/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),L,N)) -> mark(U62(isNat(N),L)) active(U62(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(V)) -> mark(U31(isNatList(V))) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U61(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [length](x0) = x0, [mark](x0) = x0, [U61](x0, x1, x2) = x0 + 2x1 + 4x2, [U31](x0) = 2x0, [active](x0) = x0, [cons](x0, x1) = 7x0 + 4x1, [isNat](x0) = 4x0, [s](x0) = 2x0, [U62](x0, x1) = x0 + 2x1, [tt] = 0, [isNatIList](x0) = 4x0 + 5, [zeros] = 0, [U21](x0) = x0, [nil] = 0, [U52](x0) = x0, [U51](x0, x1) = x0 + 2x1, [U42](x0) = x0, [U41](x0, x1) = x0 + 4x1 + 5, [isNatList](x0) = 2x0, [U11](x0) = 2x0, [0] = 0 orientation: active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt())) = 0 >= 0 = mark(tt()) active(U21(tt())) = 0 >= 0 = mark(tt()) active(U31(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V2)) = 4V2 + 5 >= 4V2 + 5 = mark(U42(isNatIList(V2))) active(U42(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 2V2 >= 2V2 = mark(U52(isNatList(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),L,N)) = 2L + 4N >= 2L + 4N = mark(U62(isNat(N),L)) active(U62(tt(),L)) = 2L >= 2L = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 4V1 >= 4V1 = mark(U11(isNatList(V1))) active(isNat(s(V1))) = 8V1 >= 4V1 = mark(U21(isNat(V1))) active(isNatIList(V)) = 4V + 5 >= 4V = mark(U31(isNatList(V))) active(isNatIList(zeros())) = 5 >= 0 = mark(tt()) active(isNatIList(cons(V1,V2))) = 28V1 + 16V2 + 5 >= 4V1 + 4V2 + 5 = mark(U41(isNat(V1),V2)) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 14V1 + 8V2 >= 4V1 + 2V2 = mark(U51(isNat(V1),V2)) active(length(nil())) = 0 >= 0 = mark(0()) active(length(cons(N,L))) = 4L + 7N >= 4L + 4N = mark(U61(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 7X1 + 4X2 >= 7X1 + 4X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X)) = 2X >= 2X = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U21(X)) = X >= X = active(U21(mark(X))) mark(U31(X)) = 2X >= 2X = active(U31(mark(X))) mark(U41(X1,X2)) = X1 + 4X2 + 5 >= X1 + 4X2 + 5 = active(U41(mark(X1),X2)) mark(U42(X)) = X >= X = active(U42(mark(X))) mark(isNatIList(X)) = 4X + 5 >= 4X + 5 = active(isNatIList(X)) mark(U51(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(isNatList(X)) = 2X >= 2X = active(isNatList(X)) mark(U61(X1,X2,X3)) = X1 + 2X2 + 4X3 >= X1 + 2X2 + 4X3 = active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = active(U62(mark(X1),X2)) mark(isNat(X)) = 4X >= 4X = active(isNat(X)) mark(s(X)) = 2X >= 2X = active(s(mark(X))) mark(length(X)) = X >= X = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 7X1 + 4X2 >= 7X1 + 4X2 = cons(X1,X2) cons(X1,mark(X2)) = 7X1 + 4X2 >= 7X1 + 4X2 = cons(X1,X2) cons(active(X1),X2) = 7X1 + 4X2 >= 7X1 + 4X2 = cons(X1,X2) cons(X1,active(X2)) = 7X1 + 4X2 >= 7X1 + 4X2 = cons(X1,X2) U11(mark(X)) = 2X >= 2X = U11(X) U11(active(X)) = 2X >= 2X = U11(X) U21(mark(X)) = X >= X = U21(X) U21(active(X)) = X >= X = U21(X) U31(mark(X)) = 2X >= 2X = U31(X) U31(active(X)) = 2X >= 2X = U31(X) U41(mark(X1),X2) = X1 + 4X2 + 5 >= X1 + 4X2 + 5 = U41(X1,X2) U41(X1,mark(X2)) = X1 + 4X2 + 5 >= X1 + 4X2 + 5 = U41(X1,X2) U41(active(X1),X2) = X1 + 4X2 + 5 >= X1 + 4X2 + 5 = U41(X1,X2) U41(X1,active(X2)) = X1 + 4X2 + 5 >= X1 + 4X2 + 5 = U41(X1,X2) U42(mark(X)) = X >= X = U42(X) U42(active(X)) = X >= X = U42(X) isNatIList(mark(X)) = 4X + 5 >= 4X + 5 = isNatIList(X) isNatIList(active(X)) = 4X + 5 >= 4X + 5 = isNatIList(X) U51(mark(X1),X2) = X1 + 2X2 >= X1 + 2X2 = U51(X1,X2) U51(X1,mark(X2)) = X1 + 2X2 >= X1 + 2X2 = U51(X1,X2) U51(active(X1),X2) = X1 + 2X2 >= X1 + 2X2 = U51(X1,X2) U51(X1,active(X2)) = X1 + 2X2 >= X1 + 2X2 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) isNatList(mark(X)) = 2X >= 2X = isNatList(X) isNatList(active(X)) = 2X >= 2X = isNatList(X) U61(mark(X1),X2,X3) = X1 + 2X2 + 4X3 >= X1 + 2X2 + 4X3 = U61(X1,X2,X3) U61(X1,mark(X2),X3) = X1 + 2X2 + 4X3 >= X1 + 2X2 + 4X3 = U61(X1,X2,X3) U61(X1,X2,mark(X3)) = X1 + 2X2 + 4X3 >= X1 + 2X2 + 4X3 = U61(X1,X2,X3) U61(active(X1),X2,X3) = X1 + 2X2 + 4X3 >= X1 + 2X2 + 4X3 = U61(X1,X2,X3) U61(X1,active(X2),X3) = X1 + 2X2 + 4X3 >= X1 + 2X2 + 4X3 = U61(X1,X2,X3) U61(X1,X2,active(X3)) = X1 + 2X2 + 4X3 >= X1 + 2X2 + 4X3 = U61(X1,X2,X3) U62(mark(X1),X2) = X1 + 2X2 >= X1 + 2X2 = U62(X1,X2) U62(X1,mark(X2)) = X1 + 2X2 >= X1 + 2X2 = U62(X1,X2) U62(active(X1),X2) = X1 + 2X2 >= X1 + 2X2 = U62(X1,X2) U62(X1,active(X2)) = X1 + 2X2 >= X1 + 2X2 = U62(X1,X2) isNat(mark(X)) = 4X >= 4X = isNat(X) isNat(active(X)) = 4X >= 4X = isNat(X) s(mark(X)) = 2X >= 2X = s(X) s(active(X)) = 2X >= 2X = s(X) length(mark(X)) = X >= X = length(X) length(active(X)) = X >= X = length(X) problem: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt())) -> mark(tt()) active(U21(tt())) -> mark(tt()) active(U31(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),L,N)) -> mark(U62(isNat(N),L)) active(U62(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(length(V1))) -> mark(U11(isNatList(V1))) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U61(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dim=1 interpretation: [length](x0) = 6x0 + 4, [mark](x0) = x0, [U61](x0, x1, x2) = 2x0 + 6x1 + 3x2 + 4, [U31](x0) = 2x0 + 1, [active](x0) = x0, [cons](x0, x1) = 4x0 + 4x1, [isNat](x0) = x0, [s](x0) = x0, [U62](x0, x1) = 2x0 + 6x1 + 4, [tt] = 0, [isNatIList](x0) = 2x0, [zeros] = 0, [U21](x0) = x0, [nil] = 0, [U52](x0) = x0, [U51](x0, x1) = 4x0 + x1, [U42](x0) = 2x0, [U41](x0, x1) = x0 + 5x1, [isNatList](x0) = x0, [U11](x0) = 6x0 + 2, [0] = 0 orientation: active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U11(tt())) = 2 >= 0 = mark(tt()) active(U21(tt())) = 0 >= 0 = mark(tt()) active(U31(tt())) = 1 >= 0 = mark(tt()) active(U41(tt(),V2)) = 5V2 >= 4V2 = mark(U42(isNatIList(V2))) active(U42(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = V2 >= V2 = mark(U52(isNatList(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),L,N)) = 6L + 3N + 4 >= 6L + 2N + 4 = mark(U62(isNat(N),L)) active(U62(tt(),L)) = 6L + 4 >= 6L + 4 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(length(V1))) = 6V1 + 4 >= 6V1 + 2 = mark(U11(isNatList(V1))) active(isNat(s(V1))) = V1 >= V1 = mark(U21(isNat(V1))) active(isNatIList(cons(V1,V2))) = 8V1 + 8V2 >= V1 + 5V2 = mark(U41(isNat(V1),V2)) active(isNatList(nil())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 4V1 + 4V2 >= 4V1 + V2 = mark(U51(isNat(V1),V2)) active(length(nil())) = 4 >= 0 = mark(0()) active(length(cons(N,L))) = 24L + 24N + 4 >= 8L + 3N + 4 = mark(U61(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X)) = 6X + 2 >= 6X + 2 = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U21(X)) = X >= X = active(U21(mark(X))) mark(U31(X)) = 2X + 1 >= 2X + 1 = active(U31(mark(X))) mark(U41(X1,X2)) = X1 + 5X2 >= X1 + 5X2 = active(U41(mark(X1),X2)) mark(U42(X)) = 2X >= 2X = active(U42(mark(X))) mark(isNatIList(X)) = 2X >= 2X = active(isNatIList(X)) mark(U51(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(isNatList(X)) = X >= X = active(isNatList(X)) mark(U61(X1,X2,X3)) = 2X1 + 6X2 + 3X3 + 4 >= 2X1 + 6X2 + 3X3 + 4 = active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) = 2X1 + 6X2 + 4 >= 2X1 + 6X2 + 4 = active(U62(mark(X1),X2)) mark(isNat(X)) = X >= X = active(isNat(X)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = 6X + 4 >= 6X + 4 = active(length(mark(X))) mark(nil()) = 0 >= 0 = active(nil()) cons(mark(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) cons(X1,mark(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) cons(active(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) cons(X1,active(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) U11(mark(X)) = 6X + 2 >= 6X + 2 = U11(X) U11(active(X)) = 6X + 2 >= 6X + 2 = U11(X) U21(mark(X)) = X >= X = U21(X) U21(active(X)) = X >= X = U21(X) U31(mark(X)) = 2X + 1 >= 2X + 1 = U31(X) U31(active(X)) = 2X + 1 >= 2X + 1 = U31(X) U41(mark(X1),X2) = X1 + 5X2 >= X1 + 5X2 = U41(X1,X2) U41(X1,mark(X2)) = X1 + 5X2 >= X1 + 5X2 = U41(X1,X2) U41(active(X1),X2) = X1 + 5X2 >= X1 + 5X2 = U41(X1,X2) U41(X1,active(X2)) = X1 + 5X2 >= X1 + 5X2 = U41(X1,X2) U42(mark(X)) = 2X >= 2X = U42(X) U42(active(X)) = 2X >= 2X = U42(X) isNatIList(mark(X)) = 2X >= 2X = isNatIList(X) isNatIList(active(X)) = 2X >= 2X = isNatIList(X) U51(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = U51(X1,X2) U51(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = U51(X1,X2) U51(active(X1),X2) = 4X1 + X2 >= 4X1 + X2 = U51(X1,X2) U51(X1,active(X2)) = 4X1 + X2 >= 4X1 + X2 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) isNatList(mark(X)) = X >= X = isNatList(X) isNatList(active(X)) = X >= X = isNatList(X) U61(mark(X1),X2,X3) = 2X1 + 6X2 + 3X3 + 4 >= 2X1 + 6X2 + 3X3 + 4 = U61(X1,X2,X3) U61(X1,mark(X2),X3) = 2X1 + 6X2 + 3X3 + 4 >= 2X1 + 6X2 + 3X3 + 4 = U61(X1,X2,X3) U61(X1,X2,mark(X3)) = 2X1 + 6X2 + 3X3 + 4 >= 2X1 + 6X2 + 3X3 + 4 = U61(X1,X2,X3) U61(active(X1),X2,X3) = 2X1 + 6X2 + 3X3 + 4 >= 2X1 + 6X2 + 3X3 + 4 = U61(X1,X2,X3) U61(X1,active(X2),X3) = 2X1 + 6X2 + 3X3 + 4 >= 2X1 + 6X2 + 3X3 + 4 = U61(X1,X2,X3) U61(X1,X2,active(X3)) = 2X1 + 6X2 + 3X3 + 4 >= 2X1 + 6X2 + 3X3 + 4 = U61(X1,X2,X3) U62(mark(X1),X2) = 2X1 + 6X2 + 4 >= 2X1 + 6X2 + 4 = U62(X1,X2) U62(X1,mark(X2)) = 2X1 + 6X2 + 4 >= 2X1 + 6X2 + 4 = U62(X1,X2) U62(active(X1),X2) = 2X1 + 6X2 + 4 >= 2X1 + 6X2 + 4 = U62(X1,X2) U62(X1,active(X2)) = 2X1 + 6X2 + 4 >= 2X1 + 6X2 + 4 = U62(X1,X2) isNat(mark(X)) = X >= X = isNat(X) isNat(active(X)) = X >= X = isNat(X) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = 6X + 4 >= 6X + 4 = length(X) length(active(X)) = 6X + 4 >= 6X + 4 = length(X) problem: active(zeros()) -> mark(cons(0(),zeros())) active(U21(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),L,N)) -> mark(U62(isNat(N),L)) active(U62(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(length(cons(N,L))) -> mark(U61(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dim=1 interpretation: [length](x0) = x0 + 2, [mark](x0) = x0, [U61](x0, x1, x2) = 4x0 + x1 + x2 + 2, [U31](x0) = 2x0, [active](x0) = x0, [cons](x0, x1) = x0 + 5x1, [isNat](x0) = x0, [s](x0) = x0, [U62](x0, x1) = x0 + x1 + 2, [tt] = 0, [isNatIList](x0) = x0, [zeros] = 0, [U21](x0) = x0, [nil] = 5, [U52](x0) = x0, [U51](x0, x1) = x0 + 4x1, [U42](x0) = 2x0, [U41](x0, x1) = x0 + 2x1, [isNatList](x0) = x0, [U11](x0) = 4x0 + 2, [0] = 0 orientation: active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U21(tt())) = 0 >= 0 = mark(tt()) active(U41(tt(),V2)) = 2V2 >= 2V2 = mark(U42(isNatIList(V2))) active(U42(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 4V2 >= V2 = mark(U52(isNatList(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),L,N)) = L + N + 2 >= L + N + 2 = mark(U62(isNat(N),L)) active(U62(tt(),L)) = L + 2 >= L + 2 = mark(s(length(L))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(s(V1))) = V1 >= V1 = mark(U21(isNat(V1))) active(isNatIList(cons(V1,V2))) = V1 + 5V2 >= V1 + 2V2 = mark(U41(isNat(V1),V2)) active(isNatList(nil())) = 5 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = V1 + 5V2 >= V1 + 4V2 = mark(U51(isNat(V1),V2)) active(length(cons(N,L))) = 5L + N + 2 >= 5L + N + 2 = mark(U61(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = X1 + 5X2 >= X1 + 5X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X)) = 4X + 2 >= 4X + 2 = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U21(X)) = X >= X = active(U21(mark(X))) mark(U31(X)) = 2X >= 2X = active(U31(mark(X))) mark(U41(X1,X2)) = X1 + 2X2 >= X1 + 2X2 = active(U41(mark(X1),X2)) mark(U42(X)) = 2X >= 2X = active(U42(mark(X))) mark(isNatIList(X)) = X >= X = active(isNatIList(X)) mark(U51(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(isNatList(X)) = X >= X = active(isNatList(X)) mark(U61(X1,X2,X3)) = 4X1 + X2 + X3 + 2 >= 4X1 + X2 + X3 + 2 = active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = active(U62(mark(X1),X2)) mark(isNat(X)) = X >= X = active(isNat(X)) mark(s(X)) = X >= X = active(s(mark(X))) mark(length(X)) = X + 2 >= X + 2 = active(length(mark(X))) mark(nil()) = 5 >= 5 = active(nil()) cons(mark(X1),X2) = X1 + 5X2 >= X1 + 5X2 = cons(X1,X2) cons(X1,mark(X2)) = X1 + 5X2 >= X1 + 5X2 = cons(X1,X2) cons(active(X1),X2) = X1 + 5X2 >= X1 + 5X2 = cons(X1,X2) cons(X1,active(X2)) = X1 + 5X2 >= X1 + 5X2 = cons(X1,X2) U11(mark(X)) = 4X + 2 >= 4X + 2 = U11(X) U11(active(X)) = 4X + 2 >= 4X + 2 = U11(X) U21(mark(X)) = X >= X = U21(X) U21(active(X)) = X >= X = U21(X) U31(mark(X)) = 2X >= 2X = U31(X) U31(active(X)) = 2X >= 2X = U31(X) U41(mark(X1),X2) = X1 + 2X2 >= X1 + 2X2 = U41(X1,X2) U41(X1,mark(X2)) = X1 + 2X2 >= X1 + 2X2 = U41(X1,X2) U41(active(X1),X2) = X1 + 2X2 >= X1 + 2X2 = U41(X1,X2) U41(X1,active(X2)) = X1 + 2X2 >= X1 + 2X2 = U41(X1,X2) U42(mark(X)) = 2X >= 2X = U42(X) U42(active(X)) = 2X >= 2X = U42(X) isNatIList(mark(X)) = X >= X = isNatIList(X) isNatIList(active(X)) = X >= X = isNatIList(X) U51(mark(X1),X2) = X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) U51(X1,mark(X2)) = X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) U51(active(X1),X2) = X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) U51(X1,active(X2)) = X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) isNatList(mark(X)) = X >= X = isNatList(X) isNatList(active(X)) = X >= X = isNatList(X) U61(mark(X1),X2,X3) = 4X1 + X2 + X3 + 2 >= 4X1 + X2 + X3 + 2 = U61(X1,X2,X3) U61(X1,mark(X2),X3) = 4X1 + X2 + X3 + 2 >= 4X1 + X2 + X3 + 2 = U61(X1,X2,X3) U61(X1,X2,mark(X3)) = 4X1 + X2 + X3 + 2 >= 4X1 + X2 + X3 + 2 = U61(X1,X2,X3) U61(active(X1),X2,X3) = 4X1 + X2 + X3 + 2 >= 4X1 + X2 + X3 + 2 = U61(X1,X2,X3) U61(X1,active(X2),X3) = 4X1 + X2 + X3 + 2 >= 4X1 + X2 + X3 + 2 = U61(X1,X2,X3) U61(X1,X2,active(X3)) = 4X1 + X2 + X3 + 2 >= 4X1 + X2 + X3 + 2 = U61(X1,X2,X3) U62(mark(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = U62(X1,X2) U62(X1,mark(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = U62(X1,X2) U62(active(X1),X2) = X1 + X2 + 2 >= X1 + X2 + 2 = U62(X1,X2) U62(X1,active(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = U62(X1,X2) isNat(mark(X)) = X >= X = isNat(X) isNat(active(X)) = X >= X = isNat(X) s(mark(X)) = X >= X = s(X) s(active(X)) = X >= X = s(X) length(mark(X)) = X + 2 >= X + 2 = length(X) length(active(X)) = X + 2 >= X + 2 = length(X) problem: active(zeros()) -> mark(cons(0(),zeros())) active(U21(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),L,N)) -> mark(U62(isNat(N),L)) active(U62(tt(),L)) -> mark(s(length(L))) active(isNat(0())) -> mark(tt()) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(length(cons(N,L))) -> mark(U61(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [length](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [mark](x0) = [0 1 0]x0 [1 0 0] , [1 1 0] [1 1 0] [1 0 0] [U61](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 0] [0 0 0] [1 0 0] , [1 0 0] [U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [active](x0) = [0 1 0]x0 [1 0 0] , [1 0 0] [1 1 0] [cons](x0, x1) = [0 0 0]x0 + [1 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [0] [isNat](x0) = [0 1 0]x0 + [1] [0 1 0] [1], [1 0 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 1 0] [1] [U62](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [0] [tt] = [1] [0], [1 0 0] [0] [isNatIList](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [zeros] = [0] [0], [1 0 0] [0] [U21](x0) = [0 0 0]x0 + [1] [1 0 0] [0], [0] [nil] = [0] [0], [1 0 0] [U52](x0) = [0 1 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] [U42](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [1 1 0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [0] [isNatList](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [0] [0] = [1] [0] orientation: [0] [0] active(zeros()) = [0] >= [0] = mark(cons(0(),zeros())) [0] [0] [0] [0] active(U21(tt())) = [1] >= [1] = mark(tt()) [0] [0] [1 1 0] [1 0 0] active(U41(tt(),V2)) = [0 0 0]V2 >= [0 0 0]V2 = mark(U42(isNatIList(V2))) [1 1 0] [1 0 0] [0] [0] active(U42(tt())) = [1] >= [1] = mark(tt()) [0] [0] [1 0 0] [1 0 0] active(U51(tt(),V2)) = [0 0 0]V2 >= [0 0 0]V2 = mark(U52(isNatList(V2))) [1 0 0] [1 0 0] [0] [0] active(U52(tt())) = [1] >= [1] = mark(tt()) [0] [0] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] active(U61(tt(),L,N)) = [0 0 0]L + [0 0 0]N + [0] >= [0 0 0]L + [0 0 0]N + [0] = mark(U62(isNat(N),L)) [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [1] [1 1 0] [1] [1 1 0] active(U62(tt(),L)) = [0 0 0]L + [0] >= [0 0 0]L = mark(s(length(L))) [1 1 0] [1] [1 1 0] [0] [0] active(isNat(0())) = [2] >= [1] = mark(tt()) [0] [0] [1 0 0] [0] [1 0 0] [0] active(isNat(s(V1))) = [0 0 0]V1 + [1] >= [0 0 0]V1 + [1] = mark(U21(isNat(V1))) [1 0 0] [0] [1 0 0] [0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] active(isNatIList(cons(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = mark(U41(isNat(V1),V2)) [1 0 0] [1 1 0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] active(isNatList(cons(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = mark(U51(isNat(V1),V2)) [1 0 0] [1 1 0] [1 0 0] [1 0 0] [2 1 0] [1 0 0] [2 1 0] [1 0 0] active(length(cons(N,L))) = [0 0 0]L + [0 0 0]N >= [0 0 0]L + [0 0 0]N = mark(U61(isNatList(L),L,N)) [2 1 0] [1 0 0] [2 1 0] [1 0 0] [0] [0] mark(zeros()) = [0] >= [0] = active(zeros()) [0] [0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] mark(cons(X1,X2)) = [0 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = active(cons(mark(X1),X2)) [1 0 0] [1 1 0] [1 0 0] [1 1 0] [0] [0] mark(0()) = [1] >= [1] = active(0()) [0] [0] [1 0 0] [1 0 0] mark(U11(X)) = [0 0 0]X >= [0 0 0]X = active(U11(mark(X))) [1 0 0] [1 0 0] [0] [0] mark(tt()) = [1] >= [1] = active(tt()) [0] [0] [1 0 0] [0] [1 0 0] [0] mark(U21(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(U21(mark(X))) [1 0 0] [0] [1 0 0] [0] [1 0 0] [1 0 0] mark(U31(X)) = [0 0 0]X >= [0 0 0]X = active(U31(mark(X))) [1 0 0] [1 0 0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] mark(U41(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(U41(mark(X1),X2)) [1 0 0] [1 1 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] mark(U42(X)) = [0 1 0]X >= [0 1 0]X = active(U42(mark(X))) [1 0 0] [1 0 0] [1 0 0] [1 0 0] mark(isNatIList(X)) = [0 0 0]X >= [0 0 0]X = active(isNatIList(X)) [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] mark(U51(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(U51(mark(X1),X2)) [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] mark(U52(X)) = [0 1 0]X >= [0 1 0]X = active(U52(mark(X))) [1 0 0] [1 0 0] [1 0 0] [1 0 0] mark(isNatList(X)) = [0 0 0]X >= [0 0 0]X = active(isNatList(X)) [1 0 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] mark(U61(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = active(U61(mark(X1),X2,X3)) [1 1 0] [1 1 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [1] mark(U62(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(U62(mark(X1),X2)) [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [1] [1 0 0] [0] [1 0 0] [0] mark(isNat(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = active(isNat(X)) [1 0 0] [0] [1 0 0] [0] [1 0 0] [1 0 0] mark(s(X)) = [0 0 0]X >= [0 0 0]X = active(s(mark(X))) [1 0 0] [1 0 0] [1 1 0] [1 1 0] mark(length(X)) = [0 0 0]X >= [0 0 0]X = active(length(mark(X))) [1 1 0] [1 1 0] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] cons(mark(X1),X2) = [0 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] cons(X1,mark(X2)) = [0 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] cons(active(X1),X2) = [0 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] cons(X1,active(X2)) = [0 0 0]X1 + [1 0 0]X2 >= [0 0 0]X1 + [1 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] U11(mark(X)) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] U11(active(X)) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] U21(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U21(X) [1 0 0] [0] [1 0 0] [0] [1 0 0] [0] [1 0 0] [0] U21(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U21(X) [1 0 0] [0] [1 0 0] [0] [1 0 0] [1 0 0] U31(mark(X)) = [0 0 0]X >= [0 0 0]X = U31(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] U31(active(X)) = [0 0 0]X >= [0 0 0]X = U31(X) [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] U41(mark(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] [1 0 0] [1 1 0] U41(X1,mark(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] [1 0 0] [1 1 0] U41(active(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] [1 0 0] [1 1 0] U41(X1,active(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] U42(mark(X)) = [0 1 0]X >= [0 1 0]X = U42(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] U42(active(X)) = [0 1 0]X >= [0 1 0]X = U42(X) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] isNatIList(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNatIList(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] isNatIList(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNatIList(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U51(mark(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] [1 0 0] [1 0 0] U51(X1,mark(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] [1 0 0] [1 0 0] U51(active(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] [1 0 0] [1 0 0] U51(X1,active(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] U52(mark(X)) = [0 1 0]X >= [0 1 0]X = U52(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] U52(active(X)) = [0 1 0]X >= [0 1 0]X = U52(X) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] isNatList(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNatList(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] isNatList(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNatList(X) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1 1 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] U61(mark(X1),X2,X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] U61(X1,mark(X2),X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] U61(X1,X2,mark(X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] U61(active(X1),X2,X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] U61(X1,active(X2),X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] [1 1 0] [1 1 0] [1 0 0] U61(X1,X2,active(X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [1 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [1] U62(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U62(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [1] U62(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U62(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [1] U62(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U62(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [1] U62(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U62(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] isNat(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = isNat(X) [0 1 0] [1] [0 1 0] [1] [1 0 0] [0] [1 0 0] [0] isNat(active(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = isNat(X) [0 1 0] [1] [0 1 0] [1] [1 0 0] [1 0 0] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] length(mark(X)) = [0 0 0]X >= [0 0 0]X = length(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] length(active(X)) = [0 0 0]X >= [0 0 0]X = length(X) [0 0 0] [0 0 0] problem: active(zeros()) -> mark(cons(0(),zeros())) active(U21(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),L,N)) -> mark(U62(isNat(N),L)) active(isNat(0())) -> mark(tt()) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(length(cons(N,L))) -> mark(U61(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U21(X)) -> active(U21(mark(X))) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dim=1 interpretation: [length](x0) = 2x0, [mark](x0) = 2x0, [U61](x0, x1, x2) = x0 + 2x1 + 4x2, [U31](x0) = 2x0, [active](x0) = x0, [cons](x0, x1) = 4x0 + 6x1, [isNat](x0) = 2x0, [s](x0) = 2x0 + 5, [U62](x0, x1) = x0 + x1, [tt] = 0, [isNatIList](x0) = 2x0, [zeros] = 0, [U21](x0) = x0 + 5, [nil] = 2, [U52](x0) = x0, [U51](x0, x1) = x0 + 2x1, [U42](x0) = x0, [U41](x0, x1) = 2x0 + 6x1, [isNatList](x0) = x0, [U11](x0) = x0, [0] = 0 orientation: active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U21(tt())) = 5 >= 0 = mark(tt()) active(U41(tt(),V2)) = 6V2 >= 4V2 = mark(U42(isNatIList(V2))) active(U42(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 2V2 >= 2V2 = mark(U52(isNatList(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),L,N)) = 2L + 4N >= 2L + 4N = mark(U62(isNat(N),L)) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(s(V1))) = 4V1 + 10 >= 4V1 + 10 = mark(U21(isNat(V1))) active(isNatIList(cons(V1,V2))) = 8V1 + 12V2 >= 8V1 + 12V2 = mark(U41(isNat(V1),V2)) active(isNatList(cons(V1,V2))) = 4V1 + 6V2 >= 4V1 + 4V2 = mark(U51(isNat(V1),V2)) active(length(cons(N,L))) = 12L + 8N >= 6L + 8N = mark(U61(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 8X1 + 12X2 >= 8X1 + 6X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X)) = 2X >= 2X = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U21(X)) = 2X + 10 >= 2X + 5 = active(U21(mark(X))) mark(U31(X)) = 4X >= 4X = active(U31(mark(X))) mark(U41(X1,X2)) = 4X1 + 12X2 >= 4X1 + 6X2 = active(U41(mark(X1),X2)) mark(U42(X)) = 2X >= 2X = active(U42(mark(X))) mark(isNatIList(X)) = 4X >= 2X = active(isNatIList(X)) mark(U51(X1,X2)) = 2X1 + 4X2 >= 2X1 + 2X2 = active(U51(mark(X1),X2)) mark(U52(X)) = 2X >= 2X = active(U52(mark(X))) mark(isNatList(X)) = 2X >= X = active(isNatList(X)) mark(U61(X1,X2,X3)) = 2X1 + 4X2 + 8X3 >= 2X1 + 2X2 + 4X3 = active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) = 2X1 + 2X2 >= 2X1 + X2 = active(U62(mark(X1),X2)) mark(isNat(X)) = 4X >= 2X = active(isNat(X)) mark(s(X)) = 4X + 10 >= 4X + 5 = active(s(mark(X))) mark(length(X)) = 4X >= 4X = active(length(mark(X))) mark(nil()) = 4 >= 2 = active(nil()) cons(mark(X1),X2) = 8X1 + 6X2 >= 4X1 + 6X2 = cons(X1,X2) cons(X1,mark(X2)) = 4X1 + 12X2 >= 4X1 + 6X2 = cons(X1,X2) cons(active(X1),X2) = 4X1 + 6X2 >= 4X1 + 6X2 = cons(X1,X2) cons(X1,active(X2)) = 4X1 + 6X2 >= 4X1 + 6X2 = cons(X1,X2) U11(mark(X)) = 2X >= X = U11(X) U11(active(X)) = X >= X = U11(X) U21(mark(X)) = 2X + 5 >= X + 5 = U21(X) U21(active(X)) = X + 5 >= X + 5 = U21(X) U31(mark(X)) = 4X >= 2X = U31(X) U31(active(X)) = 2X >= 2X = U31(X) U41(mark(X1),X2) = 4X1 + 6X2 >= 2X1 + 6X2 = U41(X1,X2) U41(X1,mark(X2)) = 2X1 + 12X2 >= 2X1 + 6X2 = U41(X1,X2) U41(active(X1),X2) = 2X1 + 6X2 >= 2X1 + 6X2 = U41(X1,X2) U41(X1,active(X2)) = 2X1 + 6X2 >= 2X1 + 6X2 = U41(X1,X2) U42(mark(X)) = 2X >= X = U42(X) U42(active(X)) = X >= X = U42(X) isNatIList(mark(X)) = 4X >= 2X = isNatIList(X) isNatIList(active(X)) = 2X >= 2X = isNatIList(X) U51(mark(X1),X2) = 2X1 + 2X2 >= X1 + 2X2 = U51(X1,X2) U51(X1,mark(X2)) = X1 + 4X2 >= X1 + 2X2 = U51(X1,X2) U51(active(X1),X2) = X1 + 2X2 >= X1 + 2X2 = U51(X1,X2) U51(X1,active(X2)) = X1 + 2X2 >= X1 + 2X2 = U51(X1,X2) U52(mark(X)) = 2X >= X = U52(X) U52(active(X)) = X >= X = U52(X) isNatList(mark(X)) = 2X >= X = isNatList(X) isNatList(active(X)) = X >= X = isNatList(X) U61(mark(X1),X2,X3) = 2X1 + 2X2 + 4X3 >= X1 + 2X2 + 4X3 = U61(X1,X2,X3) U61(X1,mark(X2),X3) = X1 + 4X2 + 4X3 >= X1 + 2X2 + 4X3 = U61(X1,X2,X3) U61(X1,X2,mark(X3)) = X1 + 2X2 + 8X3 >= X1 + 2X2 + 4X3 = U61(X1,X2,X3) U61(active(X1),X2,X3) = X1 + 2X2 + 4X3 >= X1 + 2X2 + 4X3 = U61(X1,X2,X3) U61(X1,active(X2),X3) = X1 + 2X2 + 4X3 >= X1 + 2X2 + 4X3 = U61(X1,X2,X3) U61(X1,X2,active(X3)) = X1 + 2X2 + 4X3 >= X1 + 2X2 + 4X3 = U61(X1,X2,X3) U62(mark(X1),X2) = 2X1 + X2 >= X1 + X2 = U62(X1,X2) U62(X1,mark(X2)) = X1 + 2X2 >= X1 + X2 = U62(X1,X2) U62(active(X1),X2) = X1 + X2 >= X1 + X2 = U62(X1,X2) U62(X1,active(X2)) = X1 + X2 >= X1 + X2 = U62(X1,X2) isNat(mark(X)) = 4X >= 2X = isNat(X) isNat(active(X)) = 2X >= 2X = isNat(X) s(mark(X)) = 4X + 5 >= 2X + 5 = s(X) s(active(X)) = 2X + 5 >= 2X + 5 = s(X) length(mark(X)) = 4X >= 2X = length(X) length(active(X)) = 2X >= 2X = length(X) problem: active(zeros()) -> mark(cons(0(),zeros())) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(U61(tt(),L,N)) -> mark(U62(isNat(N),L)) active(isNat(0())) -> mark(tt()) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(length(cons(N,L))) -> mark(U61(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(length(X)) -> active(length(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dim=1 interpretation: [length](x0) = 6x0 + 1, [mark](x0) = x0, [U61](x0, x1, x2) = 2x0 + 2x1 + 6x2 + 1, [U31](x0) = x0, [active](x0) = x0, [cons](x0, x1) = 5x0 + x1, [isNat](x0) = 3x0, [s](x0) = 6x0, [U62](x0, x1) = 2x0 + 2x1, [tt] = 0, [isNatIList](x0) = 2x0 + 2, [zeros] = 0, [U21](x0) = 6x0, [U52](x0) = x0, [U51](x0, x1) = 3x0 + 2x1, [U42](x0) = x0, [U41](x0, x1) = x0 + 2x1 + 2, [isNatList](x0) = 2x0, [U11](x0) = x0, [0] = 0 orientation: active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U41(tt(),V2)) = 2V2 + 2 >= 2V2 + 2 = mark(U42(isNatIList(V2))) active(U42(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 2V2 >= 2V2 = mark(U52(isNatList(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(U61(tt(),L,N)) = 2L + 6N + 1 >= 2L + 6N = mark(U62(isNat(N),L)) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(s(V1))) = 18V1 >= 18V1 = mark(U21(isNat(V1))) active(isNatIList(cons(V1,V2))) = 10V1 + 2V2 + 2 >= 3V1 + 2V2 + 2 = mark(U41(isNat(V1),V2)) active(isNatList(cons(V1,V2))) = 10V1 + 2V2 >= 9V1 + 2V2 = mark(U51(isNat(V1),V2)) active(length(cons(N,L))) = 6L + 30N + 1 >= 6L + 6N + 1 = mark(U61(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 5X1 + X2 >= 5X1 + X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X)) = X >= X = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U31(X)) = X >= X = active(U31(mark(X))) mark(U41(X1,X2)) = X1 + 2X2 + 2 >= X1 + 2X2 + 2 = active(U41(mark(X1),X2)) mark(U42(X)) = X >= X = active(U42(mark(X))) mark(isNatIList(X)) = 2X + 2 >= 2X + 2 = active(isNatIList(X)) mark(U51(X1,X2)) = 3X1 + 2X2 >= 3X1 + 2X2 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(isNatList(X)) = 2X >= 2X = active(isNatList(X)) mark(U61(X1,X2,X3)) = 2X1 + 2X2 + 6X3 + 1 >= 2X1 + 2X2 + 6X3 + 1 = active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = active(U62(mark(X1),X2)) mark(isNat(X)) = 3X >= 3X = active(isNat(X)) mark(length(X)) = 6X + 1 >= 6X + 1 = active(length(mark(X))) cons(mark(X1),X2) = 5X1 + X2 >= 5X1 + X2 = cons(X1,X2) cons(X1,mark(X2)) = 5X1 + X2 >= 5X1 + X2 = cons(X1,X2) cons(active(X1),X2) = 5X1 + X2 >= 5X1 + X2 = cons(X1,X2) cons(X1,active(X2)) = 5X1 + X2 >= 5X1 + X2 = cons(X1,X2) U11(mark(X)) = X >= X = U11(X) U11(active(X)) = X >= X = U11(X) U21(mark(X)) = 6X >= 6X = U21(X) U21(active(X)) = 6X >= 6X = U21(X) U31(mark(X)) = X >= X = U31(X) U31(active(X)) = X >= X = U31(X) U41(mark(X1),X2) = X1 + 2X2 + 2 >= X1 + 2X2 + 2 = U41(X1,X2) U41(X1,mark(X2)) = X1 + 2X2 + 2 >= X1 + 2X2 + 2 = U41(X1,X2) U41(active(X1),X2) = X1 + 2X2 + 2 >= X1 + 2X2 + 2 = U41(X1,X2) U41(X1,active(X2)) = X1 + 2X2 + 2 >= X1 + 2X2 + 2 = U41(X1,X2) U42(mark(X)) = X >= X = U42(X) U42(active(X)) = X >= X = U42(X) isNatIList(mark(X)) = 2X + 2 >= 2X + 2 = isNatIList(X) isNatIList(active(X)) = 2X + 2 >= 2X + 2 = isNatIList(X) U51(mark(X1),X2) = 3X1 + 2X2 >= 3X1 + 2X2 = U51(X1,X2) U51(X1,mark(X2)) = 3X1 + 2X2 >= 3X1 + 2X2 = U51(X1,X2) U51(active(X1),X2) = 3X1 + 2X2 >= 3X1 + 2X2 = U51(X1,X2) U51(X1,active(X2)) = 3X1 + 2X2 >= 3X1 + 2X2 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) isNatList(mark(X)) = 2X >= 2X = isNatList(X) isNatList(active(X)) = 2X >= 2X = isNatList(X) U61(mark(X1),X2,X3) = 2X1 + 2X2 + 6X3 + 1 >= 2X1 + 2X2 + 6X3 + 1 = U61(X1,X2,X3) U61(X1,mark(X2),X3) = 2X1 + 2X2 + 6X3 + 1 >= 2X1 + 2X2 + 6X3 + 1 = U61(X1,X2,X3) U61(X1,X2,mark(X3)) = 2X1 + 2X2 + 6X3 + 1 >= 2X1 + 2X2 + 6X3 + 1 = U61(X1,X2,X3) U61(active(X1),X2,X3) = 2X1 + 2X2 + 6X3 + 1 >= 2X1 + 2X2 + 6X3 + 1 = U61(X1,X2,X3) U61(X1,active(X2),X3) = 2X1 + 2X2 + 6X3 + 1 >= 2X1 + 2X2 + 6X3 + 1 = U61(X1,X2,X3) U61(X1,X2,active(X3)) = 2X1 + 2X2 + 6X3 + 1 >= 2X1 + 2X2 + 6X3 + 1 = U61(X1,X2,X3) U62(mark(X1),X2) = 2X1 + 2X2 >= 2X1 + 2X2 = U62(X1,X2) U62(X1,mark(X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = U62(X1,X2) U62(active(X1),X2) = 2X1 + 2X2 >= 2X1 + 2X2 = U62(X1,X2) U62(X1,active(X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = U62(X1,X2) isNat(mark(X)) = 3X >= 3X = isNat(X) isNat(active(X)) = 3X >= 3X = isNat(X) s(mark(X)) = 6X >= 6X = s(X) s(active(X)) = 6X >= 6X = s(X) length(mark(X)) = 6X + 1 >= 6X + 1 = length(X) length(active(X)) = 6X + 1 >= 6X + 1 = length(X) problem: active(zeros()) -> mark(cons(0(),zeros())) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(isNat(0())) -> mark(tt()) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) active(length(cons(N,L))) -> mark(U61(isNatList(L),L,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U31(X)) -> active(U31(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) mark(length(X)) -> active(length(mark(X))) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dim=1 interpretation: [length](x0) = x0 + 6, [mark](x0) = 2x0, [U61](x0, x1, x2) = x0 + x1 + 3x2, [U31](x0) = 4x0 + 6, [active](x0) = x0, [cons](x0, x1) = 6x0 + 6x1, [isNat](x0) = x0, [s](x0) = 4x0 + 4, [U62](x0, x1) = 4x0 + 2x1, [tt] = 0, [isNatIList](x0) = 2x0, [zeros] = 0, [U21](x0) = 2x0 + 2, [U52](x0) = x0, [U51](x0, x1) = x0 + 4x1, [U42](x0) = x0, [U41](x0, x1) = 4x0 + 4x1, [isNatList](x0) = 2x0, [U11](x0) = x0, [0] = 0 orientation: active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U41(tt(),V2)) = 4V2 >= 4V2 = mark(U42(isNatIList(V2))) active(U42(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 4V2 >= 4V2 = mark(U52(isNatList(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(s(V1))) = 4V1 + 4 >= 4V1 + 4 = mark(U21(isNat(V1))) active(isNatIList(cons(V1,V2))) = 12V1 + 12V2 >= 8V1 + 8V2 = mark(U41(isNat(V1),V2)) active(isNatList(cons(V1,V2))) = 12V1 + 12V2 >= 2V1 + 8V2 = mark(U51(isNat(V1),V2)) active(length(cons(N,L))) = 6L + 6N + 6 >= 6L + 6N = mark(U61(isNatList(L),L,N)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 12X1 + 12X2 >= 12X1 + 6X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X)) = 2X >= 2X = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U31(X)) = 8X + 12 >= 8X + 6 = active(U31(mark(X))) mark(U41(X1,X2)) = 8X1 + 8X2 >= 8X1 + 4X2 = active(U41(mark(X1),X2)) mark(U42(X)) = 2X >= 2X = active(U42(mark(X))) mark(isNatIList(X)) = 4X >= 2X = active(isNatIList(X)) mark(U51(X1,X2)) = 2X1 + 8X2 >= 2X1 + 4X2 = active(U51(mark(X1),X2)) mark(U52(X)) = 2X >= 2X = active(U52(mark(X))) mark(isNatList(X)) = 4X >= 2X = active(isNatList(X)) mark(U61(X1,X2,X3)) = 2X1 + 2X2 + 6X3 >= 2X1 + X2 + 3X3 = active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) = 8X1 + 4X2 >= 8X1 + 2X2 = active(U62(mark(X1),X2)) mark(isNat(X)) = 2X >= X = active(isNat(X)) mark(length(X)) = 2X + 12 >= 2X + 6 = active(length(mark(X))) cons(mark(X1),X2) = 12X1 + 6X2 >= 6X1 + 6X2 = cons(X1,X2) cons(X1,mark(X2)) = 6X1 + 12X2 >= 6X1 + 6X2 = cons(X1,X2) cons(active(X1),X2) = 6X1 + 6X2 >= 6X1 + 6X2 = cons(X1,X2) cons(X1,active(X2)) = 6X1 + 6X2 >= 6X1 + 6X2 = cons(X1,X2) U11(mark(X)) = 2X >= X = U11(X) U11(active(X)) = X >= X = U11(X) U21(mark(X)) = 4X + 2 >= 2X + 2 = U21(X) U21(active(X)) = 2X + 2 >= 2X + 2 = U21(X) U31(mark(X)) = 8X + 6 >= 4X + 6 = U31(X) U31(active(X)) = 4X + 6 >= 4X + 6 = U31(X) U41(mark(X1),X2) = 8X1 + 4X2 >= 4X1 + 4X2 = U41(X1,X2) U41(X1,mark(X2)) = 4X1 + 8X2 >= 4X1 + 4X2 = U41(X1,X2) U41(active(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = U41(X1,X2) U41(X1,active(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = U41(X1,X2) U42(mark(X)) = 2X >= X = U42(X) U42(active(X)) = X >= X = U42(X) isNatIList(mark(X)) = 4X >= 2X = isNatIList(X) isNatIList(active(X)) = 2X >= 2X = isNatIList(X) U51(mark(X1),X2) = 2X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) U51(X1,mark(X2)) = X1 + 8X2 >= X1 + 4X2 = U51(X1,X2) U51(active(X1),X2) = X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) U51(X1,active(X2)) = X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) U52(mark(X)) = 2X >= X = U52(X) U52(active(X)) = X >= X = U52(X) isNatList(mark(X)) = 4X >= 2X = isNatList(X) isNatList(active(X)) = 2X >= 2X = isNatList(X) U61(mark(X1),X2,X3) = 2X1 + X2 + 3X3 >= X1 + X2 + 3X3 = U61(X1,X2,X3) U61(X1,mark(X2),X3) = X1 + 2X2 + 3X3 >= X1 + X2 + 3X3 = U61(X1,X2,X3) U61(X1,X2,mark(X3)) = X1 + X2 + 6X3 >= X1 + X2 + 3X3 = U61(X1,X2,X3) U61(active(X1),X2,X3) = X1 + X2 + 3X3 >= X1 + X2 + 3X3 = U61(X1,X2,X3) U61(X1,active(X2),X3) = X1 + X2 + 3X3 >= X1 + X2 + 3X3 = U61(X1,X2,X3) U61(X1,X2,active(X3)) = X1 + X2 + 3X3 >= X1 + X2 + 3X3 = U61(X1,X2,X3) U62(mark(X1),X2) = 8X1 + 2X2 >= 4X1 + 2X2 = U62(X1,X2) U62(X1,mark(X2)) = 4X1 + 4X2 >= 4X1 + 2X2 = U62(X1,X2) U62(active(X1),X2) = 4X1 + 2X2 >= 4X1 + 2X2 = U62(X1,X2) U62(X1,active(X2)) = 4X1 + 2X2 >= 4X1 + 2X2 = U62(X1,X2) isNat(mark(X)) = 2X >= X = isNat(X) isNat(active(X)) = X >= X = isNat(X) s(mark(X)) = 8X + 4 >= 4X + 4 = s(X) s(active(X)) = 4X + 4 >= 4X + 4 = s(X) length(mark(X)) = 2X + 6 >= X + 6 = length(X) length(active(X)) = X + 6 >= X + 6 = length(X) problem: active(zeros()) -> mark(cons(0(),zeros())) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(isNat(0())) -> mark(tt()) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dim=1 interpretation: [length](x0) = 4x0, [mark](x0) = x0, [U61](x0, x1, x2) = x0 + 2x1 + 2x2 + 2, [U31](x0) = x0 + 4, [active](x0) = x0, [cons](x0, x1) = 4x0 + 4x1, [isNat](x0) = 4x0, [s](x0) = 4x0 + 4, [U62](x0, x1) = x0 + 4x1, [tt] = 0, [isNatIList](x0) = 4x0, [zeros] = 0, [U21](x0) = x0 + 2, [U52](x0) = 4x0, [U51](x0, x1) = x0 + 4x1, [U42](x0) = x0, [U41](x0, x1) = x0 + 4x1, [isNatList](x0) = x0, [U11](x0) = x0 + 6, [0] = 0 orientation: active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U41(tt(),V2)) = 4V2 >= 4V2 = mark(U42(isNatIList(V2))) active(U42(tt())) = 0 >= 0 = mark(tt()) active(U51(tt(),V2)) = 4V2 >= 4V2 = mark(U52(isNatList(V2))) active(U52(tt())) = 0 >= 0 = mark(tt()) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNat(s(V1))) = 16V1 + 16 >= 4V1 + 2 = mark(U21(isNat(V1))) active(isNatIList(cons(V1,V2))) = 16V1 + 16V2 >= 4V1 + 4V2 = mark(U41(isNat(V1),V2)) active(isNatList(cons(V1,V2))) = 4V1 + 4V2 >= 4V1 + 4V2 = mark(U51(isNat(V1),V2)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X)) = X + 6 >= X + 6 = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U41(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = active(U41(mark(X1),X2)) mark(U42(X)) = X >= X = active(U42(mark(X))) mark(isNatIList(X)) = 4X >= 4X = active(isNatIList(X)) mark(U51(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = active(U51(mark(X1),X2)) mark(U52(X)) = 4X >= 4X = active(U52(mark(X))) mark(isNatList(X)) = X >= X = active(isNatList(X)) mark(U61(X1,X2,X3)) = X1 + 2X2 + 2X3 + 2 >= X1 + 2X2 + 2X3 + 2 = active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = active(U62(mark(X1),X2)) mark(isNat(X)) = 4X >= 4X = active(isNat(X)) cons(mark(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) cons(X1,mark(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) cons(active(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) cons(X1,active(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) U11(mark(X)) = X + 6 >= X + 6 = U11(X) U11(active(X)) = X + 6 >= X + 6 = U11(X) U21(mark(X)) = X + 2 >= X + 2 = U21(X) U21(active(X)) = X + 2 >= X + 2 = U21(X) U31(mark(X)) = X + 4 >= X + 4 = U31(X) U31(active(X)) = X + 4 >= X + 4 = U31(X) U41(mark(X1),X2) = X1 + 4X2 >= X1 + 4X2 = U41(X1,X2) U41(X1,mark(X2)) = X1 + 4X2 >= X1 + 4X2 = U41(X1,X2) U41(active(X1),X2) = X1 + 4X2 >= X1 + 4X2 = U41(X1,X2) U41(X1,active(X2)) = X1 + 4X2 >= X1 + 4X2 = U41(X1,X2) U42(mark(X)) = X >= X = U42(X) U42(active(X)) = X >= X = U42(X) isNatIList(mark(X)) = 4X >= 4X = isNatIList(X) isNatIList(active(X)) = 4X >= 4X = isNatIList(X) U51(mark(X1),X2) = X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) U51(X1,mark(X2)) = X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) U51(active(X1),X2) = X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) U51(X1,active(X2)) = X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) U52(mark(X)) = 4X >= 4X = U52(X) U52(active(X)) = 4X >= 4X = U52(X) isNatList(mark(X)) = X >= X = isNatList(X) isNatList(active(X)) = X >= X = isNatList(X) U61(mark(X1),X2,X3) = X1 + 2X2 + 2X3 + 2 >= X1 + 2X2 + 2X3 + 2 = U61(X1,X2,X3) U61(X1,mark(X2),X3) = X1 + 2X2 + 2X3 + 2 >= X1 + 2X2 + 2X3 + 2 = U61(X1,X2,X3) U61(X1,X2,mark(X3)) = X1 + 2X2 + 2X3 + 2 >= X1 + 2X2 + 2X3 + 2 = U61(X1,X2,X3) U61(active(X1),X2,X3) = X1 + 2X2 + 2X3 + 2 >= X1 + 2X2 + 2X3 + 2 = U61(X1,X2,X3) U61(X1,active(X2),X3) = X1 + 2X2 + 2X3 + 2 >= X1 + 2X2 + 2X3 + 2 = U61(X1,X2,X3) U61(X1,X2,active(X3)) = X1 + 2X2 + 2X3 + 2 >= X1 + 2X2 + 2X3 + 2 = U61(X1,X2,X3) U62(mark(X1),X2) = X1 + 4X2 >= X1 + 4X2 = U62(X1,X2) U62(X1,mark(X2)) = X1 + 4X2 >= X1 + 4X2 = U62(X1,X2) U62(active(X1),X2) = X1 + 4X2 >= X1 + 4X2 = U62(X1,X2) U62(X1,active(X2)) = X1 + 4X2 >= X1 + 4X2 = U62(X1,X2) isNat(mark(X)) = 4X >= 4X = isNat(X) isNat(active(X)) = 4X >= 4X = isNat(X) s(mark(X)) = 4X + 4 >= 4X + 4 = s(X) s(active(X)) = 4X + 4 >= 4X + 4 = s(X) length(mark(X)) = 4X >= 4X = length(X) length(active(X)) = 4X >= 4X = length(X) problem: active(zeros()) -> mark(cons(0(),zeros())) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(isNat(0())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U21(mark(X)) -> U21(X) U21(active(X)) -> U21(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [length](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [mark](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 0] [1 0 0] [1 0 0] [U61](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 0] [0 0 0] [0 0 0] , [1 0 0] [U31](x0) = [0 0 1]x0 [0 0 0] , [1 0 0] [0] [active](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 0] [1 0 1] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [isNat](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U62](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [tt] = [0] [0], [1 0 0] [1] [isNatIList](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0] [zeros] = [0] [0], [1 0 1] [U21](x0) = [0 0 0]x0 [0 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 1]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U42](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [1] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [1 0 0] [isNatList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [U11](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [0] [0] = [0] [0] orientation: [0] [0] active(zeros()) = [0] >= [0] = mark(cons(0(),zeros())) [1] [1] [1 0 0] [1] [1 0 0] [1] active(U41(tt(),V2)) = [0 0 0]V2 + [0] >= [0 0 0]V2 + [0] = mark(U42(isNatIList(V2))) [0 0 0] [1] [0 0 0] [1] [0] [0] active(U42(tt())) = [0] >= [0] = mark(tt()) [1] [1] [1 0 1] [0] [1 0 0] [0] active(U51(tt(),V2)) = [0 0 0]V2 + [0] >= [0 0 0]V2 + [0] = mark(U52(isNatList(V2))) [0 0 0] [1] [0 0 0] [1] [0] [0] active(U52(tt())) = [0] >= [0] = mark(tt()) [1] [1] [0] [0] active(isNat(0())) = [0] >= [0] = mark(tt()) [1] [1] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 0] [1] active(isNatIList(cons(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 + [0] = mark(U41(isNat(V1),V2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 1] [0] active(isNatList(cons(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 + [0] = mark(U51(isNat(V1),V2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] mark(zeros()) = [0] >= [0] = active(zeros()) [1] [1] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 1] [0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] mark(0()) = [0] >= [0] = active(0()) [1] [1] [1 0 0] [0] [1 0 0] [0] mark(U11(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(U11(mark(X))) [0 0 0] [1] [0 0 0] [1] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [1] [1] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] mark(U41(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(U41(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] mark(U42(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(U42(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] mark(isNatIList(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isNatIList(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 1] [0] mark(U51(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(U51(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] mark(U52(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(U52(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] mark(isNatList(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isNatList(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [0] mark(U61(X1,X2,X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [0] = active(U61(mark(X1),X2,X3)) [0 0 0] [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] mark(U62(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(U62(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] mark(isNat(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isNat(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 1] [1 0 0] [1 0 1] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 1] cons(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 1] cons(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 1] cons(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] U11(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U11(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] U11(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U11(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 1] U21(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = U21(X) [0 0 0] [0] [0 0 0] [1 0 1] [1] [1 0 1] U21(active(X)) = [0 0 0]X + [0] >= [0 0 0]X = U21(X) [0 0 0] [0] [0 0 0] [1 0 0] [0] [1 0 0] U31(mark(X)) = [0 0 1]X + [1] >= [0 0 1]X = U31(X) [0 0 0] [0] [0 0 0] [1 0 0] [0] [1 0 0] U31(active(X)) = [0 0 1]X + [1] >= [0 0 1]X = U31(X) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] U41(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = U41(X1,X2) [0 0 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] [1] U41(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = U41(X1,X2) [0 0 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] [1] U41(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = U41(X1,X2) [0 0 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] [1] U41(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = U41(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] U42(mark(X)) = [0 0 0]X >= [0 0 0]X = U42(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] U42(active(X)) = [0 0 0]X >= [0 0 0]X = U42(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] isNatIList(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNatIList(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isNatIList(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNatIList(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 1] U51(mark(X1),X2) = [0 0 1]X1 + [0 0 0]X2 + [1] >= [0 0 1]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 1] U51(X1,mark(X2)) = [0 0 1]X1 + [0 0 0]X2 + [0] >= [0 0 1]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 1] U51(active(X1),X2) = [0 0 1]X1 + [0 0 0]X2 + [1] >= [0 0 1]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 1] U51(X1,active(X2)) = [0 0 1]X1 + [0 0 0]X2 + [0] >= [0 0 1]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] U52(mark(X)) = [0 0 0]X >= [0 0 0]X = U52(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] U52(active(X)) = [0 0 0]X >= [0 0 0]X = U52(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNatList(mark(X)) = [0 0 0]X >= [0 0 0]X = isNatList(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNatList(active(X)) = [0 0 0]X >= [0 0 0]X = isNatList(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U61(mark(X1),X2,X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U61(X1,mark(X2),X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U61(X1,X2,mark(X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U61(active(X1),X2,X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U61(X1,active(X2),X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U61(X1,X2,active(X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U62(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U62(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] U62(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U62(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] U62(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U62(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] U62(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U62(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNat(mark(X)) = [0 0 0]X >= [0 0 0]X = isNat(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNat(active(X)) = [0 0 0]X >= [0 0 0]X = isNat(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 0 1] [1] [1 0 1] length(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = length(X) [0 0 0] [0] [0 0 0] [1 0 1] [1] [1 0 1] length(active(X)) = [0 0 0]X + [0] >= [0 0 0]X = length(X) [0 0 0] [0] [0 0 0] problem: active(zeros()) -> mark(cons(0(),zeros())) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(U52(tt())) -> mark(tt()) active(isNat(0())) -> mark(tt()) active(isNatIList(cons(V1,V2))) -> mark(U41(isNat(V1),V2)) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [mark](x0) = [1 1 0]x0 [0 0 0] , [1 0 1] [1 0 0] [1 0 0] [U61](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 0] [0 0 0] [0 1 0] , [1 0 0] [U31](x0) = [0 0 0]x0 [0 1 0] , [1 0 1] [active](x0) = [1 1 0]x0 [0 0 0] , [1 0 1] [1 0 0] [1] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [1 0 1] [isNat](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [s](x0) = [0 0 0]x0 [1 0 1] , [1 0 1] [1 0 0] [0] [U62](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [1], [0] [tt] = [0] [0], [1 0 0] [isNatIList](x0) = [0 0 0]x0 [0 0 0] , [0] [zeros] = [1] [1], [1 0 1] [1] [U52](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 1] [1 0 0] [1] [U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [1 0 1] [U42](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [1 0 0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [isNatList](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [U11](x0) = [0 0 0]x0 [0 0 0] , [0] [0] = [0] [0] orientation: [1] [1] active(zeros()) = [1] >= [1] = mark(cons(0(),zeros())) [0] [0] [1 0 0] [1 0 0] active(U41(tt(),V2)) = [1 0 0]V2 >= [1 0 0]V2 = mark(U42(isNatIList(V2))) [0 0 0] [0 0 0] [0] [0] active(U42(tt())) = [0] >= [0] = mark(tt()) [0] [0] [1 0 0] [1] [1 0 0] [1] active(U51(tt(),V2)) = [1 0 0]V2 + [1] >= [1 0 0]V2 + [1] = mark(U52(isNatList(V2))) [0 0 0] [0] [0 0 0] [0] [1] [0] active(U52(tt())) = [1] >= [0] = mark(tt()) [0] [0] [0] [0] active(isNat(0())) = [0] >= [0] = mark(tt()) [0] [0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] active(isNatIList(cons(V1,V2))) = [1 0 1]V1 + [1 0 0]V2 + [1] >= [1 0 1]V1 + [1 0 0]V2 = mark(U41(isNat(V1),V2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] active(isNatList(cons(V1,V2))) = [1 0 1]V1 + [1 0 0]V2 + [1] >= [1 0 1]V1 + [1 0 0]V2 + [1] = mark(U51(isNat(V1),V2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1] [1] mark(zeros()) = [1] >= [1] = active(zeros()) [0] [0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] mark(cons(X1,X2)) = [1 0 1]X1 + [1 0 0]X2 + [1] >= [1 0 1]X1 + [1 0 0]X2 + [1] = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [0] [0] mark(0()) = [0] >= [0] = active(0()) [0] [0] [1 0 1] [1 0 1] mark(U11(X)) = [1 0 1]X >= [1 0 1]X = active(U11(mark(X))) [0 0 0] [0 0 0] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [0] [0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] mark(U41(X1,X2)) = [1 0 1]X1 + [1 0 0]X2 >= [1 0 1]X1 + [1 0 0]X2 = active(U41(mark(X1),X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] mark(U42(X)) = [1 0 1]X >= [1 0 1]X = active(U42(mark(X))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] mark(isNatIList(X)) = [1 0 0]X >= [1 0 0]X = active(isNatIList(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] mark(U51(X1,X2)) = [1 0 1]X1 + [1 0 0]X2 + [1] >= [1 0 1]X1 + [1 0 0]X2 + [1] = active(U51(mark(X1),X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1] [1 0 1] [1] mark(U52(X)) = [1 0 1]X + [1] >= [1 0 1]X + [1] = active(U52(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] mark(isNatList(X)) = [1 0 0]X >= [1 0 0]X = active(isNatList(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1 1 0] [1 0 1] [1 0 0] [1 1 0] mark(U61(X1,X2,X3)) = [1 0 1]X1 + [1 0 0]X2 + [1 0 0]X3 >= [1 0 1]X1 + [1 0 0]X2 + [1 0 0]X3 = active(U61(mark(X1),X2,X3)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] mark(U62(X1,X2)) = [1 0 1]X1 + [1 0 0]X2 + [0] >= [1 0 1]X1 + [1 