YES Problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(e())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 4x0, [tt] = 0, [u] = 0, [isQid](x0) = x0, [active](x0) = x0, [nil] = 0, [proper](x0) = x0, [ok](x0) = x0, [and](x0, x1) = 4x0 + x1, [isPal](x0) = x0, [__](x0, x1) = 4x0 + x1, [isNeList](x0) = x0, [o] = 0, [e] = 4, [a] = 0, [isNePal](x0) = x0, [i] = 0, [isList](x0) = x0, [mark](x0) = x0 orientation: active(__(__(X,Y),Z)) = 16X + 4Y + Z >= 4X + 4Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = 4X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(isNeList(V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 4V1 + V2 >= 4V1 + V2 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V >= V = mark(isQid(V)) active(isNeList(__(V1,V2))) = 4V1 + V2 >= 4V1 + V2 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = 4V1 + V2 >= 4V1 + V2 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = V >= V = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = 5I + 4P >= 4I + P = mark(and(isQid(I),isPal(P))) active(isPal(V)) = V >= V = mark(isNePal(V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(e())) = 4 >= 0 = mark(tt()) active(isQid(i())) = 0 >= 0 = mark(tt()) active(isQid(o())) = 0 >= 0 = mark(tt()) active(isQid(u())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(X1,active(X2)) active(and(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = and(active(X1),X2) __(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) __(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) and(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(and(X1,X2)) proper(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(and(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isList(X)) = X >= X = isList(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = X >= X = isNePal(proper(X)) proper(isPal(X)) = X >= X = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 4 >= 4 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 4X1 + X2 >= 4X1 + X2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = 4X1 + X2 >= 4X1 + X2 = ok(and(X1,X2)) isList(ok(X)) = X >= X = ok(isList(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = X >= X = ok(isNePal(X)) isPal(ok(X)) = X >= X = ok(isPal(X)) top(mark(X)) = 4X >= 4X = top(proper(X)) top(ok(X)) = 4X >= 4X = top(active(X)) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(isQid(i())) -> mark(tt()) active(isQid(o())) -> mark(tt()) active(isQid(u())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0 + 2, [tt] = 0, [u] = 2, [isQid](x0) = x0, [active](x0) = x0, [nil] = 0, [proper](x0) = x0, [ok](x0) = x0, [and](x0, x1) = x0 + x1, [isPal](x0) = 2x0, [__](x0, x1) = 2x0 + x1, [isNeList](x0) = x0, [o] = 2, [e] = 2, [a] = 0, [isNePal](x0) = 2x0, [i] = 2, [isList](x0) = x0, [mark](x0) = x0 orientation: active(__(__(X,Y),Z)) = 4X + 2Y + Z >= 2X + 2Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = 2X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(isNeList(V)) active(isList(nil())) = 0 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 2V1 + V2 >= V1 + V2 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V >= V = mark(isQid(V)) active(isNeList(__(V1,V2))) = 2V1 + V2 >= V1 + V2 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = 2V1 + V2 >= V1 + V2 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = 2V >= V = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = 6I + 4P >= I + 2P = mark(and(isQid(I),isPal(P))) active(isPal(V)) = 2V >= 2V = mark(isNePal(V)) active(isPal(nil())) = 0 >= 0 = mark(tt()) active(isQid(a())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 2 >= 0 = mark(tt()) active(isQid(o())) = 2 >= 0 = mark(tt()) active(isQid(u())) = 2 >= 0 = mark(tt()) active(__(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(active(X1),X2) __(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = mark(__(X1,X2)) __(X1,mark(X2)) = 