= [0 0 0]X + [0] = n__length(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] s(X) = [0 0 0]X + [0] >= [0 0 0]X + [0] = n__s(X) [0 0 1] [0] [0 0 1] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] cons(X1,X2) = [1 0 1]X1 + [0 1 0]X2 >= [1 0 1]X1 + [0 1 0]X2 = n__cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1] [1] nil() = [0] >= [0] = n__nil() [0] [0] [0] [0] activate(n__zeros()) = [1] >= [1] = zeros() [0] [0] [0] [0] activate(n__0()) = [1] >= [0] = 0() [1] [1] [1 0 1] [0] [1 0 1] [0] activate(n__length(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = length(activate(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] activate(n__s(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = s(activate(X)) [0 0 1] [0] [0 0 1] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] activate(n__cons(X1,X2)) = [1 0 1]X1 + [0 1 0]X2 + [1] >= [1 0 1]X1 + [0 1 0]X2 = cons(activate(X1),X2) [0 0 0] [0 1 1] [0] [0 0 0] [0 1 1] [1] [1] activate(n__nil()) = [1] >= [0] = nil() [0] [0] [0] activate(X) = X + [1] >= X = X [0] problem: zeros() -> cons(0(),n__zeros()) U41(tt(),V2) -> U42(isNatIList(activate(V2))) U51(tt(),V2) -> U52(isNatList(activate(V2))) U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L)) U62(tt(),L) -> s(length(activate(L))) isNat(n__0()) -> tt() isNat(n__s(V1)) -> U21(isNat(activate(V1))) isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) nil() -> n__nil() activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__nil()) -> nil() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [length](x0) = [1 0 0]x0 + [1] [1 0 0] [1], [0] [tt] = [1] [0], [1 0 0] [1 1 0] [1 1 1] [1] [U61](x0, x1, x2) = [0 1 0]x0 + [1 1 1]x1 + [0 0 0]x2 + [0] [0 0 0] [1 0 0] [1 0 1] [1], [1 0 0] [1 0 0] [1] [U41](x0, x1) = [0 0 0]x0 + [0 0 1]x1 + [1] [0 0 0] [0 0 0] [1], [0] [0] = [0] [0], [1 0 0] [1 1 1] [cons](x0, x1) = [0 0 0]x0 + [0 0 1]x1 [0 0 0] [1 0 1] , [1 0 0] [0] [isNat](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [1 0 0] [0] [n__length](x0) = [1 0 0]x0 + [0] [0 0 0] [1], [s](x0) = x0 , [1 0 0] [1 0 0] [0] [U62](x0, x1) = [0 0 0]x0 + [1 1 0]x1 + [1] [0 0 0] [1 0 0] [1], [n__s](x0) = x0 , [1 0 0] [1] [isNatIList](x0) = [1 0 0]x0 + [1] [0 0 0] [1], [1] [zeros] = [0] [1], [0] [n__0] = [0] [0], [0] [nil] = [0] [0], [1 0 0] [U52](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [1 0 0] [U51](x0, x1) = [1 0 0]x0 + [1 1 0]x1 [1 0 0] [0 1 0] , [1 0 0] [1 1 1] [n__cons](x0, x1) = [0 0 0]x0 + [0 0 1]x1 [0 0 0] [0 0 0] , [0] [n__nil] = [0] [0], [1 0 0] [0] [U42](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [1 0 0] [activate](x0) = [0 1 1]x0 [1 0 1] , [1 0 0] [1] [isNatList](x0) = [1 0 0]x0 + [0] [1 0 0] [1], [1 0 0] [0] [U21](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1] [n__zeros] = [0] [0] orientation: [1] [1] zeros() = [0] >= [0] = cons(0(),n__zeros()) [1] [1] [1 0 0] [1] [1 0 0] [1] U41(tt(),V2) = [0 0 1]V2 + [1] >= [0 0 0]V2 + [1] = U42(isNatIList(activate(V2))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] U51(tt(),V2) = [1 1 0]V2 + [0] >= [0 0 0]V2 + [0] = U52(isNatList(activate(V2))) [0 1 