/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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) = x0, [ok](x0) = x0, [proper](x0) = x0, [u] = 4, [o] = 4, [i] = 4, [e] = 4, [a] = 4, [isPal](x0) = 4x0, [isNePal](x0) = 4x0, [isQid](x0) = x0, [isNeList](x0) = x0, [isList](x0) = x0 + 1, [and](x0, x1) = x0 + x1, [tt] = 4, [nil] = 3, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 1 orientation: active(__(__(X,Y),Z)) = X + Y + Z + 2 >= X + Y + Z + 2 = 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 + 4 >= X = mark(X) active(isList(V)) = V + 1 >= V = mark(isNeList(V)) active(isList(nil())) = 4 >= 4 = mark(tt()) active(isList(__(V1,V2))) = V1 + V2 + 2 >= V1 + V2 + 2 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = V >= V = mark(isQid(V)) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = V1 + V2 + 1 >= V1 + V2 + 1 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = 4V >= V = mark(isQid(V)) active(isNePal(__(I,__(P,I)))) = 8I + 4P + 8 >= I + 4P = mark(and(isQid(I),isPal(P))) active(isPal(V)) = 4V >= 4V = mark(isNePal(V)) active(isPal(nil())) = 12 >= 4 = mark(tt()) active(isQid(a())) = 4 >= 4 = mark(tt()) active(isQid(e())) = 4 >= 4 = mark(tt()) active(isQid(i())) = 4 >= 4 = mark(tt()) active(isQid(o())) = 4 >= 4 = mark(tt()) active(isQid(u())) = 4 >= 4 = mark(tt()) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 3 >= 3 = ok(nil()) proper(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(proper(X1),proper(X2)) proper(tt()) = 4 >= 4 = ok(tt()) proper(isList(X)) = X + 1 >= X + 1 = isList(proper(X)) proper(isNeList(X)) = X >= X = 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()) = 4 >= 4 = ok(a()) proper(e()) = 4 >= 4 = ok(e()) proper(i()) = 4 >= 4 = ok(i()) proper(o()) = 4 >= 4 = ok(o()) proper(u()) = 4 >= 4 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isList(ok(X)) = X + 1 >= X + 1 = ok(isList(X)) isNeList(ok(X)) = X >= X = 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 >= X = top(proper(X)) top(ok(X)) = X >= X = top(active(X)) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) 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(isPal(V)) -> mark(isNePal(V)) 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)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 2, [isPal](x0) = 4x0, [isNePal](x0) = 4x0, [isQid](x0) = 3x0, [isNeList](x0) = 4x0, [isList](x0) = 4x0, [and](x0, x1) = x0 + x1, [tt] = 0, [nil] = 4, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 2x0 + x1 orientation: active(__(__(X,Y),Z)) = 4X + 2Y + Z >= 2X + 2Y + Z = mark(__(X,__(Y,Z))) active(isList(nil())) = 16 >= 0 = mark(tt()) active(isList(__(V1,V2))) = 8V1 + 4V2 >= 4V1 + 4V2 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = 4V >= 3V = mark(isQid(V)) active(isNeList(__(V1,V2))) = 8V1 + 4V2 >= 4V1 + 4V2 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = 8V1 + 4V2 >= 4V1 + 4V2 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = 4V >= 3V = mark(isQid(V)) active(isPal(V)) = 4V >= 4V = mark(isNePal(V)) active(isQid(a())) = 6 >= 0 = mark(tt()) active(isQid(e())) = 0 >= 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)) = 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()) = 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)) = 