2X1 + X2 >= 2X1 + X2 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(and(X1,X2)) proper(__(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isList(X)) = X >= X = isList(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = 2X >= 2X = isNePal(proper(X)) proper(isPal(X)) = 2X >= 2X = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 2 >= 2 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 2 >= 2 = ok(o()) proper(u()) = 2 >= 2 = ok(u()) __(ok(X1),ok(X2)) = 2X1 + X2 >= 2X1 + X2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isList(ok(X)) = X >= X = ok(isList(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = 2X >= 2X = ok(isNePal(X)) isPal(ok(X)) = 2X >= 2X = ok(isPal(X)) top(mark(X)) = X + 2 >= X + 2 = top(proper(X)) top(ok(X)) = X + 2 >= X + 2 = top(active(X)) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(isNeList(V)) active(isList(nil())) -> mark(tt()) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) -> mark(isQid(V)) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isPal(nil())) -> mark(tt()) active(isQid(a())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0 + 2, [tt] = 0, [u] = 0, [isQid](x0) = x0, [active](x0) = x0, [nil] = 4, [proper](x0) = x0, [ok](x0) = x0, [and](x0, x1) = x0 + x1, [isPal](x0) = 2x0 + 1, [__](x0, x1) = x0 + x1, [isNeList](x0) = x0, [o] = 0, [e] = 0, [a] = 0, [isNePal](x0) = 2x0 + 1, [i] = 0, [isList](x0) = x0, [mark](x0) = x0 orientation: active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X + 4 >= X = mark(X) active(__(nil(),X)) = X + 4 >= X = mark(X) active(and(tt(),X)) = X >= X = mark(X) active(isList(V)) = V >= V = mark(isNeList(V)) active(isList(nil())) = 4 >= 0 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V >= V = mark(isQid(V)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = 2V + 1 >= V = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = 4I + 2P + 1 >= I + 2P + 1 = mark(and(isQid(I),isPal(P))) active(isPal(V)) = 2V + 1 >= 2V + 1 = mark(isNePal(V)) active(isPal(nil())) = 9 >= 0 = mark(tt()) active(isQid(a())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 4 >= 4 = ok(nil()) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isList(X)) = X >= X = isList(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = 2X + 1 >= 2X + 1 = isNePal(proper(X)) proper(isPal(X)) = 2X + 1 >= 2X + 1 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isList(ok(X)) = X >= X = ok(isList(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = 2X + 1 >= 2X + 1 = ok(isNePal(X)) isPal(ok(X)) = 2X + 1 >= 2X + 1 = ok(isPal(X)) top(mark(X)) = X + 2 >= X + 2 = top(proper(X)) top(ok(X)) = X + 2 >= X + 2 = top(active(X)) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(and(tt(),X)) -> mark(X) active(isList(V)) -> mark(isNeList(V)) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isQid(a())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0, [tt] = 1, [u] = 0, [isQid](x0) = x0, [active](x0) = x0, [nil] = 0, [proper](x0) = x0, [ok](x0) = x0, [and](x0, x1) = x0 + x1, [isPal](x0) = 2x0, [__](x0, x1) = 4x0 + x1, [isNeList](x0) = 2x0, [o] = 0, [e] = 0, [a] = 1, [isNePal](x0) = 2x0, [i] = 0, [isList](x0) = 2x0, [mark](x0) = x0 orientation: active(__(__(X,Y),Z)) = 16X + 4Y + Z >= 4X + 4Y + Z = mark(__(X,__(Y,Z))) active(and(tt(),X)) = X + 1 >= X = mark(X) active(isList(V)) = 2V >= 2V = mark(isNeList(V)) active(isList(__(V1,V2))) = 8V1 + 2V2 >= 2V1 + 2V2 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = 2V >= V = mark(isQid(V)) active(isNeList(__(V1,V2))) = 8V1 + 2V2 >= 2V1 + 2V2 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = 8V1 + 2V2 >= 2V1 + 2V2 = mark(and(isNeList(V1),isList(V2))) active(isNePal(__(I,__(P,I)))) = 10I + 8P >= I + 2P = mark(and(isQid(I),isPal(P))) active(isPal(V)) = 2V >= 2V = mark(isNePal(V)) active(isQid(a())) = 