0] [0] [0 0 0] [0] [1 1 0] [1 1 1] [1] [1 0 0] [1 0 0] [0] U61(tt(),L,N) = [1 1 1]L + [0 0 0]N + [1] >= [1 1 1]L + [0 0 0]N + [1] = U62(isNat(activate(N)),activate(L)) [1 0 0] [1 0 1] [1] [1 0 0] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] U62(tt(),L) = [1 1 0]L + [1] >= [1 0 0]L + [1] = s(length(activate(L))) [1 0 0] [1] [1 0 0] [1] [0] [0] isNat(n__0()) = [1] >= [1] = tt() [0] [0] [1 0 0] [0] [1 0 0] [0] isNat(n__s(V1)) = [0 0 0]V1 + [1] >= [0 0 0]V1 + [1] = U21(isNat(activate(V1))) [0 0 1] [0] [0 0 0] [0] [1 0 0] [1 1 1] [1] [1 0 0] [1 0 0] [1] isNatIList(n__cons(V1,V2)) = [1 0 0]V1 + [1 1 1]V2 + [1] >= [0 0 0]V1 + [1 0 1]V2 + [1] = U41(isNat(activate(V1)),activate(V2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 1 1] [1] [1 0 0] [1 0 0] [1] isNatList(n__cons(V1,V2)) = [1 0 0]V1 + [1 1 1]V2 + [0] >= [1 0 0]V1 + [1 1 1]V2 + [0] = U51(isNat(activate(V1)),activate(V2)) [1 0 0] [1 1 1] [1] [1 0 0] [0 1 1] [0] [1] [1] zeros() = [0] >= [0] = n__zeros() [1] [0] [0] [0] 0() = [0] >= [0] = n__0() [0] [0] [1 0 0] [0] [1 0 0] [0] length(X) = [1 0 0]X + [1] >= [1 0 0]X + [0] = n__length(X) [1 0 0] [1] [0 0 0] [1] s(X) = X >= X = n__s(X) [1 0 0] [1 1 1] [1 0 0] [1 1 1] cons(X1,X2) = [0 0 0]X1 + [0 0 1]X2 >= [0 0 0]X1 + [0 0 1]X2 = n__cons(X1,X2) [0 0 0] [1 0 1] [0 0 0] [0 0 0] [0] [0] nil() = [0] >= [0] = n__nil() [0] [0] [1] [1] activate(n__zeros()) = [0] >= [0] = zeros() [1] [1] [0] [0] activate(n__0()) = [0] >= [0] = 0() [0] [0] [1 0 0] [0] [1 0 0] [0] activate(n__length(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = length(activate(X)) [1 0 0] [1] [1 0 0] [1] [1 0 0] [1 0 0] activate(n__s(X)) = [0 1 1]X >= [0 1 1]X = s(activate(X)) [1 0 1] [1 0 1] [1 0 0] [1 1 1] [1 0 0] [1 1 1] activate(n__cons(X1,X2)) = [0 0 0]X1 + [0 0 1]X2 >= [0 0 0]X1 + [0 0 1]X2 = cons(activate(X1),X2) [1 0 0] [1 1 1] [0 0 0] [1 0 1] [0] [0] activate(n__nil()) = [0] >= [0] = nil() [0] [0] [1 0 0] activate(X) = [0 1 1]X >= X = X [1 0 1] problem: zeros() -> cons(0(),n__zeros()) U41(tt(),V2) -> U42(isNatIList(activate(V2))) U51(tt(),V2) -> U52(isNatList(activate(V2))) U62(tt(),L) -> s(length(activate(L))) isNat(n__0()) -> tt() isNat(n__s(V1)) -> U21(isNat(activate(V1))) isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) nil() -> n__nil() activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__nil()) -> nil() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [1] [length](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0] [tt] = [0] [0], [1 1 0] [1 1 1] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 1 0] , [0] [0] = [0] [0], [1 1 0] [cons](x0, x1) = x0 + [0 0 0]x1 [0 0 1] , [1 0 1] [isNat](x0) = [0 1 0]x0 [0 0 0] , [1 0 1] [1] [n__length](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0] [s](x0) = x0 + [0] [1], [1 0 0] [1 1 1] [1] [U62](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 1 0] [1], [0] [n__s](x0) = x0 + [0] [1], [1 1 1] [isNatIList](x0) = [0 0 0]x0 [1 0 0] , [1] [zeros] = [0] [0], [0] [n__0] = [0] [0], [0] [nil] = [1] [0], [1 0 0] [U52](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [1 1 