4X >= 4X = isList(proper(X)) proper(isNeList(X)) = 4X >= 4X = isNeList(proper(X)) proper(isQid(X)) = 3X >= 3X = isQid(proper(X)) proper(isNePal(X)) = 4X >= 4X = isNePal(proper(X)) proper(isPal(X)) = 4X >= 4X = isPal(proper(X)) proper(a()) = 2 >= 2 = 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)) = 2X1 + X2 >= 2X1 + X2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isList(ok(X)) = 4X >= 4X = ok(isList(X)) isNeList(ok(X)) = 4X >= 4X = ok(isNeList(X)) isQid(ok(X)) = 3X >= 3X = ok(isQid(X)) isNePal(ok(X)) = 4X >= 4X = ok(isNePal(X)) isPal(ok(X)) = 4X >= 4X = 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(__(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(isPal(V)) -> mark(isNePal(V)) 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)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 2x0, [isNePal](x0) = x0, [isQid](x0) = x0, [isNeList](x0) = 3x0 + 1, [isList](x0) = 2x0, [and](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(isList(__(V1,V2))) = 2V1 + 2V2 >= 2V1 + 2V2 = mark(and(isList(V1),isList(V2))) active(isNeList(V)) = 3V + 1 >= V = mark(isQid(V)) active(isNeList(__(V1,V2))) = 3V1 + 3V2 + 1 >= 2V1 + 3V2 + 1 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = 3V1 + 3V2 + 1 >= 3V1 + 2V2 + 1 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = V >= V = mark(isQid(V)) active(isPal(V)) = 2V >= V = mark(isNePal(V)) active(isQid(e())) = 0 >= 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)) = 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()) = 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)) = 2X >= 2X = isList(proper(X)) proper(isNeList(X)) = 3X + 1 >= 3X + 1 = isNeList(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = X >= X = isNePal(proper(X)) proper(isPal(X)) = 2X >= 2X = 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)) = 2X >= 2X = ok(isList(X)) isNeList(ok(X)) = 3X + 1 >= 3X + 1 = ok(isNeList(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = X >= X = 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(__(V1,V2))) -> mark(and(isList(V1),isList(V2))) 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(isPal(V)) -> mark(isNePal(V)) 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)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 6x0 + 4, [isNePal](x0) = 4x0 + 2, [isQid](x0) = 2x0, [isNeList](x0) = 4x0, [isList](x0) = 4x0, [and](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 + 6 orientation: active(__(__(X,Y),Z)) = X + Y + Z + 12 >= X + Y + Z + 12 = mark(__(X,__(Y,Z))) active(isList(__(V1,V2))) = 4V1 + 4V2 + 24 >= 4V1 + 4V2 = mark(and(isList(V1),isList(V2))) active(isNeList(__(V1,V2))) = 4V1 + 4V2 + 24 >= 4V1 + 4V2 = mark(and(isList(V1),isNeList(V2))) active(isNeList(__(V1,V2))) = 4V1 + 4V2 + 24 >= 4V1 + 4V2 = mark(and(isNeList(V1),isList(V2))) active(isNePal(V)) = 4V + 2 >= 2V = mark(isQid(V)) active(isPal(V)) = 6V + 4 >= 4V + 2 = mark(isNePal(V)) active(isQid(e())) = 0 >= 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)) = X1 + X2 + 6 >= X1 + X2 + 6 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 6 >= X1 + X2 + 6 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(active(X1),X2) __(mark(X1),X2) = X1 + X2 + 6 >= X1 + X2 + 6 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 + 6 >= X1 + X2 + 6 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 + 6 >= X1 + X2 + 6 = __(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)) = 4X >= 4X = isList(proper(X)) proper(isNeList(X)) = 4X >= 4X = isNeList(proper(X)) proper(isQid(X)) = 2X >= 2X = isQid(proper(X)) proper(isNePal(X)) = 4X + 2 >= 4X + 2 = isNePal(proper(X)) proper(isPal(X)) = 6X + 4 >= 6X + 4 = 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 + 6 >= X1 + X2 + 6 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(and(X1,X2)) isList(ok(X)) = 4X >= 4X = ok(isList(X)) isNeList(ok(X)) = 4X >= 4X = ok(isNeList(X)) isQid(ok(X)) = 2X >= 2X = ok(isQid(X)) isNePal(ok(X)) = 4X + 2 >= 4X + 2 = ok(isNePal(X)) isPal(ok(X)) = 6X + 4 >= 6X + 4 = 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(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)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0 + 5, [ok](x0) = x0, [proper](x0) = x0, [u] = 2, [o] = 6, [i] = 1, [e] = 0, [a] = 0, [isPal](x0) = x0 + 2, [isNePal](x0) = x0 + 3, [isQid](x0) = x0, [isNeList](x0) = 2x0 + 4, [isList](x0) = x0, [and](x0, x1) = 2x0 + x1 + 3, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(isQid(e())) = 0 >= 0 = mark(tt()) active(isQid(i())) = 1 >= 0 = mark(tt()) active(isQid(o())) = 6 >= 0 = mark(tt()) active(isQid(u())) = 2 >= 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)) = 2X1 + X2 + 3 >= 2X1 + X2 + 3 = 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) = 2X1 + X2 + 3 >= 2X1 + X2 + 3 = mark(and(X1,X2)) proper(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(and(X1,X2)) = 2X1 + X2 + 3 >= 2X1 + X2 + 3 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isList(X)) = X >= X = isList(proper(X)) proper(isNeList(X)) = 2X + 4 >= 2X + 4 = isNeList(proper(X)) proper(isQid(X)) = X >= X = isQid(proper(X)) proper(isNePal(X)) = X + 3 >= X + 3 = isNePal(proper(X)) proper(isPal(X)) = X + 2 >= X + 2 = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 0 >= 0 = ok(e()) proper(i()) = 1 >= 1 = ok(i()) proper(o()) = 6 >= 6 = ok(o()) proper(u()) = 2 >= 2 = ok(u()) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = 2X1 + X2 + 3 >= 2X1 + X2 + 3 = ok(and(X1,X2)) isList(ok(X)) = X >= X = ok(isList(X)) isNeList(ok(X)) = 2X + 4 >= 2X + 4 = ok(isNeList(X)) isQid(ok(X)) = X >= X = ok(isQid(X)) isNePal(ok(X)) = X + 3 >= X + 3 = ok(isNePal(X)) isPal(ok(X)) = X + 2 >= X + 2 = ok(isPal(X)) top(mark(X)) = X + 5 >= X + 5 = top(proper(X)) top(ok(X)) = X + 5 >= X + 5 = top(active(X)) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isQid(e())) -> 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, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 2, [e] = 5, [a] = 0, [isPal](x0) = 2x0, [isNePal](x0) = 4x0 + 6, [isQid](x0) = 5x0, [isNeList](x0) = 4x0 + 2, [isList](x0) = 4x0 + 6, [and](x0, x1) = 2x0 + 2x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 2x0 + x1 orientation: active(__(__(X,Y),Z)) = 4X + 2Y + Z >= 2X + 2Y + Z = mark(__(X,__(Y,Z))) active(isQid(e())) = 25 >= 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)) = 2X1 + 2X2 >= 2X1 + 2X2 = 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) = 2X1 + 2X2 >= 2X1 + 2X2 = 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)) = 