0 0]X2 + [0] = active(U62(mark(X1),X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 1] mark(isNat(X)) = [1 0 1]X >= [1 0 1]X = active(isNat(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] cons(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 1] U11(mark(X)) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] U11(active(X)) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] U31(mark(X)) = [0 0 0]X >= [0 0 0]X = U31(X) [1 1 0] [0 1 0] [1 0 1] [1 0 0] U31(active(X)) = [0 0 0]X >= [0 0 0]X = U31(X) [1 1 0] [0 1 0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] U41(mark(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 1] [1 0 1] [1 0 1] [1 0 0] U41(X1,mark(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 1] [1 0 0] [1 0 1] [1 0 0] U41(active(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 1] [1 0 1] [1 0 1] [1 0 0] U41(X1,active(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 1] [1 0 1] U42(mark(X)) = [0 0 0]X >= [0 0 0]X = U42(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] U42(active(X)) = [0 0 0]X >= [0 0 0]X = U42(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] isNatIList(mark(X)) = [0 0 0]X >= [0 0 0]X = isNatIList(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] isNatIList(active(X)) = [0 0 0]X >= [0 0 0]X = isNatIList(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] U51(mark(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 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] U51(active(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 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1] [1 0 1] [1] U52(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U52(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 1] [1] U52(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U52(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 0 0] isNatList(mark(X)) = [0 0 0]X >= [0 0 0]X = isNatList(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] isNatList(active(X)) = [0 0 0]X >= [0 0 0]X = isNatList(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] U61(mark(X1),X2,X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 1 0] [0 0 0] [0 0 0] [0 1 0] [1 0 1] [1 0 1] [1 0 0] [1 0 1] [1 0 0] [1 0 0] U61(X1,mark(X2),X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 1 0] [0 0 0] [0 0 0] [0 1 0] [1 0 1] [1 0 0] [1 0 1] [1 0 1] [1 0 0] [1 0 0] U61(X1,X2,mark(X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [1 1 0] [0 0 0] [0 0 0] [0 1 0] [1 0 1] [1 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] U61(active(X1),X2,X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 1 0] [0 0 0] [0 0 0] [0 1 0] [1 0 1] [1 0 1] [1 0 0] [1 0 1] [1 0 0] [1 0 0] U61(X1,active(X2),X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 1 0] [0 0 0] [0 0 0] [0 1 0] [1 0 1] [1 0 0] [1 0 1] [1 0 1] [1 0 0] [1 0 0] U61(X1,X2,active(X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [1 1 0] [0 0 0] [0 0 0] [0 1 0] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] U62(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U62(X1,X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 0] [0] U62(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U62(X1,X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] U62(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U62(X1,X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 0] [0] U62(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U62(X1,X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 1] [1 0 1] isNat(mark(X)) = [0 0 0]X >= [0 0 0]X = isNat(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] isNat(active(X)) = [0 0 0]X >= [0 0 0]X = isNat(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [1 0 1] [1 0 1] [1 0 1] [1 0 1] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [1 0 1] [1 0 1] problem: active(zeros()) -> mark(cons(0(),zeros())) active(U41(tt(),V2)) -> mark(U42(isNatIList(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(isNat(0())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Matrix Interpretation Processor: dim=1 interpretation: [mark](x0) = 2x0, [U61](x0, x1, x2) = 4x0 + 5x1 + 2x2 + 1, [U31](x0) = x0, [active](x0) = x0, [cons](x0, x1) = 4x0 + 4x1, [isNat](x0) = x0, [s](x0) = 4x0 + 6, [U62](x0, x1) = 4x0 + 4x1, [tt] = 0, [isNatIList](x0) = x0, [zeros] = 0, [U52](x0) = x0, [U51](x0, x1) = x0 + 4x1, [U42](x0) = 2x0 + 1, [U41](x0, x1) = 4x0 + 4x1 + 6, [isNatList](x0) = 2x0, [U11](x0) = x0, [0] = 0 orientation: active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U41(tt(),V2)) = 4V2 + 6 >= 4V2 + 2 = mark(U42(isNatIList(V2))) active(U42(tt())) = 1 >= 0 = mark(tt()) active(U51(tt(),V2)) = 4V2 >= 4V2 = mark(U52(isNatList(V2))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 8V1 + 8V2 >= 2V1 + 8V2 = mark(U51(isNat(V1),V2)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 8X1 + 8X2 >= 8X1 + 4X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X)) = 2X >= 2X = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U41(X1,X2)) = 8X1 + 8X2 + 12 >= 8X1 + 4X2 + 6 = active(U41(mark(X1),X2)) mark(U42(X)) = 4X + 2 >= 4X + 1 = active(U42(mark(X))) mark(isNatIList(X)) = 2X >= X = active(isNatIList(X)) mark(U51(X1,X2)) = 2X1 + 8X2 >= 2X1 + 4X2 = active(U51(mark(X1),X2)) mark(U52(X)) = 2X >= 2X = active(U52(mark(X))) mark(isNatList(X)) = 4X >= 2X = active(isNatList(X)) mark(U61(X1,X2,X3)) = 8X1 + 10X2 + 4X3 + 2 >= 8X1 + 5X2 + 2X3 + 1 = active(U61(mark(X1),X2,X3)) mark(U62(X1,X2)) = 8X1 + 8X2 >= 8X1 + 4X2 = active(U62(mark(X1),X2)) mark(isNat(X)) = 2X >= X = active(isNat(X)) cons(mark(X1),X2) = 8X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) cons(active(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) U11(mark(X)) = 2X >= X = U11(X) U11(active(X)) = X >= X = U11(X) U31(mark(X)) = 2X >= X = U31(X) U31(active(X)) = X >= X = U31(X) U41(mark(X1),X2) = 8X1 + 4X2 + 6 >= 4X1 + 4X2 + 6 = U41(X1,X2) U41(X1,mark(X2)) = 4X1 + 8X2 + 6 >= 4X1 + 4X2 + 6 = U41(X1,X2) U41(active(X1),X2) = 4X1 + 4X2 + 6 >= 4X1 + 4X2 + 6 = U41(X1,X2) U41(X1,active(X2)) = 4X1 + 4X2 + 6 >= 4X1 + 4X2 + 6 = U41(X1,X2) U42(mark(X)) = 4X + 1 >= 2X + 1 = U42(X) U42(active(X)) = 2X + 1 >= 2X + 1 = U42(X) isNatIList(mark(X)) = 2X >= X = isNatIList(X) isNatIList(active(X)) = X >= X = isNatIList(X) U51(mark(X1),X2) = 2X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) U51(active(X1),X2) = X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) U52(mark(X)) = 2X >= X = U52(X) U52(active(X)) = X >= X = U52(X) isNatList(mark(X)) = 4X >= 2X = isNatList(X) isNatList(active(X)) = 2X >= 2X = isNatList(X) U61(mark(X1),X2,X3) = 8X1 + 5X2 + 2X3 + 1 >= 4X1 + 5X2 + 2X3 + 1 = U61(X1,X2,X3) U61(X1,mark(X2),X3) = 4X1 + 10X2 + 2X3 + 1 >= 4X1 + 5X2 + 2X3 + 1 = U61(X1,X2,X3) U61(X1,X2,mark(X3)) = 4X1 + 5X2 + 4X3 + 1 >= 4X1 + 5X2 + 2X3 + 1 = U61(X1,X2,X3) U61(active(X1),X2,X3) = 4X1 + 5X2 + 2X3 + 1 >= 4X1 + 5X2 + 2X3 + 1 = U61(X1,X2,X3) U61(X1,active(X2),X3) = 4X1 + 5X2 + 2X3 + 1 >= 4X1 + 5X2 + 2X3 + 1 = U61(X1,X2,X3) U61(X1,X2,active(X3)) = 4X1 + 5X2 + 2X3 + 1 >= 4X1 + 5X2 + 2X3 + 1 = U61(X1,X2,X3) U62(mark(X1),X2) = 8X1 + 4X2 >= 4X1 + 4X2 = U62(X1,X2) U62(X1,mark(X2)) = 4X1 + 8X2 >= 4X1 + 4X2 = U62(X1,X2) U62(active(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = U62(X1,X2) U62(X1,active(X2)) = 4X1 + 4X2 >= 4X1 + 4X2 = U62(X1,X2) isNat(mark(X)) = 2X >= X = isNat(X) isNat(active(X)) = X >= X = isNat(X) s(mark(X)) = 8X + 6 >= 4X + 6 = s(X) s(active(X)) = 4X + 6 >= 4X + 6 = s(X) problem: active(zeros()) -> mark(cons(0(),zeros())) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(isNat(0())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Matrix Interpretation Processor: dim=1 interpretation: [mark](x0) = 2x0, [U61](x0, x1, x2) = 4x0 + 4x1 + 2x2 + 1, [U31](x0) = 4x0, [active](x0) = x0, [cons](x0, x1) = 3x0 + 4x1, [isNat](x0) = x0, [s](x0) = 4x0, [U62](x0, x1) = x0 + 2x1, [tt] = 0, [isNatIList](x0) = x0 + 4, [zeros] = 0, [U52](x0) = x0, [U51](x0, x1) = 4x0 + 6x1, [U42](x0) = x0, [U41](x0, x1) = 4x0 + 4x1 + 1, [isNatList](x0) = 3x0, [U11](x0) = 2x0, [0] = 0 orientation: active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U51(tt(),V2)) = 6V2 >= 6V2 = mark(U52(isNatList(V2))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 9V1 + 12V2 >= 8V1 + 12V2 = mark(U51(isNat(V1),V2)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 6X1 + 8X2 >= 6X1 + 4X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X)) = 4X >= 4X = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(isNatIList(X)) = 2X + 8 >= X + 4 = active(isNatIList(X)) mark(U51(X1,X2)) = 8X1 + 12X2 >= 8X1 + 6X2 = active(U51(mark(X1),X2)) mark(U52(X)) = 2X >= 2X = active(U52(mark(X))) mark(isNatList(X)) = 6X >= 3X = active(isNatList(X)) mark(U62(X1,X2)) = 2X1 + 4X2 >= 2X1 + 2X2 = active(U62(mark(X1),X2)) mark(isNat(X)) = 2X >= X = active(isNat(X)) cons(mark(X1),X2) = 6X1 + 4X2 >= 3X1 + 4X2 = cons(X1,X2) cons(active(X1),X2) = 3X1 + 4X2 >= 3X1 + 4X2 = cons(X1,X2) U11(mark(X)) = 4X >= 2X = U11(X) U11(active(X)) = 2X >= 2X = U11(X) U31(mark(X)) = 8X >= 4X = U31(X) U31(active(X)) = 4X >= 4X = U31(X) U41(mark(X1),X2) = 8X1 + 4X2 + 1 >= 4X1 + 4X2 + 1 = U41(X1,X2) U41(X1,mark(X2)) = 4X1 + 8X2 + 1 >= 4X1 + 4X2 + 1 = U41(X1,X2) U41(active(X1),X2) = 4X1 + 4X2 + 1 >= 4X1 + 4X2 + 1 = U41(X1,X2) U41(X1,active(X2)) = 4X1 + 4X2 + 1 >= 4X1 + 4X2 + 1 = U41(X1,X2) U42(mark(X)) = 2X >= X = U42(X) U42(active(X)) = X >= X = U42(X) isNatIList(mark(X)) = 2X + 4 >= X + 4 = isNatIList(X) isNatIList(active(X)) = X + 4 >= X + 4 = isNatIList(X) U51(mark(X1),X2) = 8X1 + 6X2 >= 4X1 + 6X2 = U51(X1,X2) U51(active(X1),X2) = 4X1 + 6X2 >= 4X1 + 6X2 = U51(X1,X2) U52(mark(X)) = 2X >= X = U52(X) U52(active(X)) = X >= X = U52(X) isNatList(mark(X)) = 6X >= 3X = isNatList(X) isNatList(active(X)) = 3X >= 3X = isNatList(X) U61(mark(X1),X2,X3) = 8X1 + 4X2 + 2X3 + 1 >= 4X1 + 4X2 + 2X3 + 1 = U61(X1,X2,X3) U61(X1,mark(X2),X3) = 4X1 + 8X2 + 2X3 + 1 >= 4X1 + 4X2 + 2X3 + 1 = U61(X1,X2,X3) U61(X1,X2,mark(X3)) = 4X1 + 4X2 + 4X3 + 1 >= 4X1 + 4X2 + 2X3 + 1 = U61(X1,X2,X3) U61(active(X1),X2,X3) = 4X1 + 4X2 + 2X3 + 1 >= 4X1 + 4X2 + 2X3 + 1 = U61(X1,X2,X3) U61(X1,active(X2),X3) = 4X1 + 4X2 + 2X3 + 1 >= 4X1 + 4X2 + 2X3 + 1 = U61(X1,X2,X3) U61(X1,X2,active(X3)) = 4X1 + 4X2 + 2X3 + 1 >= 4X1 + 4X2 + 2X3 + 1 = U61(X1,X2,X3) U62(mark(X1),X2) = 2X1 + 2X2 >= X1 + 2X2 = U62(X1,X2) U62(X1,mark(X2)) = X1 + 4X2 >= X1 + 2X2 = U62(X1,X2) U62(active(X1),X2) = X1 + 2X2 >= X1 + 2X2 = U62(X1,X2) U62(X1,active(X2)) = X1 + 2X2 >= X1 + 2X2 = U62(X1,X2) isNat(mark(X)) = 2X >= X = isNat(X) isNat(active(X)) = X >= X = isNat(X) s(mark(X)) = 8X >= 4X = s(X) s(active(X)) = 4X >= 4X = s(X) problem: active(zeros()) -> mark(cons(0(),zeros())) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(isNat(0())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U31(mark(X)) -> U31(X) U31(active(X)) -> U31(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(X1,mark(X2)) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) U62(X1,active(X2)) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [mark](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 0] [1 0 1] [1 0 1] [U61](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 [1 0 1] [0 0 0] [0 0 0] , [1 0 1] [U31](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [0] [active](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 1 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1] [isNat](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 1] [0] [s](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [1 0 1] [U62](x0, x1) = [1 0 1]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1] [tt] = [0] [0], [1 0 0] [1] [isNatIList](x0) = [0 0 0]x0 + [0] [1 0 1] [0], [0] [zeros] = [1] [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] [U42](x0) = [1 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1 0 0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [1 0 1] [0 0 0] , [1 0 0] [1] [isNatList](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1] [U11](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [0] [0] = [0] [0] orientation: [0] [0] active(zeros()) = [0] >= [0] = mark(cons(0(),zeros())) [1] [1] [1 0 0] [1] [1 0 0] [1] active(U51(tt(),V2)) = [0 0 0]V2 + [0] >= [0 0 0]V2 + [0] = mark(U52(isNatList(V2))) [0 0 0] [1] [0 0 0] [1] [1] [1] active(isNat(0())) = [0] >= [0] = mark(tt()) [1] [1] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] active(isNatList(cons(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 + [0] = mark(U51(isNat(V1),V2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] mark(zeros()) = [0] >= [0] = active(zeros()) [1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] mark(0()) = [0] >= [0] = active(0()) [1] [1] [1 0 0] [1] [1 0 0] [1] mark(U11(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(U11(mark(X))) [0 0 0] [1] [0 0 0] [1] [1] [1] mark(tt()) = [0] >= [0] = active(tt()) [1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [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] = active(U51(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] mark(U52(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(U52(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] mark(isNatList(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isNatList(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 