1 >= 1 = mark(tt()) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(active(X1),X2) __(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) __(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(and(X1,X2)) proper(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(tt()) = 1 >= 1 = ok(tt()) proper(isList(X)) = 2X >= 2X = isList(proper(X)) proper(isNeList(X)) = 2X >= 2X = isNeList(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = 2X >= 2X = isNePal(proper(X)) proper(isPal(X)) = 2X >= 2X = isPal(proper(X)) proper(a()) = 1 >= 1 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 4X1 + X2 >= 4X1 + X2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isList(ok(X)) = 2X >= 2X = ok(isList(X)) isNeList(ok(X)) = 2X >= 2X = ok(isNeList(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = 2X >= 2X = ok(isNePal(X)) isPal(ok(X)) = 2X >= 2X = ok(isPal(X)) top(mark(X)) = X >= X = top(proper(X)) top(ok(X)) = X >= X = top(active(X)) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isList(V)) -> mark(isNeList(V)) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isNePal(__(I,__(P,I)))) -> mark(and(isQid(I),isPal(P))) active(isPal(V)) -> mark(isNePal(V)) active(isQid(a())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 2x0 + 1, [tt] = 0, [u] = 2, [isQid](x0) = x0, [active](x0) = x0, [nil] = 2, [proper](x0) = x0, [ok](x0) = x0, [and](x0, x1) = x0 + x1 + 4, [isPal](x0) = 2x0 + 2, [__](x0, x1) = x0 + x1 + 4, [isNeList](x0) = x0, [o] = 0, [e] = 0, [a] = 0, [isNePal](x0) = 2x0 + 2, [i] = 0, [isList](x0) = x0, [mark](x0) = x0 orientation: active(__(__(X,Y),Z)) = X + Y + Z + 8 >= X + Y + Z + 8 = mark(__(X,__(Y,Z))) active(isList(V)) = V >= V = mark(isNeList(V)) active(isList(__(V1,V2))) = V1 + V2 + 4 >= V1 + V2 + 4 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V >= V = mark(isQid(V)) active(isNeList(__(V1,V2))) = V1 + V2 + 4 >= V1 + V2 + 4 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = V1 + V2 + 4 >= V1 + V2 + 4 = mark(and(isNeList(V1),isList(V2))) active(isNePal(__(I,__(P,I)))) = 4I + 2P + 18 >= I + 2P + 6 = mark(and(isQid(I),isPal(P))) active(isPal(V)) = 2V + 2 >= 2V + 2 = mark(isNePal(V)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 4 >= X1 + X2 + 4 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 + 4 >= X1 + X2 + 4 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = __(proper(X1),proper(X2)) proper(nil()) = 2 >= 2 = ok(nil()) proper(and(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isList(X)) = X >= X = isList(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = 2X + 2 >= 2X + 2 = isNePal(proper(X)) proper(isPal(X)) = 2X + 2 >= 2X + 2 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 2 >= 2 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = ok(and(X1,X2)) isList(ok(X)) = X >= X = ok(isList(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = 2X + 2 >= 2X + 2 = ok(isNePal(X)) isPal(ok(X)) = 2X + 2 >= 2X + 2 = ok(isPal(X)) top(mark(X)) = 2X + 1 >= 2X + 1 = top(proper(X)) top(ok(X)) = 2X + 1 >= 2X + 1 = top(active(X)) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isList(V)) -> mark(isNeList(V)) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isPal(V)) -> mark(isNePal(V)) active(isQid(a())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0 + 4, [tt] = 0, [u] = 0, [isQid](x0) = x0, [active](x0) = x0, [nil] = 2, [proper](x0) = x0, [ok](x0) = x0, [and](x0, x1) = x0 + x1, [isPal](x0) = 2x0 + 7, [__](x0, x1) = x0 + x1, [isNeList](x0) = x0, [o] = 0, [e] = 0, [a] = 0, [isNePal](x0) = 2x0 + 4, [i] = 0, [isList](x0) = x0, [mark](x0) = x0 orientation: active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(isList(V)) = V >= V = mark(isNeList(V)) active(isList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V >= V = mark(isQid(V)) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = V1 + V2 >= V1 + V2 = mark(and(isNeList(V1),isList(V2))) active(isPal(V)) = 2V + 7 >= 2V + 4 = mark(isNePal(V)) active(isQid(a())) = 0 >= 0 = mark(tt()) active(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 2 >= 2 = ok(nil()) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isList(X)) = X >= X = isList(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = 2X + 4 >= 2X + 4 = isNePal(proper(X)) proper(isPal(X)) = 2X + 7 >= 2X + 7 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isList(ok(X)) = X >= X = ok(isList(X)) isNeList(ok(X)) = X >= X = ok(isNeList(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = 2X + 4 >= 2X + 4 = ok(isNePal(X)) isPal(ok(X)) = 2X + 7 >= 2X + 7 = ok(isPal(X)) top(mark(X)) = X + 4 >= X + 4 = top(proper(X)) top(ok(X)) = X + 4 >= X + 4 = top(active(X)) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isList(V)) -> mark(isNeList(V)) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(isQid(a())) -> mark(tt()) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [top](x0) = [0 0 0]x0 [0 0 0] , [0] [tt] = [0] [1], [1] [u] = [0] [0], [1 0 0] [isQid](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [0] [active](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [0] [nil] = [0] [1], [1 0 0] [0] [proper](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [1 1 0] [0] [ok](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [and](x0, x1) = x0 + [0 0 0]x1 [0 0 0] , [1 0 0] [isPal](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 1 0]x1 [0 0 0] [0 0 0] , [1 0 0] [0] [isNeList](x0) = [0 1 0]x0 + [0] [1 0 0] [1], [0] [o] = [0] [0], [0] [e] = [0] [1], [1] [a] = [0] [0], [1 0 0] [isNePal](x0) = [0 1 0]x0 [0 0 0] , [0] [i] = [0] [0], [1 0 0] [isList](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [mark](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [1 0 0] active(__(__(X,Y),Z)) = [0 0 0]X + [0 0 0]Y + [0 1 0]Z + [0] >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z = mark(__(X,__(Y,Z))) [0 0 0] [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] active(isList(V)) = [0 1 0]V + [0] >= [0 0 0]V = mark(isNeList(V)) [0 0 0] [1] [0 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] active(isList(__(V1,V2))) = [0 0 0]V1 + [0 1 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isList(V1),isList(V2))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] active(isNeList(V)) = [0 1 0]V + [0] >= [0 0 0]V = mark(isQid(V)) [0 0 0] [1] [0 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] active(isNeList(__(V1,V2))) = [0 0 0]V1 + [0 1 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isList(V1),isNeList(V2))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] active(isNeList(__(V1,V2))) = [0 0 0]V1 + [0 1 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 = mark(and(isNeList(V1),isList(V2))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] active(isQid(a())) = [0] >= [0] = mark(tt()) [1] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] active(__(X1,X2)) = [0 0 0]X1 + [0 1 0]X2 + [0] >= [0 0 0]X1 + [0 1 0]X2 = __(active(X1),X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] active(__(X1,X2)) = [0 0 0]X1 + [0 1 0]X2 + [0] >= [0 0 0]X1 + [0 1 0]X2 = __(X1,active(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] active(and(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [0] >= [0 1 0]X1 + [0 0 0]X2 + [0] = and(active(X1),X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(mark(X1),X2) = [0 0 0]X1 + [0 1 