2X1 + 2X2 >= 2X1 + 2X2 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isList(X)) = 4X + 6 >= 4X + 6 = isList(proper(X)) proper(isNeList(X)) = 4X + 2 >= 4X + 2 = isNeList(proper(X)) proper(isQid(X)) = 5X >= 5X = isQid(proper(X)) proper(isNePal(X)) = 4X + 6 >= 4X + 6 = isNePal(proper(X)) proper(isPal(X)) = 2X >= 2X = isPal(proper(X)) proper(a()) = 0 >= 0 = ok(a()) proper(e()) = 5 >= 5 = ok(e()) proper(i()) = 2 >= 2 = ok(i()) proper(o()) = 0 >= 0 = ok(o()) proper(u()) = 0 >= 0 = ok(u()) __(ok(X1),ok(X2)) = 2X1 + X2 >= 2X1 + X2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = 2X1 + 2X2 >= 2X1 + 2X2 = ok(and(X1,X2)) isList(ok(X)) = 4X + 6 >= 4X + 6 = ok(isList(X)) isNeList(ok(X)) = 4X + 2 >= 4X + 2 = ok(isNeList(X)) isQid(ok(X)) = 5X >= 5X = ok(isQid(X)) isNePal(ok(X)) = 4X + 6 >= 4X + 6 = 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(__(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) = 4x0, [ok](x0) = x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 2x0, [isNePal](x0) = x0, [isQid](x0) = 4x0, [isNeList](x0) = x0, [isList](x0) = 2x0, [and](x0, x1) = x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 2x0 + x1 + 4 orientation: active(__(__(X,Y),Z)) = 4X + 2Y + Z + 12 >= 2X + 2Y + Z + 8 = mark(__(X,__(Y,Z))) active(__(X1,X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = __(active(X1),X2) active(__(X1,X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = __(X1,active(X2)) active(and(X1,X2)) = X1 + X2 >= X1 + X2 = and(active(X1),X2) __(mark(X1),X2) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = mark(__(X1,X2)) __(X1,mark(X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = mark(__(X1,X2)) and(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(and(X1,X2)) proper(__(X1,X2)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = __(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)) = 2X >= 2X = isList(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(isQid(X)) = 4X >= 4X = isQid(proper(X)) proper(isNePal(X)) = X >= X = isNePal(proper(X)) proper(isPal(X)) = 2X >= 2X = 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)) = 2X1 + X2 + 4 >= 2X1 + X2 + 4 = 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)) = X >= X = ok(isNeList(X)) isQid(ok(X)) = 4X >= 4X = ok(isQid(X)) isNePal(ok(X)) = X >= X = ok(isNePal(X)) isPal(ok(X)) = 2X >= 2X = ok(isPal(X)) top(mark(X)) = 4X >= 4X = top(proper(X)) top(ok(X)) = 4X >= 4X = top(active(X)) problem: 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, [ok](x0) = 2x0, [proper](x0) = x0, [u] = 0, [o] = 0, [i] = 0, [e] = 0, [a] = 0, [isPal](x0) = 2x0, [isNePal](x0) = 4x0, [isQid](x0) = 4x0, [isNeList](x0) = x0, [isList](x0) = 4x0, [and](x0, x1) = 4x0 + x1, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 6, [active](x0) = 2x0, [__](x0, x1) = 2x0 + x1 orientation: active(__(X1,X2)) = 4X1 + 2X2 >= 4X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = 4X1 + 2X2 >= 2X1 + 2X2 = __(X1,active(X2)) active(and(X1,X2)) = 8X1 + 2X2 >= 8X1 + X2 = and(active(X1),X2) __(mark(X1),X2) = 2X1 + X2 + 12 >= 2X1 + X2 + 6 = mark(__(X1,X2)) __(X1,mark(X2)) = 2X1 + X2 + 6 >= 2X1 + X2 + 6 = mark(__(X1,X2)) and(mark(X1),X2) = 4X1 + X2 + 24 >= 4X1 + X2 + 6 = 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)) = 