1] [0] mark(U62(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(U62(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] mark(isNat(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isNat(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] cons(mark(X1),X2) = [0 0 0]X1 + [0 1 0]X2 >= [0 0 0]X1 + [0 1 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1 0 0] [1 0 0] cons(active(X1),X2) = [0 0 0]X1 + [0 1 0]X2 >= [0 0 0]X1 + [0 1 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] U11(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U11(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 0] [1] U11(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U11(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 1] U31(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = U31(X) [0 0 0] [0] [0 0 0] [1 0 1] [1] [1 0 1] U31(active(X)) = [0 0 0]X + [0] >= [0 0 0]X = U31(X) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] U41(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [1 0 1] [0 0 0] [1] [1 0 1] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U41(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [1 0 1] [0 0 0] [1 0 1] [0 0 0] [1 0 1] [1 0 0] [0] [1 0 0] [1 0 0] U41(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [1 0 1] [0 0 0] [1] [1 0 1] [0 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] U41(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [1 0 1] [0 0 0] [1 0 1] [0 0 0] [1 0 0] [1] [1 0 0] [1] U42(mark(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = U42(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 0] [1] U42(active(X)) = [1 0 1]X + [0] >= [1 0 0]X + [0] = U42(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] isNatIList(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNatIList(X) [1 0 1] [1] [1 0 1] [0] [1 0 1] [1] [1 0 0] [1] isNatIList(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNatIList(X) [1 0 1] [1] [1 0 1] [0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U51(mark(X1),X2) = [1 0 0]X1 + [0 0 0]X2 >= [1 0 0]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1 0 0] [1 0 0] U51(active(X1),X2) = [1 0 1]X1 + [0 0 0]X2 >= [1 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] U52(mark(X)) = [0 0 0]X >= [0 0 0]X = U52(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] U52(active(X)) = [0 0 0]X >= [0 0 0]X = U52(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] isNatList(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNatList(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 0] [1] isNatList(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNatList(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 1] [1 0 1] [0] [1 0 0] [1 0 1] [1 0 1] U61(mark(X1),X2,X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [1 0 1] [0 0 0] [0 0 0] [1] [1 0 1] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 1] [1] [1 0 0] [1 0 1] [1 0 1] U61(X1,mark(X2),X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [1 0 1] [0 0 0] [0 0 0] [0] [1 0 1] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 1] [1] [1 0 0] [1 0 1] [1 0 1] U61(X1,X2,mark(X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [1 0 1] [0 0 0] [0 0 0] [0] [1 0 1] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [0] [1 0 0] [1 0 1] [1 0 1] U61(active(X1),X2,X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [1 0 1] [0 0 0] [0 0 0] [1] [1 0 1] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 1] [1] [1 0 0] [1 0 1] [1 0 1] U61(X1,active(X2),X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [1 0 1] [0 0 0] [0 0 0] [0] [1 0 1] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 1] [1] [1 0 0] [1 0 1] [1 0 1] U61(X1,X2,active(X3)) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [1 0 1] [0 0 0] [0 0 0] [0] [1 0 1] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 1] U62(mark(X1),X2) = [1 0 1]X1 + [0 0 0]X2 + [1] >= [1 0 1]X1 + [0 0 0]X2 = U62(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 1] U62(X1,mark(X2)) = [1 0 1]X1 + [0 0 0]X2 + [0] >= [1 0 1]X1 + [0 0 0]X2 = U62(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [0] [1 0 0] [1 0 1] U62(active(X1),X2) = [1 0 1]X1 + [0 0 0]X2 + [1] >= [1 0 1]X1 + [0 0 0]X2 = U62(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 1] U62(X1,active(X2)) = [1 0 1]X1 + [0 0 0]X2 + [0] >= [1 0 1]X1 + [0 0 0]X2 = U62(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] isNat(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNat(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 0] [1] isNat(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNat(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 1] [0] s(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = s(X) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1] [1 0 1] [0] s(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = s(X) [0 0 0] [1] [0 0 0] [1] problem: active(zeros()) -> mark(cons(0(),zeros())) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(isNat(0())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) Matrix Interpretation Processor: dim=1 interpretation: [mark](x0) = 2x0, [U61](x0, x1, x2) = x0 + 2x1 + x2 + 6, [active](x0) = x0, [cons](x0, x1) = 4x0 + 4x1, [isNat](x0) = 2x0, [U62](x0, x1) = 2x0 + 4x1, [tt] = 0, [isNatIList](x0) = x0 + 6, [zeros] = 0, [U52](x0) = x0, [U51](x0, x1) = x0 + 2x1, [U42](x0) = 4x0 + 4, [U41](x0, x1) = x0 + 2x1 + 1, [isNatList](x0) = x0, [U11](x0) = 4x0 + 2, [0] = 0 orientation: active(zeros()) = 0 >= 0 = mark(cons(0(),zeros())) active(U51(tt(),V2)) = 2V2 >= 2V2 = mark(U52(isNatList(V2))) active(isNat(0())) = 0 >= 0 = mark(tt()) active(isNatList(cons(V1,V2))) = 4V1 + 4V2 >= 4V1 + 4V2 = mark(U51(isNat(V1),V2)) mark(zeros()) = 0 >= 0 = active(zeros()) mark(cons(X1,X2)) = 8X1 + 8X2 >= 8X1 + 4X2 = active(cons(mark(X1),X2)) mark(0()) = 0 >= 0 = active(0()) mark(U11(X)) = 8X + 4 >= 8X + 2 = active(U11(mark(X))) mark(tt()) = 0 >= 0 = active(tt()) mark(U51(X1,X2)) = 2X1 + 4X2 >= 2X1 + 2X2 = active(U51(mark(X1),X2)) mark(U52(X)) = 2X >= 2X = active(U52(mark(X))) mark(isNatList(X)) = 2X >= X = active(isNatList(X)) mark(U62(X1,X2)) = 4X1 + 8X2 >= 4X1 + 4X2 = active(U62(mark(X1),X2)) mark(isNat(X)) = 4X >= 2X = active(isNat(X)) cons(mark(X1),X2) = 8X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) cons(active(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) U11(mark(X)) = 8X + 2 >= 4X + 2 = U11(X) U11(active(X)) = 4X + 2 >= 4X + 2 = U11(X) U41(mark(X1),X2) = 2X1 + 2X2 + 1 >= X1 + 2X2 + 1 = U41(X1,X2) U41(X1,mark(X2)) = X1 + 4X2 + 1 >= X1 + 2X2 + 1 = U41(X1,X2) U41(active(X1),X2) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = U41(X1,X2) U41(X1,active(X2)) = X1 + 2X2 + 1 >= X1 + 2X2 + 1 = U41(X1,X2) U42(mark(X)) = 8X + 4 >= 4X + 4 = U42(X) U42(active(X)) = 4X + 4 >= 4X + 4 = U42(X) isNatIList(mark(X)) = 2X + 6 >= X + 6 = isNatIList(X) isNatIList(active(X)) = X + 6 >= X + 6 = isNatIList(X) U51(mark(X1),X2) = 2X1 + 2X2 >= X1 + 2X2 = U51(X1,X2) U51(active(X1),X2) = X1 + 2X2 >= X1 + 2X2 = U51(X1,X2) U52(mark(X)) = 2X >= X = U52(X) U52(active(X)) = X >= X = U52(X) isNatList(mark(X)) = 2X >= X = isNatList(X) isNatList(active(X)) = X >= X = isNatList(X) U61(mark(X1),X2,X3) = 2X1 + 2X2 + X3 + 6 >= X1 + 2X2 + X3 + 6 = U61(X1,X2,X3) U61(active(X1),X2,X3) = X1 + 2X2 + X3 + 6 >= X1 + 2X2 + X3 + 6 = U61(X1,X2,X3) U62(mark(X1),X2) = 4X1 + 4X2 >= 2X1 + 4X2 = U62(X1,X2) U62(active(X1),X2) = 2X1 + 4X2 >= 2X1 + 4X2 = U62(X1,X2) isNat(mark(X)) = 4X >= 2X = isNat(X) isNat(active(X)) = 2X >= 2X = isNat(X) problem: active(zeros()) -> mark(cons(0(),zeros())) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(isNat(0())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(U62(X1,X2)) -> active(U62(mark(X1),X2)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 1] [mark](x0) = [0 0 0]x0 [0 1 1] , [1 0 0] [1 0 0] [1 0 0] [0] [U61](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 + [1] [0 0 0] [0 0 0] [0 0 0] [0], [1 1 0] [active](x0) = [0 0 0]x0 [0 1 1] , [1 0 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 1 1] [0 0 1] , [1 0 0] [isNat](x0) = [0 0 1]x0 [0 0 0] , [1 0 0] [1 0 0] [0] [U62](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 1 1] [0 1 0] [1], [0] [tt] = [1] [0], [1 0 0] [0] [isNatIList](x0) = [0 0 1]x0 + [0] [0 0 0] [1], [0] [zeros] = [1] [0], [1 0 0] [U52](x0) = [0 0 0]x0 [0 1 1] , [1 0 0] [1 0 0] [U51](x0, x1) = [0 0 0]x0 + [0 0 1]x1 [0 1 1] [0 0 0] , [1 0 0] [0] [U42](x0) = [0 0 0]x0 + [0] [1 0 0] [1], [1 0 0] [1 0 0] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [1 0 0] , [1 0 0] [isNatList](x0) = [0 0 1]x0 [0 0 0] , [1 0 0] [0] [U11](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [0] [0] = [0] [1] orientation: [1] [1] active(zeros()) = [0] >= [0] = mark(cons(0(),zeros())) [1] [1] [1 0 1] [0] [1 0 1] active(U51(tt(),V2)) = [0 0 0]V2 + [0] >= [0 0 0]V2 = mark(U52(isNatList(V2))) [0 0 1] [1] [0 0 1] [1] [1] active(isNat(0())) = [0] >= [0] = mark(tt()) [1] [1] [1 1 1] [1 0 1] [1 0 1] [1 0 1] active(isNatList(cons(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = mark(U51(isNat(V1),V2)) [0 1 1] [0 0 1] [0 0 1] [0 0 1] [1] [1] mark(zeros()) = [0] >= [0] = active(zeros()) [1] [1] [1 1 1] [1 0 1] [1 1 1] [1 0 0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(cons(mark(X1),X2)) [0 1 1] [0 0 1] [0 1 1] [0 0 1] [1] [0] mark(0()) = [0] >= [0] = active(0()) [1] [1] [1] [1] mark(tt()) = [0] >= [0] = active(tt()) [1] [1] [1 1 1] [1 0 1] [1 1 1] [1 0 1] mark(U51(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(U51(mark(X1),X2)) [0 1 1] [0 0 1] [0 1 1] [0 0 1] [1 1 1] [1 1 1] mark(U52(X)) = [0 0 0]X >= [0 0 0]X = active(U52(mark(X))) [0 1 1] [0 1 1] [1 0 1] [1 0 1] mark(isNatList(X)) = [0 0 0]X >= [0 0 0]X = active(isNatList(X)) [0 0 1] [0 0 1] [1 1 1] [1 1 0] [1] [1 1 1] [1 0 0] [0] mark(U62(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(U62(mark(X1),X2)) [0 1 1] [0 1 0] [1] [0 1 1] [0 1 0] [1] [1 0 1] [1 0 1] mark(isNat(X)) = [0 0 0]X >= [0 0 0]X = active(isNat(X)) [0 0 1] [0 0 1] [1 1 1] [1 0 0] [1 0 0] [1 0 0] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 1 1] [0 0 1] [0 1 1] [0 0 1] [1 1 0] [1 0 0] [1 0 0] [1 0 0] cons(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 1 1] [0 0 1] [0 1 1] [0 0 1] [1 1 1] [0] [1 0 0] [0] U11(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U11(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [0] [1 0 0] [0] U11(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U11(X) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1 0 0] [1 0 0] [1 0 0] U41(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [0 1 1] [1 0 0] [0 0 1] [1 0 0] [1 0 0] [1 1 1] [1 0 0] [1 0 0] U41(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [0 0 1] [1 1 1] [0 0 1] [1 0 0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] U41(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [0 1 1] [1 0 0] [0 0 1] [1 0 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] U41(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U41(X1,X2) [0 0 1] [1 1 0] [0 0 1] [1 0 0] [1 1 1] [0] [1 0 0] [0] U42(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U42(X) [1 1 1] [1] [1 0 0] [1] [1 1 0] [0] [1 0 0] [0] U42(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U42(X) [1 1 0] [1] [1 0 0] [1] [1 1 1] [0] [1 0 0] [0] isNatIList(mark(X)) = [0 1 1]X + [0] >= [0 0 1]X + [0] = isNatIList(X) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 0 0] [0] isNatIList(active(X)) = [0 1 1]X + [0] >= [0 0 1]X + [0] = isNatIList(X) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1 0 0] [1 0 0] [1 0 0] U51(mark(X1),X2) = [0 0 0]X1 + [0 0 1]X2 >= [0 0 0]X1 + [0 0 1]X2 = U51(X1,X2) [0 1 1] [0 0 0] [0 1 1] [0 0 0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] U51(active(X1),X2) = [0 0 0]X1 + [0 0 1]X2 >= [0 0 0]X1 + [0 0 1]X2 = U51(X1,X2) [0 1 1] [0 0 0] [0 1 1] [0 0 0] [1 1 1] [1 0 0] U52(mark(X)) = [0 0 0]X >= [0 0 0]X = U52(X) [0 1 1] [0 1 1] [1 1 0] [1 0 0] U52(active(X)) = [0 0 0]X >= [0 0 0]X = U52(X) [0 1 1] [0 1 1] [1 1 1] [1 0 0] isNatList(mark(X)) = [0 1 1]X >= [0 0 1]X = isNatList(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] isNatList(active(X)) = [0 1 1]X >= [0 0 1]X = isNatList(X) [0 0 0] [0 0 0] [1 1 1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [0] U61(mark(X1),X2,X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [1] = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] [1 1 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [0] U61(active(X1),X2,X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [1] = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] [1 1 1] [1 0 0] [0] [1 0 0] [1 0 0] [0] U62(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U62(X1,X2) [0 1 1] [0 1 0] [1] [0 1 1] [0 1 0] [1] [1 1 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] U62(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U62(X1,X2) [0 1 1] [0 1 0] [1] [0 1 1] [0 1 0] [1] [1 1 1] [1 0 0] isNat(mark(X)) = [0 1 1]X >= [0 0 1]X = isNat(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] isNat(active(X)) = [0 1 1]X >= [0 0 1]X = isNat(X) [0 0 0] [0 0 