1] [U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [1 0 0] , [1 1 0] [n__cons](x0, x1) = x0 + [0 0 0]x1 [0 0 1] , [0] [n__nil] = [1] [0], [1 0 0] [U42](x0) = [0 0 0]x0 [0 0 0] , [activate](x0) = x0 , [1 1 1] [isNatList](x0) = [0 0 0]x0 [1 0 0] , [1 0 0] [U21](x0) = [0 0 0]x0 [0 0 0] , [1] [n__zeros] = [0] [0] orientation: [1] [1] zeros() = [0] >= [0] = cons(0(),n__zeros()) [0] [0] [1 1 1] [1 1 1] U41(tt(),V2) = [0 0 0]V2 >= [0 0 0]V2 = U42(isNatIList(activate(V2))) [0 1 0] [0 0 0] [1 1 1] [1 1 1] U51(tt(),V2) = [0 0 0]V2 >= [0 0 0]V2 = U52(isNatList(activate(V2))) [1 0 0] [0 0 0] [1 1 1] [1] [1 0 1] [1] U62(tt(),L) = [0 0 0]L + [0] >= [0 0 0]L + [0] = s(length(activate(L))) [0 1 0] [1] [0 0 0] [1] [0] [0] isNat(n__0()) = [0] >= [0] = tt() [0] [0] [1 0 1] [1] [1 0 1] isNat(n__s(V1)) = [0 1 0]V1 + [0] >= [0 0 0]V1 = U21(isNat(activate(V1))) [0 0 0] [0] [0 0 0] [1 1 1] [1 1 1] [1 1 1] [1 1 1] isNatIList(n__cons(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = U41(isNat(activate(V1)),activate(V2)) [1 0 0] [1 1 0] [0 0 0] [0 1 0] [1 1 1] [1 1 1] [1 1 1] [1 1 1] isNatList(n__cons(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = U51(isNat(activate(V1)),activate(V2)) [1 0 0] [1 1 0] [0 0 0] [1 0 0] [1] [1] zeros() = [0] >= [0] = n__zeros() [0] [0] [0] [0] 0() = [0] >= [0] = n__0() [0] [0] [1 0 1] [1] [1 0 1] [1] length(X) = [0 0 0]X + [0] >= [0 0 0]X + [0] = n__length(X) [0 0 0] [0] [0 0 0] [0] [0] [0] s(X) = X + [0] >= X + [0] = n__s(X) [1] [1] [1 1 0] [1 1 0] cons(X1,X2) = X1 + [0 0 0]X2 >= X1 + [0 0 0]X2 = n__cons(X1,X2) [0 0 1] [0 0 1] [0] [0] nil() = [1] >= [1] = n__nil() [0] [0] [1] [1] activate(n__zeros()) = [0] >= [0] = zeros() [0] [0] [0] [0] activate(n__0()) = [0] >= [0] = 0() [0] [0] [1 0 1] [1] [1 0 1] [1] activate(n__length(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = length(activate(X)) [0 0 0] [0] [0 0 0] [0] [0] [0] activate(n__s(X)) = X + [0] >= X + [0] = s(activate(X)) [1] [1] [1 1 0] [1 1 0] activate(n__cons(X1,X2)) = X1 + [0 0 0]X2 >= X1 + [0 0 0]X2 = cons(activate(X1),X2) [0 0 1] [0 0 1] [0] [0] activate(n__nil()) = [1] >= [1] = nil() [0] [0] activate(X) = X >= X = X problem: zeros() -> cons(0(),n__zeros()) U41(tt(),V2) -> U42(isNatIList(activate(V2))) U51(tt(),V2) -> U52(isNatList(activate(V2))) U62(tt(),L) -> s(length(activate(L))) isNat(n__0()) -> tt() isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) nil() -> n__nil() activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__nil()) -> nil() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [length](x0) = [0 0 0]x0 [0 1 0] , [0] [tt] = [0] [1], [1 0 0] [1 0 0] [0] [U41](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [0] [0 0 0] [0 1 0] [1], [0] [0] = [0] [0], [1 0 0] [1 0 0] [cons](x0, x1) = [0 0 1]x0 + [0 1 0]x1 [0 0 0] [0 0 0] , [1 0 0] [0] [isNat](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 1 0] [n__length](x0) = [0 0 0]x0 [0 1 0] , [1 1 0] [s](x0) = [0 0 0]x0 [0 1 1] , [1 0 1] [1 1 0] [0] [U62](x0, x1) = [0 0 0]x0 + [1 1 0]x1 + [0] [0 0 0] [0 1 0] [1], [1 1 0] [n__s](x0) = [0 0 0]x0 [0 1 1] , [1 0 0] [0] [isNatIList](x0) = [0 1 