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(__(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] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(__(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] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(and(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] proper(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(proper(X1),proper(X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [0] [0] proper(nil()) = [1] >= [1] = ok(nil()) [1] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] proper(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = and(proper(X1),proper(X2)) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [0] [0] proper(tt()) = [1] >= [1] = ok(tt()) [1] [0] [1 0 0] [0] [1 0 0] [0] proper(isList(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isList(proper(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] proper(isNeList(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNeList(proper(X)) [1 0 0] [1] [1 0 0] [1] [1 0 0] [0] [1 0 0] [0] proper(isQid(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isQid(proper(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] proper(isNePal(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNePal(proper(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] proper(isPal(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isPal(proper(X)) [0 0 0] [0] [0 0 0] [0] [1] [1] proper(a()) = [1] >= [1] = ok(a()) [0] [0] [0] [0] proper(e()) = [1] >= [1] = ok(e()) [1] [0] [0] [0] proper(i()) = [1] >= [1] = ok(i()) [0] [0] [0] [0] proper(o()) = [1] >= [1] = ok(o()) [0] [0] [1] [1] proper(u()) = [1] >= [1] = ok(u()) [0] [0] [1 1 0] [1 1 0] [0] [1 0 0] [1 1 0] [0] __(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = ok(__(X1,X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 1 0] [0] [1 1 0] [1 0 0] [0] and(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = ok(and(X1,X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [0] [1 1 0] [0] isList(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isList(X)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [0] [1 1 0] [0] isNeList(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isNeList(X)) [1 1 0] [1] [0 0 0] [0] [1 1 0] [0] [1 1 0] [0] isQid(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isQid(X)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [0] [1 1 0] [0] isNePal(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isNePal(X)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [0] [1 1 0] [0] isPal(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isPal(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] top(mark(X)) = [0 0 0]X >= [0 0 0]X = top(proper(X)) [0 0 0] [0 0 0] [1 1 0] [1 0 0] top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X)) [0 0 0] [0 0 0] problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isList(V)) -> mark(isNeList(V)) active(isList(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [top](x0) = [0 0 0]x0 [0 0 0] , [0] [tt] = [0] [0], [0] [u] = [0] [0], [1 0 1] [isQid](x0) = [0 0 0]x0 [1 0 0] , [active](x0) = x0 , [1] [nil] = [0] [0], [proper](x0) = x0 , [ok](x0) = x0 , [1 0 0] [1 0 0] [0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 1 0] [0 0 0] [0], [1 0 1] [0] [isPal](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [1 0 0] [0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 1 1] [0 1 1] [0], [1 0 1] [0] [isNeList](x0) = [0 0 0]x0 + [1] [1 1 0] [0], [0] [o] = [0] [0], [1] [e] = [0] [0], [1] [a] = [0] [0], [1 0 1] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [0] [i] = [0] [0], [1 1 1] [0] [isList](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [1 0 0] [0] [mark](x0) = [0 0 0]x0 + [1] [0 1 0] [0] orientation: [1 0 0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [1 0 0] [0] active(__(__(X,Y),Z)) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [1] >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [1] = mark(__(X,__(Y,Z))) [0 1 1] [0 1 1] [0 1 1] [1] [0 0 0] [0 0 0] [0 0 0] [1] [1 1 1] [0] [1 0 1] [0] active(isList(V)) = [0 0 0]V + [1] >= [0 0 0]V + [1] = mark(isNeList(V)) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1 