0] problem: active(zeros()) -> mark(cons(0(),zeros())) active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(isNat(0())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [mark](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [1 0 0] [1 0 0] [U61](x0, x1, x2) = [1 1 0]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 0] [0 0 0] [0 0 0] , [1 1 0] [active](x0) = [0 0 1]x0 [0 0 0] , [1 1 1] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [isNat](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [U62](x0, x1) = [1 1 0]x0 + [0 0 0]x1 [1 0 0] [0 0 0] , [0] [tt] = [0] [0], [1 0 0] [isNatIList](x0) = [0 0 0]x0 [0 0 0] , [0] [zeros] = [1] [1], [1 1 1] [U52](x0) = [0 0 0]x0 [0 0 0] , [1 1 1] [1 0 0] [U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U42](x0) = [0 0 0]x0 [1 1 0] , [1 0 0] [1 0 0] [0] [U41](x0, x1) = [0 0 0]x0 + [1 1 1]x1 + [1] [0 0 0] [0 0 0] [0], [1 0 0] [isNatList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [0] [0] = [0] [0] orientation: [1] [0] active(zeros()) = [1] >= [0] = mark(cons(0(),zeros())) [0] [0] [1 0 0] [1 0 0] active(U51(tt(),V2)) = [0 0 0]V2 >= [0 0 0]V2 = mark(U52(isNatList(V2))) [0 0 0] [0 0 0] [0] [0] active(isNat(0())) = [0] >= [0] = mark(tt()) [0] [0] [1 1 1] [1 0 0] [1 0 0] [1 0 0] active(isNatList(cons(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 >= [0 0 0]V1 + [0 0 0]V2 = mark(U51(isNat(V1),V2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1] [1] mark(zeros()) = [1] >= [1] = active(zeros()) [0] [0] [1 1 1] [1 0 0] [1 1 1] [1 0 0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [0] [0] [1 1 1] [1 0 0] [1 1 1] [1 0 0] mark(U51(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(U51(mark(X1),X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 1 1] mark(U52(X)) = [0 0 0]X >= [0 0 0]X = active(U52(mark(X))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] mark(isNatList(X)) = [0 0 0]X >= [0 0 0]X = active(isNatList(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] mark(isNat(X)) = [0 0 0]X >= [0 0 0]X = active(isNat(X)) [0 0 0] [0 0 0] [1 1 1] [1 0 0] [1 1 1] [1 0 0] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 0 0] [1 1 1] [1 0 0] cons(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] U11(mark(X)) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] U11(active(X)) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] [0] [1 0 0] [1 0 0] [0] U41(mark(X1),X2) = [0 0 0]X1 + [1 1 1]X2 + [1] >= [0 0 0]X1 + [1 1 1]X2 + [1] = U41(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 0] [0] U41(X1,mark(X2)) = [0 0 0]X1 + [1 1 1]X2 + [1] >= [0 0 0]X1 + [1 1 1]X2 + [1] = U41(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] U41(active(X1),X2) = [0 0 0]X1 + [1 1 1]X2 + [1] >= [0 0 0]X1 + [1 1 1]X2 + [1] = U41(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 1 0] [0] [1 0 0] [1 0 0] [0] U41(X1,active(X2)) = [0 0 0]X1 + [1 1 1]X2 + [1] >= [0 0 0]X1 + [1 1 1]X2 + [1] = U41(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 0] U42(mark(X)) = [0 0 0]X >= [0 0 0]X = U42(X) [1 1 1] [1 1 0] [1 1 0] [1 0 0] U42(active(X)) = [0 0 0]X >= [0 0 0]X = U42(X) [1 1 1] [1 1 0] [1 0 1] [1 0 0] isNatIList(mark(X)) = [0 0 0]X >= [0 0 0]X = isNatIList(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] isNatIList(active(X)) = [0 0 0]X >= [0 0 0]X = isNatIList(X) [0 0 0] [0 0 0] [1 1 1] [1 0 0] [1 1 1] [1 0 0] U51(mark(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 1 1] [1 0 0] [1 1 1] [1 0 0] U51(active(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 1 1] [1 1 1] U52(mark(X)) = [0 0 0]X >= [0 0 0]X = U52(X) [0 0 0] [0 0 0] [1 1 1] [1 1 1] U52(active(X)) = [0 0 0]X >= [0 0 0]X = U52(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] isNatList(mark(X)) = [0 0 0]X >= [0 0 0]X = isNatList(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] isNatList(active(X)) = [0 0 0]X >= [0 0 0]X = isNatList(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U61(mark(X1),X2,X3) = [1 1 1]X1 + [0 0 0]X2 + [0 0 0]X3 >= [1 1 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U61(active(X1),X2,X3) = [1 1 1]X1 + [0 0 0]X2 + [0 0 0]X3 >= [1 1 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1 0 0] [1 0 0] U62(mark(X1),X2) = [1 1 1]X1 + [0 0 0]X2 >= [1 1 0]X1 + [0 0 0]X2 = U62(X1,X2) [1 0 1] [0 0 0] [1 0 0] [0 0 0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] U62(active(X1),X2) = [1 1 1]X1 + [0 0 0]X2 >= [1 1 0]X1 + [0 0 0]X2 = U62(X1,X2) [1 1 0] [0 0 0] [1 0 0] [0 0 0] [1 0 1] [1 0 0] isNat(mark(X)) = [0 0 0]X >= [0 0 0]X = isNat(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] isNat(active(X)) = [0 0 0]X >= [0 0 0]X = isNat(X) [0 0 0] [0 0 0] problem: active(U51(tt(),V2)) -> mark(U52(isNatList(V2))) active(isNat(0())) -> mark(tt()) active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) Matrix Interpretation Processor: dim=1 interpretation: [mark](x0) = x0, [U61](x0, x1, x2) = 2x0 + x1 + x2, [active](x0) = x0, [cons](x0, x1) = x0 + x1, [isNat](x0) = x0, [U62](x0, x1) = 2x0 + 4x1 + 2, [tt] = 2, [isNatIList](x0) = 2x0, [zeros] = 2, [U52](x0) = x0, [U51](x0, x1) = x0 + 4x1, [U42](x0) = 2x0 + 5, [U41](x0, x1) = 4x0 + 4x1 + 6, [isNatList](x0) = 4x0, [U11](x0) = 4x0 + 2, [0] = 4 orientation: active(U51(tt(),V2)) = 4V2 + 2 >= 4V2 = mark(U52(isNatList(V2))) active(isNat(0())) = 4 >= 2 = mark(tt()) active(isNatList(cons(V1,V2))) = 4V1 + 4V2 >= V1 + 4V2 = mark(U51(isNat(V1),V2)) mark(zeros()) = 2 >= 2 = active(zeros()) mark(cons(X1,X2)) = X1 + X2 >= X1 + X2 = active(cons(mark(X1),X2)) mark(tt()) = 2 >= 2 = active(tt()) mark(U51(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = active(U51(mark(X1),X2)) mark(U52(X)) = X >= X = active(U52(mark(X))) mark(isNatList(X)) = 4X >= 4X = active(isNatList(X)) mark(isNat(X)) = X >= X = active(isNat(X)) cons(mark(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) cons(active(X1),X2) = X1 + X2 >= X1 + X2 = cons(X1,X2) U11(mark(X)) = 4X + 2 >= 4X + 2 = U11(X) U11(active(X)) = 4X + 2 >= 4X + 2 = U11(X) U41(mark(X1),X2) = 4X1 + 4X2 + 6 >= 4X1 + 4X2 + 6 = U41(X1,X2) U41(X1,mark(X2)) = 4X1 + 4X2 + 6 >= 4X1 + 4X2 + 6 = U41(X1,X2) U41(active(X1),X2) = 4X1 + 4X2 + 6 >= 4X1 + 4X2 + 6 = U41(X1,X2) U41(X1,active(X2)) = 4X1 + 4X2 + 6 >= 4X1 + 4X2 + 6 = U41(X1,X2) U42(mark(X)) = 2X + 5 >= 2X + 5 = U42(X) U42(active(X)) = 2X + 5 >= 2X + 5 = U42(X) isNatIList(mark(X)) = 2X >= 2X = isNatIList(X) isNatIList(active(X)) = 2X >= 2X = isNatIList(X) U51(mark(X1),X2) = X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) U51(active(X1),X2) = X1 + 4X2 >= X1 + 4X2 = U51(X1,X2) U52(mark(X)) = X >= X = U52(X) U52(active(X)) = X >= X = U52(X) isNatList(mark(X)) = 4X >= 4X = isNatList(X) isNatList(active(X)) = 4X >= 4X = isNatList(X) U61(mark(X1),X2,X3) = 2X1 + X2 + X3 >= 2X1 + X2 + X3 = U61(X1,X2,X3) U61(active(X1),X2,X3) = 2X1 + X2 + X3 >= 2X1 + X2 + X3 = U61(X1,X2,X3) U62(mark(X1),X2) = 2X1 + 4X2 + 2 >= 2X1 + 4X2 + 2 = U62(X1,X2) U62(active(X1),X2) = 2X1 + 4X2 + 2 >= 2X1 + 4X2 + 2 = U62(X1,X2) isNat(mark(X)) = X >= X = isNat(X) isNat(active(X)) = X >= X = isNat(X) problem: active(isNatList(cons(V1,V2))) -> mark(U51(isNat(V1),V2)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(mark(X1),X2) -> U62(X1,X2) U62(active(X1),X2) -> U62(X1,X2) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [0] [mark](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 1 1] [1 0 0] [1 0 0] [U61](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 0] [0 0 0] [0 0 0] , [1 0 1] [active](x0) = [0 1 0]x0 [0 0 0] , [1 0 1] [1 0 0] [1] [cons](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [1 1 1] [isNat](x0) = [0 0 0]x0 [0 0 0] , [1 1 1] [1 0 0] [U62](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [tt] = [0] [0], [1 1 1] [isNatIList](x0) = [0 0 0]x0 [0 0 0] , [0] [zeros] = [0] [0], [1 0 1] [0] [U52](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 1] [1 0 0] [U51](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 1 1] [U42](x0) = [0 0 0]x0 [0 0 0] , [1 1 1] [1 1 1] [U41](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 1 1] [isNatList](x0) = [1 0 1]x0 [0 0 0] , [1 1 1] [U11](x0) = [0 0 0]x0 [0 0 0] orientation: [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] [0] active(isNatList(cons(V1,V2))) = [1 0 1]V1 + [1 0 0]V2 + [1] >= [0 0 0]V1 + [0 0 0]V2 + [1] = mark(U51(isNat(V1),V2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [0] [0] mark(zeros()) = [1] >= [0] = active(zeros()) [0] [0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] mark(cons(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [0 0 0]X2 + [1] = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [0] [0] mark(tt()) = [1] >= [0] = active(tt()) [0] [0] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] [0] mark(U51(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [0 0 0]X2 + [1] = active(U51(mark(X1),X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1] [1 0 1] [1] mark(U52(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = active(U52(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 1 1] [0] [1 1 1] mark(isNatList(X)) = [1 0 1]X + [1] >= [1 0 1]X = active(isNatList(X)) [0 0 0] [0] [0 0 0] [1 1 1] [0] [1 1 1] mark(isNat(X)) = [0 0 0]X + [1] >= [0 0 0]X = active(isNat(X)) [0 0 0] [0] [0 0 0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] cons(mark(X1),X2) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] cons(active(X1),X2) = [0 1 0]X1 + [0 0 0]X2 + [0] >= [0 1 0]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1] [1 1 1] U11(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = U11(X) [0 0 0] [0] [0 0 0] [1 1 1] [1 1 1] U11(active(X)) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 1 1] [1 1 1] [1] [1 1 1] [1 1 1] U41(mark(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] [1 1 1] [1 1 1] [1] [1 1 1] [1 1 1] U41(X1,mark(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] [1 1 1] [1 1 1] [1 1 1] [1 1 1] U41(active(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 1 1] [1 1 1] [1 1 1] [1 1 1] U41(X1,active(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 1 1] [1] [1 1 1] U42(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = U42(X) [0 0 0] [0] [0 0 0] [1 1 1] [1 1 1] U42(active(X)) = [0 0 0]X >= [0 0 0]X = U42(X) [0 0 0] [0 0 0] [1 1 1] [1] [1 1 1] isNatIList(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = isNatIList(X) [0 0 0] [0] [0 0 0] [1 1 1] [1 1 1] isNatIList(active(X)) = [0 0 0]X >= [0 0 0]X = isNatIList(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] [0] [1 0 1] [1 0 0] U51(mark(X1),X2) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] U51(active(X1),X2) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [0] [1 0 1] [0] U52(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U52(X) [0 0 0] [1] [0 0 0] [1] [1 0 1] [0] [1 0 1] [0] U52(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U52(X) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 1] isNatList(mark(X)) = [1 0 1]X + [0] >= [1 0 1]X = isNatList(X) [0 0 0] [0] [0 0 0] [1 1 1] [1 1 1] isNatList(active(X)) = [1 0 1]X >= [1 0 1]X = isNatList(X) [0 0 0] [0 0 0] [1 1 1] [1 0 0] [1 0 0] [1] [1 1 1] [1 0 0] [1 0 0] U61(mark(X1),X2,X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 0 0] [1 0 0] [1 1 1] [1 0 0] [1 0 0] U61(active(X1),X2,X3) = [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 >= [0 0 0]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] U62(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = U62(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 1 1] [1 0 0] [1 1 1] [1 0 0] U62(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = U62(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 1] [1] [1 1 1] isNat(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = isNat(X) [0 0 0] [0] [0 0 0] [1 1 1] [1 1 1] isNat(active(X)) = [0 0 0]X >= [0 0 0]X = isNat(X) [0 0 0] [0 0 0] problem: mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [mark](x0) = [1 1 0]x0 [0 0 1] , [1 0 0] [1 0 0] [1 0 0] [U61](x0, x1, x2) = [1 0 1]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 0] [0 0 0] [0 0 0] , [1 0 0] [active](x0) = [1 0 0]x0 [0 0 1] , [1 0 0] [1 0 0] [1] [cons](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [0] [0 0 1] [0 0 0] [0], [1 0 0] [isNat](x0) = [0 0 1]x0 [0 0 0] , [1 0 0] [1 0 0] [1] [U62](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [1 0 0] [0 0 0] [1], [0] [tt] = [0] [0], [1 0 0] [0] [isNatIList](x0) = [0 0 0]x0 + [1] [1 0 0] [0], [0] [zeros] = [0] [1], [1 0 0] [U52](x0) = [0 0 1]x0 [0 0 1] , [1 0 0] [1 0 0] [U51](x0, x1) = [0 0 1]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [1 0 0] [U42](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] [isNatList](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [0] [U11](x0) = [0 0 0]x0 + [0] [1 0 0] [1] orientation: [1] [0] mark(zeros()) = [0] >= [0] = active(zeros()) [1] [1] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] mark(cons(X1,X2)) = [1 0 1]X1 + [1 0 0]X2 + [1] >= [1 0 1]X1 + [1 0 0]X2 + [1] = active(cons(mark(X1),X2)) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [0] [0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] mark(U51(X1,X2)) = [1 0 1]X1 + [1 0 0]X2 >= [1 0 1]X1 + [1 0 0]X2 = active(U51(mark(X1),X2)) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [1 0 1] [1 0 1] mark(U52(X)) = [1 0 1]X >= [1 0 1]X = active(U52(mark(X))) [0 0 1] [0 0 1] [1 0 1] [1 0 0] mark(isNatList(X)) = [1 0 0]X >= [1 0 0]X = active(isNatList(X)) [0 0 1] [0 0 1] [1 0 0] [1 0 0] mark(isNat(X)) = [1 0 1]X >= [1 0 0]X = active(isNat(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1] [1 0 0] [1 0 0] [1] cons(mark(X1),X2) = [0 0 1]X1 + [0 0 0]X2 + [0] >= [0 0 1]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] cons(active(X1),X2) = [0 0 1]X1 + [0 0 0]X2 + [0] >= [0 0 1]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] U11(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U11(X) [1 0 0] [1] [1 0 0] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U41(active(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] U41(X1,active(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] U42(active(X)) = [0 0 0]X >= [0 0 0]X = U42(X) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] [0] isNatIList(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNatIList(X) [1 0 0] [0] [1 0 0] [0] [1 0 1] [1 0 0] [1 0 0] [1 0 0] U51(mark(X1),X2) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U51(active(X1),X2) = [0 0 1]X1 + [0 0 0]X2 >= [0 0 1]X1 + [0 0 0]X2 = U51(X1,X2) [0 0 1] [0 0 0] [0 0 1] [0 0 0] [1 0 1] [1 0 0] U52(mark(X)) = [0 0 1]X >= [0 0 1]X = U52(X) [0 0 1] [0 0 1] [1 0 0] [1 0 0] U52(active(X)) = [0 0 1]X >= [0 0 1]X = U52(X) [0 0 1] [0 0 1] [1 0 0] [1 0 0] isNatList(active(X)) = [0 0 0]X >= [0 0 0]X = isNatList(X) [0 0 1] [0 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] U61(active(X1),X2,X3) = [1 0 1]X1 + [0 0 0]X2 + [0 0 0]X3 >= [1 0 1]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [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] [1] U62(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = U62(X1,X2) [1 0 0] [0 0 0] [1] [1 0 0] [0 0 0] [1] [1 0 0] [1 0 0] isNat(active(X)) = [0 0 1]X >= [0 0 1]X = isNat(X) [0 0 0] [0 0 0] problem: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [mark](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [1 0 0] [1 0 0] [U61](x0, x1, x2) = [1 0 1]x0 + [0 0 0]x1 + [0 0 0]x2 [0 0 0] [0 0 0] [0 0 0] , [1 0 1] [0] [active](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [1 1 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1] [isNat](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1 0 0] [1] [U62](x0, x1) = [1 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [0] [tt] = [0] [0], [1 0 0] [1] [isNatIList](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1] [U52](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [1 1 0] [U51](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [U42](x0) = [0 0 0]x0 [1 0 0] , [1 0 1] [1 0 0] [0] [U41](x0, x1) = [0 0 0]x0 + [1 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [1 0 0] [1] [isNatList](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [0] [U11](x0) = [0 0 0]x0 + [1] [0 0 0] [0] orientation: [1 0 0] [1 1 0] [0] [1 0 0] [1 1 0] [0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [1] [1] [1 0 0] [1 1 0] [0] [1 0 0] [1 1 0] [0] mark(U51(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(U51(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] mark(U52(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(U52(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] mark(isNatList(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isNatList(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] mark(isNat(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(isNat(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 1 0] [1 0 0] [1 1 0] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 1 0] [1 0 0] [1 1 0] cons(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [0] [1 0 0] [0] U11(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U11(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [0] U41(active(X1),X2) = [0 0 0]X1 + [1 0 0]X2 + [1] >= [0 0 0]X1 + [1 0 0]X2 + [1] = U41(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 0] [0] U41(X1,active(X2)) = [0 0 0]X1 + [1 0 1]X2 + [1] >= [0 0 0]X1 + [1 0 0]X2 + [1] = U41(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 0] U42(active(X)) = [0 0 0]X >= [0 0 0]X = U42(X) [1 0 1] [1 0 0] [1 0 1] [1] [1 0 0] [1] isNatIList(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNatIList(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] U51(mark(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 1] [1 1 0] [1 0 0] [1 1 0] U51(active(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] [1 0 0] [1] U52(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U52(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 0] [1] U52(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U52(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 0] [1] isNatList(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNatList(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [1 0 0] U61(active(X1),X2,X3) = [1 0 1]X1 + [0 0 0]X2 + [0 0 0]X3 + [1] >= [1 0 1]X1 + [0 0 0]X2 + [0 0 0]X3 = U61(X1,X2,X3) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1] [1 0 0] [1 0 0] [1] U62(active(X1),X2) = [1 0 1]X1 + [0 0 0]X2 + [0] >= [1 0 0]X1 + [0 0 0]X2 + [0] = U62(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1] [1 0 0] [1] isNat(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNat(X) [0 0 0] [0] [0 0 0] [0] problem: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X)) -> active(U52(mark(X))) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Matrix Interpretation Processor: dim=1 interpretation: [mark](x0) = 4x0, [U61](x0, x1, x2) = 4x0 + x1 + x2, [active](x0) = x0, [cons](x0, x1) = x0 + 2x1, [isNat](x0) = 2x0, [U62](x0, x1) = 4x0 + x1 + 2, [tt] = 0, [isNatIList](x0) = 4x0 + 7, [U52](x0) = 4x0 + 6, [U51](x0, x1) = 4x0 + 4x1, [U42](x0) = 2x0 + 2, [U41](x0, x1) = 2x0 + x1 + 7, [isNatList](x0) = x0, [U11](x0) = 4x0 + 4 orientation: mark(cons(X1,X2)) = 4X1 + 8X2 >= 4X1 + 2X2 = active(cons(mark(X1),X2)) mark(tt()) = 0 >= 0 = active(tt()) mark(U51(X1,X2)) = 16X1 + 16X2 >= 16X1 + 4X2 = active(U51(mark(X1),X2)) mark(U52(X)) = 16X + 24 >= 16X + 6 = active(U52(mark(X))) mark(isNatList(X)) = 4X >= X = active(isNatList(X)) mark(isNat(X)) = 8X >= 2X = active(isNat(X)) cons(mark(X1),X2) = 4X1 + 2X2 >= X1 + 2X2 = cons(X1,X2) cons(active(X1),X2) = X1 + 2X2 >= X1 + 2X2 = cons(X1,X2) U11(active(X)) = 4X + 4 >= 4X + 4 = U11(X) U41(X1,active(X2)) = 2X1 + X2 + 7 >= 2X1 + X2 + 7 = U41(X1,X2) U42(active(X)) = 2X + 2 >= 2X + 2 = U42(X) isNatIList(active(X)) = 4X + 7 >= 4X + 7 = isNatIList(X) U51(mark(X1),X2) = 16X1 + 4X2 >= 4X1 + 4X2 = U51(X1,X2) U51(active(X1),X2) = 4X1 + 4X2 >= 4X1 + 4X2 = U51(X1,X2) U52(mark(X)) = 16X + 6 >= 4X + 6 = U52(X) U52(active(X)) = 4X + 6 >= 4X + 6 = U52(X) isNatList(active(X)) = X >= X = isNatList(X) U61(active(X1),X2,X3) = 4X1 + X2 + X3 >= 4X1 + X2 + X3 = U61(X1,X2,X3) U62(active(X1),X2) = 4X1 + X2 + 2 >= 4X1 + X2 + 2 = U62(X1,X2) isNat(active(X)) = 2X >= 2X = isNat(X) problem: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) DP Processor: DPs: mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> U51#(mark(X1),X2) cons#(mark(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) U11#(active(X)) -> U11#(X) U41#(X1,active(X2)) -> U41#(X1,X2) U42#(active(X)) -> U42#(X) isNatIList#(active(X)) -> isNatIList#(X) U51#(mark(X1),X2) -> U51#(X1,X2) U51#(active(X1),X2) -> U51#(X1,X2) U52#(mark(X)) -> U52#(X) U52#(active(X)) -> U52#(X) isNatList#(active(X)) -> isNatList#(X) U61#(active(X1),X2,X3) -> U61#(X1,X2,X3) U62#(active(X1),X2) -> U62#(X1,X2) isNat#(active(X)) -> isNat#(X) TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) TDG Processor: DPs: mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> U51#(mark(X1),X2) cons#(mark(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) U11#(active(X)) -> U11#(X) U41#(X1,active(X2)) -> U41#(X1,X2) U42#(active(X)) -> U42#(X) isNatIList#(active(X)) -> isNatIList#(X) U51#(mark(X1),X2) -> U51#(X1,X2) U51#(active(X1),X2) -> U51#(X1,X2) U52#(mark(X)) -> U52#(X) U52#(active(X)) -> U52#(X) isNatList#(active(X)) -> isNatList#(X) U61#(active(X1),X2,X3) -> U61#(X1,X2,X3) U62#(active(X1),X2) -> U62#(X1,X2) isNat#(active(X)) -> isNat#(X) TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) graph: isNat#(active(X)) -> isNat#(X) -> isNat#(active(X)) -> isNat#(X) U62#(active(X1),X2) -> U62#(X1,X2) -> U62#(active(X1),X2) -> U62#(X1,X2) U61#(active(X1),X2,X3) -> U61#(X1,X2,X3) -> U61#(active(X1),X2,X3) -> U61#(X1,X2,X3) isNatList#(active(X)) -> isNatList#(X) -> isNatList#(active(X)) -> isNatList#(X) U52#(mark(X)) -> U52#(X) -> U52#(active(X)) -> U52#(X) U52#(mark(X)) -> U52#(X) -> U52#(mark(X)) -> U52#(X) U52#(active(X)) -> U52#(X) -> U52#(active(X)) -> U52#(X) U52#(active(X)) -> U52#(X) -> U52#(mark(X)) -> U52#(X) isNatIList#(active(X)) -> isNatIList#(X) -> isNatIList#(active(X)) -> isNatIList#(X) U42#(active(X)) -> U42#(X) -> U42#(active(X)) -> U42#(X) U41#(X1,active(X2)) -> U41#(X1,X2) -> U41#(X1,active(X2)) -> U41#(X1,X2) U11#(active(X)) -> U11#(X) -> U11#(active(X)) -> U11#(X) U51#(mark(X1),X2) -> U51#(X1,X2) -> U51#(active(X1),X2) -> U51#(X1,X2) U51#(mark(X1),X2) -> U51#(X1,X2) -> U51#(mark(X1),X2) -> U51#(X1,X2) U51#(active(X1),X2) -> U51#(X1,X2) -> U51#(active(X1),X2) -> U51#(X1,X2) U51#(active(X1),X2) -> U51#(X1,X2) -> U51#(mark(X1),X2) -> U51#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(active(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) mark#(U51(X1,X2)) -> U51#(mark(X1),X2) -> U51#(active(X1),X2) -> U51#(X1,X2) mark#(U51(X1,X2)) -> U51#(mark(X1),X2) -> U51#(mark(X1),X2) -> U51#(X1,X2) mark#(U51(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2)) -> U51#(mark(X1),X2) mark#(U51(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(U51(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) -> cons#(active(X1),X2) -> cons#(X1,X2) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2)) -> U51#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) SCC Processor: #sccs: 12 #rules: 16 #arcs: 32/324 DPs: mark#(U51(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Subterm Criterion Processor: simple projection: pi(mark#) = 0 problem: DPs: TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Qed DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Subterm Criterion Processor: simple projection: pi(cons#) = 0 problem: DPs: TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Qed DPs: U51#(mark(X1),X2) -> U51#(X1,X2) U51#(active(X1),X2) -> U51#(X1,X2) TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Subterm Criterion Processor: simple projection: pi(U51#) = 0 problem: DPs: TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Qed DPs: U11#(active(X)) -> U11#(X) TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Subterm Criterion Processor: simple projection: pi(U11#) = 0 problem: DPs: TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Qed DPs: U41#(X1,active(X2)) -> U41#(X1,X2) TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Subterm Criterion Processor: simple projection: pi(U41#) = 1 problem: DPs: TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Qed DPs: U42#(active(X)) -> U42#(X) TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Subterm Criterion Processor: simple projection: pi(U42#) = 0 problem: DPs: TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Qed DPs: isNatIList#(active(X)) -> isNatIList#(X) TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Subterm Criterion Processor: simple projection: pi(isNatIList#) = 0 problem: DPs: TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Qed DPs: U52#(mark(X)) -> U52#(X) U52#(active(X)) -> U52#(X) TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Subterm Criterion Processor: simple projection: pi(U52#) = 0 problem: DPs: TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Qed DPs: isNatList#(active(X)) -> isNatList#(X) TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Subterm Criterion Processor: simple projection: pi(isNatList#) = 0 problem: DPs: TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Qed DPs: U61#(active(X1),X2,X3) -> U61#(X1,X2,X3) TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Subterm Criterion Processor: simple projection: pi(U61#) = 0 problem: DPs: TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Qed DPs: U62#(active(X1),X2) -> U62#(X1,X2) TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Subterm Criterion Processor: simple projection: pi(U62#) = 0 problem: DPs: TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Qed DPs: isNat#(active(X)) -> isNat#(X) TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Subterm Criterion Processor: simple projection: pi(isNat#) = 0 problem: DPs: TRS: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) U11(active(X)) -> U11(X) U41(X1,active(X2)) -> U41(X1,X2) U42(active(X)) -> U42(X) isNatIList(active(X)) -> isNatIList(X) U51(mark(X1),X2) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U52(mark(X)) -> U52(X) U52(active(X)) -> U52(X) isNatList(active(X)) -> isNatList(X) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U62(active(X1),X2) -> U62(X1,X2) isNat(active(X)) -> isNat(X) Qed