0]x0 + [1] [0 1 0] [1], [0] [zeros] = [1] [0], [0] [n__0] = [0] [0], [0] [nil] = [0] [0], [1 0 0] [U52](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [1 1 0] [U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [n__cons](x0, x1) = [0 0 1]x0 + [0 1 0]x1 [0 0 0] [0 0 0] , [0] [n__nil] = [0] [0], [1 0 0] [0] [U42](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [activate](x0) = x0 , [1 1 0] [1] [isNatList](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0] [n__zeros] = [1] [0] orientation: [0] [0] zeros() = [1] >= [1] = cons(0(),n__zeros()) [0] [0] [1 0 0] [0] [1 0 0] [0] U41(tt(),V2) = [0 1 0]V2 + [0] >= [0 0 0]V2 + [0] = U42(isNatIList(activate(V2))) [0 1 0] [1] [0 0 0] [1] [1 1 0] [1] [1 1 0] [1] U51(tt(),V2) = [0 0 0]V2 + [0] >= [0 0 0]V2 + [0] = U52(isNatList(activate(V2))) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1] [1 1 0] U62(tt(),L) = [1 1 0]L + [0] >= [0 0 0]L = s(length(activate(L))) [0 1 0] [1] [0 1 0] [0] [0] isNat(n__0()) = [0] >= [0] = tt() [1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] isNatIList(n__cons(V1,V2)) = [0 0 1]V1 + [0 1 0]V2 + [1] >= [0 0 0]V1 + [0 1 0]V2 + [0] = U41(isNat(activate(V1)),activate(V2)) [0 0 1] [0 1 0] [1] [0 0 0] [0 1 0] [1] [1 0 1] [1 1 0] [1] [1 0 1] [1 1 0] [1] isNatList(n__cons(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 + [0] = U51(isNat(activate(V1)),activate(V2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [0] [0] zeros() = [1] >= [1] = n__zeros() [0] [0] [0] [0] 0() = [0] >= [0] = n__0() [0] [0] [1 1 0] [1 1 0] length(X) = [0 0 0]X >= [0 0 0]X = n__length(X) [0 1 0] [0 1 0] [1 1 0] [1 1 0] s(X) = [0 0 0]X >= [0 0 0]X = n__s(X) [0 1 1] [0 1 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] cons(X1,X2) = [0 0 1]X1 + [0 1 0]X2 >= [0 0 1]X1 + [0 1 0]X2 = n__cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] nil() = [0] >= [0] = n__nil() [0] [0] [0] [0] activate(n__zeros()) = [1] >= [1] = zeros() [0] [0] [0] [0] activate(n__0()) = [0] >= [0] = 0() [0] [0] [1 1 0] [1 1 0] activate(n__length(X)) = [0 0 0]X >= [0 0 0]X = length(activate(X)) [0 1 0] [0 1 0] [1 1 0] [1 1 0] activate(n__s(X)) = [0 0 0]X >= [0 0 0]X = s(activate(X)) [0 1 1] [0 1 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] activate(n__cons(X1,X2)) = [0 0 1]X1 + [0 1 0]X2 >= [0 0 1]X1 + [0 1 0]X2 = cons(activate(X1),X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] activate(n__nil()) = [0] >= [0] = nil() [0] [0] activate(X) = X >= X = X problem: zeros() -> cons(0(),n__zeros()) U41(tt(),V2) -> U42(isNatIList(activate(V2))) U51(tt(),V2) -> U52(isNatList(activate(V2))) isNat(n__0()) -> tt() isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) nil() -> n__nil() activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__nil()) -> nil() activate(X) -> X Matrix Interpretation Processor: dim=1 interpretation: [length](x0) = x0, [tt] = 0, [U41](x0, x1) = x0 + 4x1 + 4, [0] = 0, [cons](x0, x1) = 4x0 + 4x1, [isNat](x0) = x0, [n__length](x0) = x0, [s](x0) = x0, [n__s](x0) = x0, [isNatIList](x0) = 2x0 + 4, [zeros] = 0, [n__0] = 0, [nil] = 4, [U52](x0) = x0, [U51](x0, x1) = 