1 1] [1] [1 1 1] [1 1 1] [0] active(isList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [1] >= [0 0 0]V1 + [0 0 0]V2 + [1] = mark(and(isList(V1),isList(V2))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 1] [0] [1 0 1] [0] active(isNeList(V)) = [0 0 0]V + [1] >= [0 0 0]V + [1] = mark(isQid(V)) [1 1 0] [0] [0 0 0] [0] [1 1 1] [1 1 1] [0] [1 1 1] [1 0 1] [0] active(isNeList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [1] >= [0 0 0]V1 + [0 0 0]V2 + [1] = mark(and(isList(V1),isNeList(V2))) [1 0 0] [1 0 0] [1] [0 0 0] [0 0 0] [1] [1 1 1] [1 1 1] [0] [1 0 1] [1 1 1] [0] active(isNeList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [1] >= [0 0 0]V1 + [0 0 0]V2 + [1] = mark(and(isNeList(V1),isList(V2))) [1 0 0] [1 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(active(X1),X2) [0 1 1] [0 1 1] [0] [0 1 1] [0 1 1] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(X1,active(X2)) [0 1 1] [0 1 1] [0] [0 1 1] [0 1 1] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] active(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = and(active(X1),X2) [0 1 0] [0 0 0] [0] [0 1 0] [0 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = mark(__(X1,X2)) [0 1 0] [0 1 1] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = mark(__(X1,X2)) [0 1 1] [0 1 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = mark(and(X1,X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] proper(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(proper(X1),proper(X2)) [0 1 1] [0 1 1] [0] [0 1 1] [0 1 1] [0] [1] [1] proper(nil()) = [0] >= [0] = ok(nil()) [0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] proper(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = and(proper(X1),proper(X2)) [0 1 0] [0 0 0] [0] [0 1 0] [0 0 0] [0] [0] [0] proper(tt()) = [0] >= [0] = ok(tt()) [0] [0] [1 1 1] [0] [1 1 1] [0] proper(isList(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isList(proper(X)) [0 0 0] [1] [0 0 0] [1] [1 0 1] [0] [1 0 1] [0] proper(isNeList(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNeList(proper(X)) [1 1 0] [0] [1 1 0] [0] [1 0 1] [1 0 1] proper(isQid(X)) = [0 0 0]X >= [0 0 0]X = isQid(proper(X)) [1 0 0] [1 0 0] [1 0 1] [1 0 1] proper(isNePal(X)) = [0 0 0]X >= [0 0 0]X = isNePal(proper(X)) [0 0 0] [0 0 0] [1 0 1] [0] [1 0 1] [0] proper(isPal(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isPal(proper(X)) [0 0 0] [0] [0 0 0] [0] [1] [1] proper(a()) = [0] >= [0] = ok(a()) [0] [0] [1] [1] proper(e()) = [0] >= [0] = ok(e()) [0] [0] [0] [0] proper(i()) = [0] >= [0] = ok(i()) [0] [0] [0] [0] proper(o()) = [0] >= [0] = ok(o()) [0] [0] [0] [0] proper(u()) = [0] >= [0] = ok(u()) [0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] __(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = ok(__(X1,X2)) [0 1 1] [0 1 1] [0] [0 1 1] [0 1 1] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] and(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = ok(and(X1,X2)) [0 1 0] [0 0 0] [0] [0 1 0] [0 0 0] [0] [1 1 1] [0] [1 1 1] [0] isList(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isList(X)) [0 0 0] [1] [0 0 0] [1] [1 0 1] [0] [1 0 1] [0] isNeList(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isNeList(X)) [1 1 0] [0] [1 1 0] [0] [1 0 1] [1 0 1] isQid(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isQid(X)) [1 0 0] [1 0 0] [1 0 1] [1 0 1] isNePal(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isNePal(X)) [0 0 0] [0 0 0] [1 0 1] [0] [1 0 1] [0] isPal(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isPal(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] top(mark(X)) = [0 0 0]X >= [0 0 0]X = top(proper(X)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X)) [0 0 0] [0 0 0] problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isList(V)) -> mark(isNeList(V)) active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0, [tt] = 