4X1 + X2 >= 4X1 + X2 = and(proper(X1),proper(X2)) proper(tt()) = 0 >= 0 = ok(tt()) proper(isList(X)) = 4X >= 4X = isList(proper(X)) proper(isNeList(X)) = X >= X = isNeList(proper(X)) proper(isQid(X)) = 4X >= 4X = isQid(proper(X)) proper(isNePal(X)) = 4X >= 4X = isNePal(proper(X)) proper(isPal(X)) = 2X >= 2X = 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)) = 4X1 + 2X2 >= 4X1 + 2X2 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = 8X1 + 2X2 >= 8X1 + 2X2 = ok(and(X1,X2)) isList(ok(X)) = 8X >= 8X = ok(isList(X)) isNeList(ok(X)) = 2X >= 2X = ok(isNeList(X)) isQid(ok(X)) = 8X >= 8X = ok(isQid(X)) isNePal(ok(X)) = 8X >= 8X = ok(isNePal(X)) isPal(ok(X)) = 4X >= 4X = ok(isPal(X)) top(mark(X)) = 2X + 13 >= 2X + 1 = top(proper(X)) top(ok(X)) = 4X + 1 >= 4X + 1 = top(active(X)) problem: 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)) 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) = 2x0 + 1, [ok](x0) = 2x0 + 1, [proper](x0) = 4x0, [u] = 4, [o] = 4, [i] = 4, [e] = 2, [a] = 1, [isPal](x0) = 6x0 + 5, [isNePal](x0) = 4x0, [isQid](x0) = 5x0 + 2, [isNeList](x0) = 6x0, [isList](x0) = 4x0 + 2, [and](x0, x1) = 4x0 + 4x1 + 4, [tt] = 4, [nil] = 1, [mark](x0) = x0 + 4, [active](x0) = 2x0, [__](x0, x1) = 4x0 + x1 orientation: active(__(X1,X2)) = 8X1 + 2X2 >= 8X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = 8X1 + 2X2 >= 4X1 + 2X2 = __(X1,active(X2)) active(and(X1,X2)) = 8X1 + 8X2 + 8 >= 8X1 + 4X2 + 4 = and(active(X1),X2) __(X1,mark(X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = mark(__(X1,X2)) proper(__(X1,X2)) = 16X1 + 4X2 >= 16X1 + 4X2 = __(proper(X1),proper(X2)) proper(nil()) = 4 >= 3 = ok(nil()) proper(and(X1,X2)) = 16X1 + 16X2 + 16 >= 16X1 + 16X2 + 4 = and(proper(X1),proper(X2)) proper(tt()) = 16 >= 9 = ok(tt()) proper(isList(X)) = 16X + 8 >= 16X + 2 = isList(proper(X)) proper(isNeList(X)) = 24X >= 24X = isNeList(proper(X)) proper(isQid(X)) = 20X + 8 >= 20X + 2 = isQid(proper(X)) proper(isNePal(X)) = 16X >= 16X = isNePal(proper(X)) proper(isPal(X)) = 24X + 20 >= 24X + 5 = isPal(proper(X)) proper(a()) = 4 >= 3 = ok(a()) proper(e()) = 8 >= 5 = ok(e()) proper(i()) = 16 >= 9 = ok(i()) proper(o()) = 16 >= 9 = ok(o()) proper(u()) = 16 >= 9 = ok(u()) __(ok(X1),ok(X2)) = 8X1 + 2X2 + 5 >= 8X1 + 2X2 + 1 = ok(__(X1,X2)) and(ok(X1),ok(X2)) = 8X1 + 8X2 + 12 >= 8X1 + 8X2 + 9 = ok(and(X1,X2)) isList(ok(X)) = 8X + 6 >= 8X + 5 = ok(isList(X)) isNeList(ok(X)) = 12X + 6 >= 12X + 1 = ok(isNeList(X)) isQid(ok(X)) = 10X + 7 >= 10X + 5 = ok(isQid(X)) isNePal(ok(X)) = 8X + 4 >= 8X + 1 = ok(isNePal(X)) isPal(ok(X)) = 12X + 11 >= 12X + 11 = ok(isPal(X)) top(ok(X)) = 4X + 3 >= 4X + 1 = top(active(X)) problem: active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(isNeList(X)) -> isNeList(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) isPal(ok(X)) -> ok(isPal(X)) Matrix Interpretation Processor: dim=1 interpretation: [ok](x0) = 4x0 + 2, [proper](x0) = 7x0 + 3, [isPal](x0) = 4x0 + 2, [isNePal](x0) = 4x0 + 3, [isNeList](x0) = x0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 3x0 + 4x1 + 4 orientation: active(__(X1,X2)) = 3X1 + 4X2 + 4 >= 3X1 + 4X2 + 4 = __(active(X1),X2) active(__(X1,X2)) = 3X1 + 4X2 + 4 >= 3X1 + 4X2 + 4 = __(X1,active(X2)) __(X1,mark(X2)) = 3X1 + 4X2 + 4 >= 3X1 + 4X2 + 4 = mark(__(X1,X2)) proper(__(X1,X2)) = 21X1 + 28X2 + 31 >= 21X1 + 28X2 + 25 = __(proper(X1),proper(X2)) proper(isNeList(X)) = 7X + 3 >= 7X + 3 = isNeList(proper(X)) proper(isNePal(X)) = 28X + 24 >= 28X + 15 = isNePal(proper(X)) isPal(ok(X)) = 16X + 10 >= 16X + 10 = ok(isPal(X)) problem: active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) proper(isNeList(X)) -> isNeList(proper(X)) isPal(ok(X)) -> ok(isPal(X)) Matrix Interpretation Processor: dim=1 interpretation: [ok](x0) = x0 + 1, [proper](x0) = 5x0 + 5, [isPal](x0) = 2x0 + 1, [isNeList](x0) = 5x0 + 5, [mark](x0) = x0 + 4, [active](x0) = x0 + 2, [__](x0, x1) = x0 + x1 + 2 orientation: active(__(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = __(X1,active(X2)) __(X1,mark(X2)) = X1 + X2 + 6 >= X1 + X2 + 6 = mark(__(X1,X2)) proper(isNeList(X)) = 25X + 30 >= 25X + 30 = isNeList(proper(X)) isPal(ok(X)) = 2X + 3 >= 2X + 2 = ok(isPal(X)) problem: active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) proper(isNeList(X)) -> isNeList(proper(X)) Matrix Interpretation Processor: dim=1 interpretation: [proper](x0) = 7x0 + 2, [isNeList](x0) = x0 + 3, [mark](x0) = x0, [active](x0) = x0 + 4, [__](x0, x1) = x0 + x1 orientation: active(__(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 + 4 >= X1 + X2 + 4 = __(X1,active(X2)) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = mark(__(X1,X2)) proper(isNeList(X)) = 7X + 23 >= 7X + 5 = isNeList(proper(X)) problem: active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [mark](x0) = [0 1 0]x0 [0 0 0] , [1 1 1] [0] [active](x0) = [0 0 0]x0 + [1] [1 1 1] [0], [1 0 0] [1 1 0] [0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 1 1] [0 0 1] [0] orientation: [1 1 1] [1 1 1] [1] [1 1 1] [1 1 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) [1 1 1] [1 1 1] [1] [1 1 1] [0 0 1] [1] [1 1 1] [1 1 1] [1] [1 0 0] [1 1 1] [1] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = __(X1,active(X2)) [1 1 1] [1 1 1] [1] [0 1 1] [1 1 1] [0] [1 0 0] [1 1 0] [0] [1 0 0] [1 1 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 0 0] [0] [0 0 0] [0 0 0] [0] problem: active(__(X1,X2)) -> __(X1,active(X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [0] [mark](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 0 1] [active](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [1 1 0] [0] [__](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [0] [0 0 0] [0 0 1] [1] orientation: [1 0 0] [1 1 1] [1] [1 0 0] [1 0 1] [0] active(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = __(X1,active(X2)) [0 0 0] [0 0 1] [1] [0 0 0] [0 0 1] [1] [1 0 0] [1 1 1] [1] [1 0 0] [1 1 1] [1] __(X1,mark(X2)) = [0 0 0]X1 + [0 1 0]X2 + [1] >= [0 0 0]X1 + [0 1 0]X2 + [1] = mark(__(X1,X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] problem: __(X1,mark(X2)) -> mark(__(X1,X2)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [mark](x0) = [0 0 1]x0 + [0] [0 1 1] [1], [1 0 0] [1 0 1] [__](x0, x1) = [0 0 0]x0 + [0 1 0]x1 [0 0 0] [0 0 1] orientation: [1 0 0] [1 1 1] [1] [1 0 0] [1 0 1] [0] __(X1,mark(X2)) = [0 0 0]X1 + [0 0 1]X2 + [0] >= [0 0 0]X1 + [0 0 1]X2 + [0] = mark(__(X1,X2)) [0 0 0] [0 1 1] [1] [0 0 0] [0 1 1] [1] problem: Qed