4x0 + 4x1, [n__cons](x0, x1) = 4x0 + 4x1, [n__nil] = 2, [U42](x0) = x0, [activate](x0) = 2x0, [isNatList](x0) = 2x0, [n__zeros] = 0 orientation: zeros() = 0 >= 0 = cons(0(),n__zeros()) U41(tt(),V2) = 4V2 + 4 >= 4V2 + 4 = U42(isNatIList(activate(V2))) U51(tt(),V2) = 4V2 >= 4V2 = U52(isNatList(activate(V2))) isNat(n__0()) = 0 >= 0 = tt() isNatIList(n__cons(V1,V2)) = 8V1 + 8V2 + 4 >= 2V1 + 8V2 + 4 = U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) = 8V1 + 8V2 >= 8V1 + 8V2 = U51(isNat(activate(V1)),activate(V2)) zeros() = 0 >= 0 = n__zeros() 0() = 0 >= 0 = n__0() length(X) = X >= X = n__length(X) s(X) = X >= X = n__s(X) cons(X1,X2) = 4X1 + 4X2 >= 4X1 + 4X2 = n__cons(X1,X2) nil() = 4 >= 2 = n__nil() activate(n__zeros()) = 0 >= 0 = zeros() activate(n__0()) = 0 >= 0 = 0() activate(n__length(X)) = 2X >= 2X = length(activate(X)) activate(n__s(X)) = 2X >= 2X = s(activate(X)) activate(n__cons(X1,X2)) = 8X1 + 8X2 >= 8X1 + 4X2 = cons(activate(X1),X2) activate(n__nil()) = 4 >= 4 = nil() activate(X) = 2X >= X = X problem: zeros() -> cons(0(),n__zeros()) U41(tt(),V2) -> U42(isNatIList(activate(V2))) U51(tt(),V2) -> U52(isNatList(activate(V2))) isNat(n__0()) -> tt() isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__nil()) -> nil() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [length](x0) = [0 0 0]x0 [0 0 0] , [0] [tt] = [1] [0], [1 1 0] [1 0 0] [0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [0] [0] = [0] [1], [1 0 0] [1 0 1] [cons](x0, x1) = [0 1 1]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [0] [isNat](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 1] [n__length](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [s](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [n__s](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [isNatIList](x0) = [0 0 0]x0 + [1] [1 1 0] [0], [0] [zeros] = [1] [0], [0] [n__0] = [0] [1], [0] [nil] = [0] [0], [1 0 0] [U52](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] [1 0 1] [n__cons](x0, x1) = [0 1 1]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1] [n__nil] = [0] [0], [1 0 0] [U42](x0) = [0 1 0]x0 [0 0 0] , [0] [activate](x0) = x0 + [1] [0], [1 0 0] [isNatList](x0) = [1 0 0]x0 [0 0 0] , [0] [n__zeros] = [0] [0] orientation: [0] [0] zeros() = [1] >= [1] = cons(0(),n__zeros()) [0] [0] [1 0 0] [1] [1 0 0] [1] U41(tt(),V2) = [0 0 0]V2 + [1] >= [0 0 0]V2 + [1] = U42(isNatIList(activate(V2))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] U51(tt(),V2) = [0 0 0]V2 >= [0 0 0]V2 = U52(isNatList(activate(V2))) [0 0 0] [0 0 0] [0] [0] isNat(n__0()) = [1] >= [1] = tt() [0] [0] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 0] [1] isNatIList(n__cons(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 + [1] >= [0 0 0]V1 + [0 0 0]V2 + [1] = U41(isNat(activate(V1)),activate(V2)) [1 1 1] [1 0 1] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] isNatList(n__cons(V1,V2)) = [1 0 0]V1 + [1 0 1]V2 >= [0 0 0]V1 + [0 0 0]V2 = U51(isNat(activate(V1)),activate(V2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] zeros() = [1] >= [0] = n__zeros() [0] [0] [0] [0] 