0, [u] = 0, [isQid](x0) = x0, [active](x0) = x0, [nil] = 4, [proper](x0) = x0, [ok](x0) = x0, [and](x0, x1) = x0 + x1 + 2, [isPal](x0) = 4x0, [__](x0, x1) = 3x0 + x1 + 7, [isNeList](x0) = x0 + 1, [o] = 0, [e] = 4, [a] = 0, [isNePal](x0) = 4x0, [i] = 3, [isList](x0) = x0 + 4, [mark](x0) = x0 + 1 orientation: active(__(__(X,Y),Z)) = 9X + 3Y + Z + 28 >= 3X + 3Y + Z + 15 = mark(__(X,__(Y,Z))) active(isList(V)) = V + 4 >= V + 2 = mark(isNeList(V)) active(isNeList(V)) = V + 1 >= V + 1 = mark(isQid(V)) active(isNeList(__(V1,V2))) = 3V1 + V2 + 8 >= V1 + V2 + 8 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = 3V1 + V2 + 8 >= V1 + V2 + 8 = mark(and(isNeList(V1),isList(V2))) active(__(X1,X2)) = 3X1 + X2 + 7 >= 3X1 + X2 + 7 = __(active(X1),X2) active(__(X1,X2)) = 3X1 + X2 + 7 >= 3X1 + X2 + 7 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = and(active(X1),X2) __(mark(X1),X2) = 3X1 + X2 + 10 >= 3X1 + X2 + 8 = mark(__(X1,X2)) __(X1,mark(X2)) = 3X1 + X2 + 8 >= 3X1 + X2 + 8 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 + 3 >= X1 + X2 + 3 = mark(and(X1,X2)) proper(__(X1,X2)) = 3X1 + X2 + 7 >= 3X1 + X2 + 7 = __(proper(X1),proper(X2)) proper(nil()) = 4 >= 4 = ok(nil()) proper(and(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isList(X)) = X + 4 >= X + 4 = isList(proper(X)) proper(isNeList(X)) = X + 1 >= X + 1 = isNeList(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = 4X >= 4X = isNePal(proper(X)) proper(isPal(X)) = 4X >= 4X = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 4 >= 4 = ok(e()) proper(i()) = 3 >= 3 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 3X1 + X2 + 7 >= 3X1 + X2 + 7 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = ok(and(X1,X2)) isList(ok(X)) = X + 4 >= X + 4 = ok(isList(X)) isNeList(ok(X)) = X + 1 >= X + 1 = ok(isNeList(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = 4X >= 4X = ok(isNePal(X)) isPal(ok(X)) = 4X >= 4X = ok(isPal(X)) top(mark(X)) = X + 1 >= X = top(proper(X)) top(ok(X)) = X >= X = top(active(X)) problem: active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) __(X1,mark(X2)) -> mark(__(X1,X2)) and(mark(X1),X2) -> mark(and(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(and(X1,X2)) -> and(proper(X1),proper(X2)) proper(tt()) -> ok(tt()) proper(isList(X)) -> isList(proper(X)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isQid(X)) -> isQid(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(a()) -> ok(a()) proper(e()) -> ok(e()) proper(i()) -> ok(i()) proper(o()) -> ok(o()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 4x0, [tt] = 6, [u] = 0, [isQid](x0) = 4x0 + 2, [active](x0) = x0, [nil] = 4, [proper](x0) = 2x0, [ok](x0) = x0, [and](x0, x1) = 4x0 + 4x1 + 6, [isPal](x0) = x0, [__](x0, x1) = 4x0 + 4x1 + 5, [isNeList](x0) = 4x0 + 4, [o] = 6, [e] = 1, [a] = 5, [isNePal](x0) = x0 + 4, [i] = 0, [isList](x0) = 4x0, [mark](x0) = x0 + 2 orientation: active(isNeList(V)) = 4V + 4 >= 4V + 4 = mark(isQid(V)) active(isNeList(__(V1,V2))) = 16V1 + 16V2 + 24 >= 16V1 + 16V2 + 24 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = 16V1 + 16V2 + 24 >= 16V1 + 16V2 + 24 = mark(and(isNeList(V1),isList(V2))) active(__(X1,X2)) = 4X1 + 4X2 + 5 >= 4X1 + 4X2 + 5 = __(active(X1),X2) active(__(X1,X2)) = 4X1 + 4X2 + 5 >= 4X1 + 4X2 + 5 = __(X1,active(X2)) active(and(X1,X2)) = 4X1 + 4X2 + 6 >= 4X1 + 4X2 + 6 = and(active(X1),X2) __(X1,mark(X2)) = 4X1 + 4X2 + 13 >= 4X1 + 4X2 + 7 = mark(__(X1,X2)) and(mark(X1),X2) = 4X1 + 4X2 + 14 >= 4X1 + 4X2 + 8 = mark(and(X1,X2)) proper(__(X1,X2)) = 8X1 + 8X2 + 10 >= 8X1 + 8X2 + 5 = __(proper(X1),proper(X2)) proper(nil()) = 8 >= 4 = ok(nil()) proper(and(X1,X2)) = 8X1 + 8X2 + 12 >= 8X1 + 8X2 + 6 = and(proper(X1),proper(X2)) proper(tt()) = 12 >= 6 = ok(tt()) proper(isList(X)) = 8X >= 8X = isList(proper(X)) proper(isNeList(X)) = 8X + 8 >= 8X + 4 = isNeList(proper(X)) proper(isQid(X)) = 8X + 4 >= 8X + 2 = isQid(proper(X)) proper(isNePal(X)) = 2X + 8 >= 2X + 4 = isNePal(proper(X)) proper(isPal(X)) = 2X >= 2X = isPal(proper(X)) proper(a()) = 10 >= 5 = ok(a()) proper(e()) = 2 >= 1 = ok(e()) proper(i()) = 0 >= 0 = ok(i()) proper(o()) = 12 >= 6 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 4X1 + 4X2 + 5 >= 4X1 + 4X2 + 5 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = 4X1 + 4X2 + 6 >= 4X1 + 4X2 + 6 = ok(and(X1,X2)) isList(ok(X)) = 4X >= 4X = ok(isList(X)) isNeList(ok(X)) = 4X + 4 >= 4X + 4 = ok(isNeList(X)) isQid(ok(X)) = 4X + 2 >= 4X + 2 = ok(isQid(X)) isNePal(ok(X)) = X + 4 >= X + 4 = ok(isNePal(X)) isPal(ok(X)) = X >= X = ok(isPal(X)) top(ok(X)) = 4X >= 4X = top(active(X)) problem: active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(and(X1,X2)) -> and(active(X1),X2) proper(isList(X)) -> isList(proper(X)) proper(isPal(X)) -> isPal(proper(X)) proper(i()) -> ok(i()) proper(u()) -> ok(u()) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) and(ok(X1),ok(X2)) -> ok(and(X1,X2)) isList(ok(X)) -> ok(isList(X)) isNeList(ok(X)) -> ok(isNeList(X)) isQid(ok(X)) -> ok(isQid(X)) isNePal(ok(X)) -> ok(isNePal(X)) isPal(ok(X)) -> ok(isPal(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 2x0 + 5, [u] = 7, [isQid](x0) = 2x0, [active](x0) = 2x0, [proper](x0) = 3x0 + 1, [ok](x0) = 2x0 + 2, [and](x0, x1) = x0 + x1 + 1, [isPal](x0) = 7x0 + 5, [__](x0, x1) = 2x0 + 2x1 + 1, [isNeList](x0) = 4x0, [isNePal](x0) = 4x0, [i] = 4, [isList](x0) = 2x0 + 1, [mark](x0) = 4x0 orientation: active(isNeList(V)) = 8V >= 8V = mark(isQid(V)) active(isNeList(__(V1,V2))) = 16V1 + 16V2 + 8 >= 8V1 + 16V2 + 8 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = 16V1 + 16V2 + 8 >= 16V1 + 8V2 + 8 = mark(and(isNeList(V1),isList(V2))) active(__(X1,X2)) = 4X1 + 4X2 + 2 >= 4X1 + 2X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = 4X1 + 4X2 + 2 >= 2X1 + 4X2 + 1 = __(X1,active(X2)) active(and(X1,X2)) = 2X1 + 2X2 + 2 >= 2X1 + X2 + 1 = and(active(X1),X2) proper(isList(X)) = 6X + 4 >= 6X + 3 = isList(proper(X)) proper(isPal(X)) = 21X + 16 >= 21X + 12 = isPal(proper(X)) proper(i()) = 13 >= 10 = ok(i()) proper(u()) = 22 >= 16 = ok(u()) __(ok(X1),ok(X2)) = 4X1 + 4X2 + 9 >= 4X1 + 4X2 + 4 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = 2X1 + 2X2 + 5 >= 2X1 + 2X2 + 4 = ok(and(X1,X2)) isList(ok(X)) = 4X + 5 >= 4X + 4 = ok(isList(X)) isNeList(ok(X)) = 8X + 8 >= 8X + 2 = ok(isNeList(X)) isQid(ok(X)) = 4X + 4 >= 4X + 2 = ok(isQid(X)) isNePal(ok(X)) = 8X + 8 >= 8X + 2 = ok(isNePal(X)) isPal(ok(X)) = 14X + 19 >= 14X + 12 = ok(isPal(X)) top(ok(X)) = 4X + 9 >= 4X + 5 = top(active(X)) problem: active(isNeList(V)) -> mark(isQid(V)) active(isNeList(__(V1,V2))) -> mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) -> mark(and(isNeList(V1),isList(V2))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [isQid](x0) = [0 0 1]x0 + [1] [0 0 0] [0], [1 0 0] [1] [active](x0) = [0 0 0]x0 + [0] [0 1 1] [0], [1 0 0] [1 0 0] [0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [0] [isNeList](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [1 0 0] [isList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [mark](x0) = [0 0 0]x0 [0 1 0] orientation: [1 0 0] [1] [1 0 0] [0] active(isNeList(V)) = [0 0 0]V + [0] >= [0 0 0]V + [0] = mark(isQid(V)) [0 0 1] [1] [0 0 1] [1] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [0] active(isNeList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 + [0] = mark(and(isList(V1),isNeList(V2))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [0] active(isNeList(__(V1,V2))) = [0 0 0]V1 + [0 0 0]V2 + [0] >= [0 0 0]V1 + [0 0 0]V2 + [0] = mark(and(isNeList(V1),isList(V2))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] problem: Qed