0() = [0] >= [0] = n__0() [1] [1] [1 0 1] [1 0 1] length(X) = [0 0 0]X >= [0 0 0]X = n__length(X) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] s(X) = [0 0 0]X + [1] >= [0 0 0]X = n__s(X) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 1] cons(X1,X2) = [0 1 1]X1 + [0 0 0]X2 >= [0 1 1]X1 + [0 0 0]X2 = n__cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] activate(n__zeros()) = [1] >= [1] = zeros() [0] [0] [0] [0] activate(n__0()) = [1] >= [0] = 0() [1] [1] [1 0 1] [0] [1 0 1] activate(n__length(X)) = [0 0 0]X + [1] >= [0 0 0]X = length(activate(X)) [0 0 0] [0] [0 0 0] [1 0 0] [0] [1 0 0] [0] activate(n__s(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = s(activate(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 1] [0] activate(n__cons(X1,X2)) = [0 1 1]X1 + [0 0 0]X2 + [1] >= [0 1 1]X1 + [0 0 0]X2 + [1] = cons(activate(X1),X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1] [0] activate(n__nil()) = [1] >= [0] = nil() [0] [0] [0] activate(X) = X + [1] >= X = X [0] problem: zeros() -> cons(0(),n__zeros()) U41(tt(),V2) -> U42(isNatIList(activate(V2))) U51(tt(),V2) -> U52(isNatList(activate(V2))) isNat(n__0()) -> tt() isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(X) -> X Matrix Interpretation Processor: dim=1 interpretation: [length](x0) = x0 + 2, [tt] = 0, [U41](x0, x1) = x0 + 2x1, [0] = 0, [cons](x0, x1) = 7x0 + 4x1, [isNat](x0) = 2x0, [n__length](x0) = x0 + 1, [s](x0) = 2x0 + 2, [n__s](x0) = 2x0 + 2, [isNatIList](x0) = x0, [zeros] = 0, [n__0] = 0, [U52](x0) = x0, [U51](x0, x1) = 4x0 + 6x1, [n__cons](x0, x1) = 7x0 + 4x1, [U42](x0) = x0, [activate](x0) = 2x0, [isNatList](x0) = 3x0, [n__zeros] = 0 orientation: zeros() = 0 >= 0 = cons(0(),n__zeros()) U41(tt(),V2) = 2V2 >= 2V2 = U42(isNatIList(activate(V2))) U51(tt(),V2) = 6V2 >= 6V2 = U52(isNatList(activate(V2))) isNat(n__0()) = 0 >= 0 = tt() isNatIList(n__cons(V1,V2)) = 7V1 + 4V2 >= 4V1 + 4V2 = U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) = 21V1 + 12V2 >= 16V1 + 12V2 = U51(isNat(activate(V1)),activate(V2)) zeros() = 0 >= 0 = n__zeros() 0() = 0 >= 0 = n__0() length(X) = X + 2 >= X + 1 = n__length(X) s(X) = 2X + 2 >= 2X + 2 = n__s(X) cons(X1,X2) = 7X1 + 4X2 >= 7X1 + 4X2 = n__cons(X1,X2) activate(n__zeros()) = 0 >= 0 = zeros() activate(n__0()) = 0 >= 0 = 0() activate(n__length(X)) = 2X + 2 >= 2X + 2 = length(activate(X)) activate(n__s(X)) = 4X + 4 >= 4X + 2 = s(activate(X)) activate(n__cons(X1,X2)) = 14X1 + 8X2 >= 14X1 + 4X2 = cons(activate(X1),X2) activate(X) = 2X >= X = X problem: zeros() -> cons(0(),n__zeros()) U41(tt(),V2) -> U42(isNatIList(activate(V2))) U51(tt(),V2) -> U52(isNatList(activate(V2))) isNat(n__0()) -> tt() isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) zeros() -> n__zeros() 0() -> n__0() s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [length](x0) = [0 0 0]x0 [0 0 0] , [0] [tt] = [1] [0], [1 0 0] [1 0 0] [0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [0] [0] = [0] [0], [1 0 1] [1 0 0] [0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [1 0 0] [0 0 0] [1], [1 0 0] [0] [isNat](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [1] [n__length](x0) = [0 1 1]x0 + [0] [1 0 0] [1], [1 0 0] [1] [s](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [n__s](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isNatIList](x0) = [0 0 1]x0 [1 0 0] , [0] [zeros] = [1] [1], [0] [n__0] = [0] [0], [1 0 0] [U52](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [1] [U51](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [1 0 1] [1 0 0] [0] [n__cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [1 0 0] [0 0 0] [1], [1 0 0] [U42](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [activate](x0) = [0 1 1]x0 [0 0 1] , [1 0 0] [1] [isNatList](x0) = [0 0 0]x0 + [1] [0 1 0] [0], [0] [n__zeros] = [0] [1] orientation: [0] [0] zeros() = [1] >= [1] = cons(0(),n__zeros()) [1] [1] [1 0 0] [0] [1 0 0] U41(tt(),V2) = [0 0 0]V2 + [1] >= [0 0 0]V2 = U42(isNatIList(activate(V2))) [0 0 0] [0] [0 0 0] [1 0 0] [1] [1 0 0] [1] U51(tt(),V2) = [0 0 0]V2 + [1] >= [0 0 0]V2 + [0] = U52(isNatList(activate(V2))) [0 0 0] [0] [0 0 0] [0] [0] [0] isNat(n__0()) = [1] >= [1] = tt() [0] [0] [1 0 1] [1 0 0] [0] [1 0 0] [1 0 0] [0] isNatIList(n__cons(V1,V2)) = [1 0 0]V1 + [0 0 0]V2 + [1] >= [0 0 0]V1 + [0 0 0]V2 + [1] = U41(isNat(activate(V1)),activate(V2)) [1 0 1] [1 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 0] [1] [1 0 0] [1 0 0] [1] isNatList(n__cons(V1,V2)) = [0 0 0]V1 + [0 0 0]V2 + [1] >= [0 0 0]V1 + [0 0 0]V2 + [1] = U51(isNat(activate(V1)),activate(V2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [0] [0] zeros() = [1] >= [0] = n__zeros() [1] [1] [0] [0] 0() = [0] >= [0] = n__0() [0] [0] [1 0 0] [1] [1 0 0] s(X) = [0 0 0]X + [0] >= [0 0 0]X = n__s(X) [0 0 0] [1] [0 0 0] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] cons(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0] = n__cons(X1,X2) [1 0 0] [0 0 0] [1] [1 0 0] [0 0 0] [1] [0] [0] activate(n__zeros()) = [1] >= [1] = zeros() [1] [1] [0] [0] activate(n__0()) = [0] >= [0] = 0() [0] [0] [1 0 0] [1] [1 0 0] activate(n__length(X)) = [1 1 1]X + [1] >= [0 0 0]X = length(activate(X)) [1 0 0] [1] [0 0 0] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] activate(n__cons(X1,X2)) = [1 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = cons(activate(X1),X2) [1 0 0] [0 0 0] [1] [1 0 0] [0 0 0] [1] [1 0 0] activate(X) = [0 1 1]X >= X = X [0 0 1] problem: zeros() -> cons(0(),n__zeros()) U41(tt(),V2) -> U42(isNatIList(activate(V2))) U51(tt(),V2) -> U52(isNatList(activate(V2))) isNat(n__0()) -> tt() isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) zeros() -> n__zeros() 0() -> n__0() cons(X1,X2) -> n__cons(X1,X2) activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(X) -> X Unfolding Processor: loop length: 9 terms: U41(tt(),n__zeros()) U42(isNatIList(activate(n__zeros()))) U42(isNatIList(zeros())) U42(isNatIList(cons(0(),n__zeros()))) U42(isNatIList(n__cons(0(),n__zeros()))) U42(U41(isNat(activate(0())),activate(n__zeros()))) U42(U41(isNat(0()),activate(n__zeros()))) U42(U41(isNat(n__0()),activate(n__zeros()))) U42(U41(tt(),activate(n__zeros()))) context: U42([]) substitution: Qed